Industrial Engineering

Part 1Lecture 1

Work Measurement

Work measurement refer to the estimation of standard time, that is the time allowed for completing one piece of job using the given method. This is the time taken by an average experienced worker for the job with provisions for delays beyond the workers control.

There are several techniques used for estimation of standard time in industry. These include time study, work sampling, standard data, and predetermined time systems.

Application:

Standard times for different operations in industry are useful for several applications like

Estimating material machinery and equipment requirements. Estimating the production cost per unit as an input to

o Preparation of budgets o Determination of selling price o Make or buy decision

Estimating manpower requirements. Estimating delivery schedules and planning the work Balancing the work of operators working in a group. Estimating performance of workers and use as basis for incentive payment to those direct and in

director labor who show greater productivity.

Time Study is the most versatile and the most widely used.

Definition: Time study is a technique to estimate the time to be allowed to a qualified and well-trained worker working at a normal pace to complete a specified task.

This technique is based on measuring the work content of the task when performed by the prescribed method, with the allowance for fatigue and for personal and unavoidable delays.

Time Study Procedure:

The procedure for time study can best be described step-wise, which are self explanatory.

Step 1: Define objective of the study. This involves statement of the use of the result, the preci9sion desired, and the required level of confidence in the estimated time standards.

Step 2: Analyse the operation to determine whether standard method and conditions exist and whether the operator is properly trained. If need is felt for method study or further training of operator, the same may be completed before starting the time study.

Step 3: Select Operator to be studied if there is more than one operator doing the same task.

Step 4: Record information about the standard method, operation, operator, product, equipment, quality and conditions.

Step 5: Divide the operation into reasonably small elements.

Step 6: Time the operator for each of the elements. Record the data for a few number of cycles. Use the data to estimate the total numbers of observations to be taken.

Step 7: Collect and record the data of required number of cycles by timing and rating the operator.

Step 8: For each element calculate the representative watch time. Multiply it by the rating factory to get normal time.

Normal time = Observed time * Rating factor

Add the normal time of various elements to obtain the normal time for the whole operation.

Step 9: Determine allowances for various delays from the company's policy book or by conducting an independent study.

Step 10: Determine standard time by adding allowances to the normal time of operation.

Standard time = Normal time + allowances

Time Study Equipment

The following equipment is needed for time study work.

Timing device Time study observation sheet Time study observation board Other equipment

Timing Device

The stop watch (Figure1) and the electronic timer are the most widely used timing devices used for time study. The two perform the same function with the difference that electronics timer can measure time to the second or third decimal of a second and can keep a large volume of time data in memory.

Time Study Observation Sheet

It is a printed form with space provided for nothing down the necessary information about the operation being studied like name of operation, drawing number, name of the operator, name of time study person, and the date and place of study. Space are provided in the form for writing detailed description of the process (element-wise), recording stop-watch readings for each element of the process, performance rating(s) of the operator, and computation Figure 2 Shows a typical time study observation sheet.

Time Study Board

It is a light -weight board used for holding the observation sheet and stopwatch in position. It is of size slightly larger than that of observation sheet used. Generally, the watch is mounted at the center of the top edge or as shown in Figure 3 near the upper right-hand corner of the board. The board has a clamp to hold

the observation sheet. During the time study, the board is held against the body and the upper left arm by the time study person in such a way that the watch could be operated by the thumb/index finger of the left hand. Watch readings are recorded on the observation sheet by the right hand.

Other Equipment

This includes pencil, eraser and device like tachometer for checking the speed, etc.

Normal Performance

There is no universal concept of Normal Performance. However, it is generally defined as the working rate of an average qualified worker working under capable supervision but not under any incentive wage payment scheme. This rate of working is characterized by the fairly steady exertion of reasonable effort, and can be maintained day after day without undue physical or mental fatigue.

The level of normal performance differs considerably from one company to another. What company A calls 100 percent performance, company B may call 80 percent, company C may call 125 percent and so on. It is important to understand that the level that a company selects for normal performance is not critical but maintaining that level uniform among time study person and constant with the passage of time within the company is extremely important.

There are, of course, some universally accepted benchmark examples of normal performance, like dealing 52 cards in four piles in 0.5 minute, and walking at 3 miles per hour (4.83 km/hr). In order to make use of these benchmarks, it is important that a complete description about these be fully understood, like in the case of card dealing, what is the distance of each pile with respect to the dealer, technique of grasping, moving and disposal of the cards.

Some companies make use of video films or motion pictures for establishing what they consider as normal speed or normal rate of movement of body members. Such films are made of typical factory jobs with the operator working at the desired normal pace. These films are reported to be useful in demonstrating the level of performance expected from the operators and also for training of time study staff.

Performance Rating

During the time study, time study engineer carefully observes the performance of the operator. This performance seldom conforms to the exact definition of normal or standard. Therefore, it becomes necessary to apply some 'adjustment' to the mean observed time to arrive at the time that the normal operator would have needed to do that job when working at an average pace. This 'adjustment' is called Performance Rating.

Determination of performance rating is an important step in the work measurement procedures. It is based entirely on the experience, training, and judgment of the work-study engineer. It is the step most subjective and therefore is subject to criticism.

It is the procedure in which the time study engineer compares the performance of operator(s) under observation to the Normal Performance and determines a factor called Rating Factor.

System of Rating

There are several systems of rating, the performance of operator on the job. These are

1. Pace Rating 2. Westinghouse System of Rating 3. Objective Rating 4. Synthetic Rating

A brief description of each rating method follows

Pace Rating

Under this system, performance is evaluated by considering the rate of accomplishment of the work per unit time. The study person measures the effectiveness of the operator against the concept of normal performance and then assigns a percentage to indicate the ratio of the observed performance to normal or standard performance.

In this method, which is also called the speed rating method, the time study person judges the operators speed of movements, i.e. the rate at which he is applying himself, or in other words "how fast" the operator the motions involved.

Westinghouse System of Rating

This method considers four factors in evaluating the performance of the operator : Skill, effort, conditions and Consistency.

Skill may be defined as proficiency at following a given method. It is demonstrated by co ordination of mind and hands. A person's skill in given operation increases with his experience on the job, because increased familiarity with work bring speed, smoothness of motions and freedom from hesitations.

The Westinghouse system lists six classes of skill as poor fair, average, good, excellent in a Table1. The time study person evaluates the skill displayed by the operator and puts it in one of the six classes. As equipment % value of each class of skill is provided in the table, the rating is translated into its equivalent percentage value, which ranges from +15 % (for super skill) to -22 % (for poor skill).

In a similar fashion, the ratings for effort, conditions, and consistency are given using Table2 for each of the factors. By algebraically combining the ratings with respect to each of the four factors, the final performance-rating factor is estimated.

Objective Rating

In this system, speed of movements and job difficulty are rated separately and the two estimates are combined into a single value. Rating of speed or pace is done as described earlier, and the rating of job difficulty is done by selecting adjustment factors corresponding to characteristics of operation with respect to (i) amount of body used, (ii) foot pedals, (iii) bimanual ness, (iv) eye-hand co ordination, (v) handling requirements and (vi) weight handled or resistance encountered Mundel and Danner have given Table3 of % values (adjustment factor) for the effects of various difficulties in the operation performed.

For an operation under study, the numerical value for each of the six factors is assigned, and the algebraic sum of the numerical values called job difficulty adjustment factor is estimated.

The rating factor R can be expressed as

R = P x D

Where : P = Pace rating factor D = Job difficulty adjustment factor.

Synthetic Rating

This method of rating has two main advantages over other methods that (i) it does not rely on the judgment of the time study person and (ii) it give consistent results.

The time study is made as usual. Some manually controlled elements of the work cycle are selected. Using a PMT system (Pre-determined motion time system), the times for these elements are determined. The times of these elements are the performance factor is determined for each of the selected elements.

Performance or Rating Factor,   R = P / A

Where P = Predetermined motion time of the element ,      A = Average actual Observed time of the element.

The overall rating factor is the mean of rating factors determined for the selected elements, which is applied uniformly to all the manually controlled elements of the work cycle.

Example

A work cycle has been divided into 8 elements and time study has been conducted. The average observed times for the elements are as :

Element No. 1 2 3 4 5 6 7 8

Element Type M M P M M M M M

Average actual time

(minutes)0.14 0.16 0.30 0.52 0.26 0.45 0.34 0.15

M = Manually Controlled , P = Power Controlled

Total observed time of work cycle = 2.32 min.

Suppose we select elements number 2,5 and 8 (These must be manually controlled elements). By using some PMT system, suppose we determine the times of these elements as

Elements No. 2 5 8PMT System times(mins) 0.145 0.255 0.140

Rating factor for element 2 = 0.145 / 0.16 = 90.06 %.

Rating factor for element 2 = 0.255 / 0.26 = 98.08 %.

Rating factor for element 2 = 0.140 / 0.15 = 96.66 %.

The mean of the rating factors of selected elements = 94.93 % or say 95 % is the rating factor that will be used for all the manual elements of the work cycle.

The normal time of the cycle is calculated as given in the following table.

Element No. 1 2 3 4 5 6 7 8

Element Type M M P M M M M M

Average actual

time(min)0.14 0.16 0.30 0.52 0.26 0.45 0.34 0.15

PMT system time(min) 0.145 0.255 0.14

Performance Rating Factor

95 95 100 95 95 95 95 95

Normal Cycle Time

= 0.95(0.14+0.16+0.52+0.26+0.45+0.34+0.15)+1.00(0.30)

=1.92+0.30

=2.22 minutes

Allowances

The readings of any time study are taken over a relatively short period of time. The normal time arrived at, therefore does not include unavoidable delay and other legitimate lost time, for example, in waiting for materials, tools or equipment; periodic inspection of parts; interruptions due to legitimate personal need, etc. It is necessary and important that the time study person applies some adjustment, or allowances to compensate for such losses, so that fair time standard is established for the given job.

Allowances are generally applied to total cycle time as some percentage of it, but sometimes these are given separately as some % for machine time and some other % for manual effort time. However no allowance are given for interruptions which maybe due to factor which are within the operator's control or which are avoidable.

Most companies allow the following allowances to their employees.

Delay Allowance Fatigue Allowance Personal Allowance Special Allowance

Delay Allowance

This time allowance is given to an operator for the numerous interruptions that he experiences every day during the course of his work. These interruptions include interruptions from the supervisor, inspector, planners, expediters, fellow workers, production personnel and others. This allowance also covers interruptions due to material irregularities, difficulty in maintaining specifications and tolerances, and interference delays where the operator has to attend to more than one machine.

Fatigue Allowance

This allowance can be divided into two parts: (i) basic fatigue allowance and (ii) variable fatigue allowance. The basic fatigue allowance is given to the operator to compensate for the energy expended for carrying out the work and to alleviate monotony. For an operator who is doing light work while seated, under good working conditions and under normal demands on the sensory or motor system, a 4% of normal time is considered adequate. This can be treated as a constant allowance.

The magnitude of variable fatigue allowance given to the operator depends upon the severity of the factor or conditions, which cause extra (more than normal) fatigue to him. As we know, fatigue is not homogeneous, it range from strictly physical to purely psychological and includes combinations of the two. on some people it has a marked effect while on others, it has apparently little or no effect. Whatever may be the kind of fatigue-physical or mental, the result is same-it reduces the work output of operator. The major factors that cause more than just the basic fatigue includes sever working conditions, especially with respect to noise, illumination, heat and humidity; the nature of work, especially with respect to posture, muscular exertion and tediousness and like that.

It is true that in modern industry, heavy manual work, and thus muscular fatigue is reducing day by day but mechanization is promoting other fatigue components like monotony and mental stress. Because fatigue in

totality cannot be eliminated, proper allowance has to be given for adverse working conditions and repetitiveness of the work.

Personal Allowance

This is allowed to compensate for the time spent by worker in meeting the physical needs. A normal person requires a periodic break in the production routine. The amount of personal time required by operator varies with the individual more than with the kind of work, though it is seen that workers need more personal time when the work is heavy and done under unfavorable conditions.

The amount of this allowance can be determined by making all-day time study or work sampling. Mostly, a 5 % allowance for personal time (nearly 24 minutes in 8 hours) is considered appropriate.

Special Allowance

These allowances are given under certain special circumstances. Some of allowances and the conditions under which they are given are:

Small Lot Allowance: This allowance is given when the actual production period is too short to allow the worker to come out of the initial learning period. When an operator completes several small-lot jobs on different setups during the day, an allowance as high as 15 percent may be given to allow the operator to make normal earnings.

Training Allowance: This allowance is provided when work is done by trainee to allow him to maker reasonable earnings. It may be a sliding allowance, which progressively decreases to zero over certain length of time. If the effect of learning on the job is known, the rate of decrease of the training allowance can be set accordingly.

Rework Allowance: This allowance is provided on certain operation when it is known that some present of parts made are spoiled due to factors beyond the operator's control. The time in which these spoiled parts may be reworked is converted into allowance.

Different organizations have decided upon the amount of allowances to be given to different operators by taking help from the specialists / consultants in the field and through negotiations between the management and the trade unions. ILO has given its recommendations about the magnitude of various allowances, Table 4.

Example:

In making a time study of a laboratory technician performing an analysis of processed food in a canning factory, the following times were noted for a particular operation.

Run 1 2 3 4 5 6 7 8 9 10 11 12

Operation time(sec.)

21 21 16 19 20 16 20 19 19 20 40 19

Run 13 14 15 16 17 18 19 20 21 22 23 24Operation time(sec.) 21 18 23 19 15 18 18 19 21 20 20 19

If the technician's performance has been rated at 120 percent, and the company policy for allowance (personal, fatigue, etc.) stipulates 13 percent,

(i) Determine the normal time.

(ii)Determine the standard time.

Watch readings falling 50 % above and 25 % below the average may be considered as abnormal.

Ans :

Work Sampling

Work Sampling (also sometimes called ratio delay study) is a technique of getting facts about utilization of machines or human beings through a large number of instantaneous observations taken at random time intervals. The ratio of observations of a given activity to the total observations approximates the percentage of time that the process is in that state of activity. For example, if 500 instantaneous observations taken at random intervals over a few weeks show that a lathe operator was doing productive work in 365 observations and in the remaining 135 observations he was found 'idle' for miscellaneous reasons, then it can be taken that the operator remains idle (135/500) x 100 = 27 % 0f the time. Obviously, the accuracy of the result depends on the number of observations. However, in most applications there is usually a limit beyond which greater accuracy of data is not economically worthwhile.

Use of Work Sampling for Standard Time Determination

Work sampling can be very useful for establishing time standards on both direct and indirect labor jobs. The procedure for conducting work sampling study for determining standard time of a job can be described step-wise.

Procedure

Step 1. Define the problem. (i) Describe the job for which the standard time is to be determined. (ii) Unambiguously State and discriminate between the two classes of activities of operator on the job: what are the activities of job with which if operator is found engaged would entitle him to be in 'working" state. This would imply that when operator will be found engaged in any activity other than those would entitle him to be in "Not Working" state.

Step 2. Design the Sampling plan. (i) Estimate satisfactory number of observations to be made. (ii) Decide on the period of study, e.g. two days, one week, etc. (iii) Prepare detailed plan for taking the observations. This will include observation schedule, exact method of observing, design of observation sheet route to be followed, the particular person to be observed at the observation time, etc.

Step 3. Contact the person concerned and take them in confidence regarding conduct of the study.

Step 4. Collect the data at the pre-decided random times.

We will now briefly discuss some important issues involved in the procedure.

Number of Observations

As we know, result of study based on larger number of observations are more accurate, but taking more and more observation consume time and thus is costly. A cost-benefit trade-off has thus to be struck. In practice, the following methods are used for estimation of the number of observation to be made.

(i) Based on judgment. The study person can decide the necessary number of observations based on his judgment. The correctness of the number may be in doubt but estimate is often quick and adequate in many cases.

(ii) Using cumulative plot of results. As the study progresses the results (of the proportion of time devoted to the given activity, i.e. Pi from the cumulative number of observations are plotted at the end of each shift or day. A typical plot is shown in Figure4. Since the accuracy of the result improves with increasing number of observation, the study can be continued until the cumulative Pi appears to stabilize and collection of further data seems to have negligible effect on the value of Pi.

(iii) Use of statistics. In this method, by considering the important of the decision to be based on the results of study, a maximum tolerable sampling error in terms of confidence level and desired accuracy in the results is specified. A pilot study is then made in which a few observations are taken to obtain a preliminary estimate of Pi. The number of observations N necessary are then calculated using the following expression

Where  S = desired relative accuracy

              Pi = estimate of proportion of time devoted to activity expressed as a decimal, e.g. 5 % = 0.05

               = a factor depending on the confidence level.

= 1, 2, 3 for confidence levels of 68 %, 95 % and 99 % respectively.

N = total number of observations needed.

The number of observations estimated from the above relation using a value of Pi obtained from a preliminary study would be only a first estimate. In actual practice, as the work sampling study proceeds, say at the end of each day, a new calculation should be made by using increasingly reliable value of Pi obtained from the cumulative number of observations made.

Determination of Observation Schedule

The number of instantaneous observations to be made each day mainly depends upon nature of operation. For example, for non-repetitive operations or for operations in which some elements occur in frequently, it is advisable to take observations more frequently so that the chance of obtaining all the facts improves. It also depends on the availability of time with the person making the study. In general, about 50 observations per day is a good figure. The exact (random) schedule of the observations is prepared by using random number table or any other technique.

Design of Observation Sheet

A sample observation sheet for recording the data with respect to whether at the pre-decided time, the worker on job is in 'working' state or 'non-working' state is shown in figure5. It contains the relevant information about the job, the operators on job, etc. At the end of each day, calculation can be done on the percent of time workers on the job (on an average) spend on activities, which are considered as part of the work method.

Standard Time Determination

In this method of work measurement, the observed time for a given job is estimated as the working time divided by the number of units produced during that time.

Where  T = Total study period

N = Number of units produced in study period

= Total number of observations made in study period

i =Number of observations in which worker(s) was found in 'working' state

The normal time (NT) is found by multiplying the observed time by the average performing index (rating factor).

Where = Average rating factor =

Finally, the standard time is found by adding allowances to the normal time.

Example

A work sampling study was made of a cargo loading operation for the purpose of developing its standard time. The study was conducted for duration of minutes during which 3000, 1500 instantaneous observations were made at random intervals. The results of study indicated that the worker on the job was working 80 percent of the time and loaded 360 pieces of cargo during the study period. The work analyst rated the performance at 90 %. If the management wishes to permit a 13 % allowance for fatigue, delays and

personal time, what is the standard time of this operation?

Ans:

Here,   Total period                       = 1500 minutes

Working fraction              = 80 percent

Average rating                  = 90 percent

Number of units loaded = 360

Allowances                       = 13 %

Advantages and Disadvantages of Work Sampling in Comparison with Time Study.

Advantage

Economical

1. Many operators or activities are difficult or uneconomical to measure by time study can readily be measured by work sampling.

2. Two or more studies can be simultaneously made of several operators or machines by a single observer. Ordinarily a work study engineer can study only one operator at a time when continuous time study is made.

3. It usually requires fewer man-hours to make a work sampling study than to make a continuous time study. The cost may also be about a third of the cost of a continuous time study.

4. No stopwatch or other time measuring device is needed for work sampling studies.

5. It usually requires less time to calculate the results of work sampling study. Mark sensing cards may be used which can be fed directly to the computing machines to obtain the results just instantaneously.

Flexible

         6.  A work sampling study may be interrupted at any time without affecting the results.

         7.  Operators are not closely watched for long period of time. This decreases the chance of getting erroneous results for when a worker is observed continuously for a long period, it is probable that he will not

follow his usual routine exactly during that period.

Less Erroneous

         8.  Observations may be taken over a period of days or weeks. This decreases the chance of day-to-day or week-to-week variations that may affect the results.

Operators Like It

         9.   Work sampling studies are preferred to continuous time study by the operators being studied. Some people do not like to be observed continuously for long periods of time.

Observers Like It

        10.  Work sampling studies are less fatiguing and less tedious to make on the part of time study engineer.

Applications

        11.   Work sampling is applicable to a wide variety of situations in manufacturing, distribution, or service industries.

        12.  Work sampling is useful when determine the nature of the distribution of work activities within a gang operation.

Disadvantage

1. Work sampling is not economical for the study of a single operator or operation or machine. Also, work-sampling study may be uneconomical for studying operators or machines located over wide areas.

2. Work sampling study does not provide elemental time data.

3. The operator may change his work pattern when he sees the observer. For instance, he may try to look productive and make the results of study erroneous.

4. No record is usually made of the method being used by the operator Therefore a new study has to be made when a method change occurs in any element of operation.

5. Compared to stop watch time study, the statistical approach of work sampling study is difficult to understand by workers.

Computerized Work Sampling

Use of a computer can save as much as 30 to 40 percent of the total work sampling study cost. This is because too much clerical effort is involved in summarizing work sampling data, e.g. in determining the number of observations required, determining the daily observations required, determining the number of trips to the area being studied per day, determining the time of each observation, calculating the accuracy of results, plotting data on control charts and like that. Computers can be made use for mechanization of the repetitive calculations, display of control charts and calculation of daily as well as cumulative results.

Predetermined Motion Time System

A predetermined motion time system (PMTS) may be defined as a procedure that analyzes any manual activity in terms of basic or fundamental motions required to performing it. Each of these motions is

assigned a previously established standard time value in such a way that the timings for the individual motions can be synthesized to obtain the total time for the performance of the activity.

The main use of PMTS lies in the estimation of time for the performance of a task before it is performed. The procedure is particularly useful to some organizations because it does not require troublesome rating with each study.

Applications of PMTS are for

(i) Determination of job time standards.

(ii) Comparing the times for alternative proposed methods so as to find the economics of the proposals prior to production run.

(iii) Estimation of manpower, equipment and space requirements prior to setting up the facilities and start of production.

(iv) Developing tentative work layouts for assembly line prior to their working.

(v) Checking direct time study results.

A number of PMTS are in use, some of which have been developed by individual organizations for their own use, while other organizations have publicized for universal applications.

The following are commonly used PMT systems

Work factor (1938) Method Time Measurement (1948) Basic Motion Time (1951) Dimension Motion Time (1954)

Some important factors which be considered while selecting a PMT system for application to particular industry are

1. Cost of Installation. This consists mainly of the cost of getting expert for applying the system under consideration.

2. Application Cost. This is determined by the length of time needed to set a time standard by the system under consideration.

3. Performance Level of the System. The level of performance embodied in the system under consideration may be different from the normal performance established in the industry where the system is to be used. However, this problem can be overcome by 'calibration' which is nothing but multiplying the times given in the Tables by some constant or by the application of an adjustment allowance.

4. Consistency of Standards. Consistency of standards set by a system on various jobs is a vital factor to consider. For this, the system can be applied on a trial basis on a set of operations in the plant and examined for consistency among them.

5. Nature of Operation. Best results are likely to be achieved if the type and nature of operations in the plant are similar to the nature and type of operations studied during the development of the system under consideration.

Advantages and limitations of using PMT systems

Advantage

Compared to other work measurement techniques, all PMT system claim the following advantages:

1. There is no need to actually observe the operation running. This means the estimation of time to perform a job can be made from the drawings even before the job is actually done. This feature is very useful in production planning, forecasting, equipment selection etc.

2. The use of PMT eliminates the need of troublesome and controversial performance rating. For the sole reason of avoiding performance rating, some companies have been using this technique.

3. The use of PM times forces the analyst to study the method in detail. This sometimes helps to further improve the method.

4. A bye-product of the use of PM time is a detailed record of the method of operation. This is advantageous for installation of method, for instructional purposes, and for detection and verification of any change that might occur in the method in future.

5. The PM times can be usefully employed to establish elemental standard data for setting time standards on jobs done on various types of machines and equipment.

6. The basic times determined with the use of PMT system are relatively more consistent.

Limitations

There are two main limitations to the use of PMT system for establishing time standards. These are : (i) its application to only manual contents of job and (ii) the need of trained personnel. Although PMT system eliminates the use of rating, quite a bit of judgment is still necessarily exercised at different stages.

Motion Study

Motion study is a technique of analyzing the body motions employed in doing a task in order to eliminate or reduce ineffective movements and facilitates effective movements. By using motion study and the principles of motion economy the task is redesigned to be more effective and less time consuming.

The Gilbreths pioneered the study of manual motions and developed basic laws of motion economy that are still relevant today. They were also responsible for the development of detailed motion picture studies, termed as Micro Motion Studies, which are extremely useful for analyzing highly repetitive manual operations. With the improvement in technology, of course, video camera has replaced the traditional motion picture film camera.

In a broad sense, motion study encompasses micro motion study and both have the same objective: job simplification so that it is less fatiguing and less time consuming while motion study involves a simple visual analysis, micro motion study uses more expensive equipment. The two types of studies may be compared to viewing a task under a magnifying glass versus viewing the same under a microscope. The added detail revealed by the microscope may be needed in exceptional cases when even a minute improvement in motions matters, i.e. on extremely short repetitive tasks.

Taking the cine films @ 16 to 20 frames per second with motion picture camera, developing the film and analyzing the film for micro motion study had always been considered a costly affair. To save on the cost of developing the film and the cost of film itself, a technique was used in which camera took only 5 to 10 frames per minute. This saved on the time of film analysis too. In applications where infrequent shots of camera could provide almost same information, the technique proved fruitful and acquired the name Memo Motion Study.

Traditionally, the data from micro motion studies are recorded on a Simultaneous Motion (simo) Chart while

that from motion studies are recorded on a Right Hand - Left Hand Process Chart.

Therbligs

As result of several motion studies conducted Gilbreths concluded that any work can be done by using a combination of 17 basic motions, called Therbligs (Gilbreth spelled backward). These can be classified as effective therbligs and ineffective therbligs. Effective therbligs take the work progress towards completion. Attempts can be made to shorten them but they cannot be eliminated. Ineffective therbligs do not advance the progress of work and therefore attempts should be made to eliminate them by applying the Principles of Motion Economy. Table5 gives the therbligs along with their symbols and descriptions.

SIMO Chart

It is a graphic representation of the sequence of the therbligs or group of therbligs performed by body members of operator. It is drawn on a common time scale. In other words, it is a two-hand process chart drawn in terms of therbligs and with a time scale, see Figure6 making the Simo Chart. A video film or a motion picture film is shot of the operation. The film is analyzed frame by frame. For the left hand, the sequence of therbligs (or group of therbligs) with their time values are recorded on the column corresponding to the left hand. The symbols are added against the length of column representing the duration of the group of therbligs. The procedure is repeated for the right and other body members (if any) involved in carrying out the operation.

It is generally not possible to time individual therbligs. A certain number of therbligs may be grouped into an element large enough to be measured as can be seen in Figure7.

Uses of Simo Chart

From the motion analysis shown about the motions of the two hands (or other body members) involved in doing an operation, inefficient motion pattern can be identified and any violation of the principle of motion economy can be easily noticed. The chart, therefore, helps in improving the method of doing the operation so that balanced two-handed actions with coordinated foot and eye motions can be achieved and ineffective motion can be either reduced or eliminated. The result is a smoother, more rhythmic work cycle that keeps both delays and operator fatigue to the minimum extent.

Cycle graph and Chrono cycle graph

These techniques of analyzing the paths of motion made by an operator were developed by the Gilbreths. To make a cycle graph, a small electric bulb is attached to the finger, hand, or any other part of the body whose motion is to be recorded. By using still Photography, the path of light of bulb (in other words, that of the body member) as it moves through space for one complete cycle is photographed by keeping the working area relatively less illuminated. More than one camera may be used in different planes to get more details. The resulting picture (cycle graph) shows a permanent record of the motion pattern employed in the form of a closed loop of white continuous line with the working area in the background. A cycle graph does not indicate the direction or speed of motion.

It can be used for

Improving the motion pattern and Training purposes in that two cycle graphs may be shown with one indicating a better motion

pattern than the other.

The Chrono cycle graph is similar to the cycle graph, but the power supply to the bulb is interrupted regularly by using an electric circuit. The bulb is thus made to flash. The procedure for taking photograph remains the same. The resulting picture (Chrono cycle graph), instead of showing continuous line of motion pattern, shows short dashes of line spaced in proportion to the speed of the body member photographed. Wide spacing would represent fast moves while close spacing would represent slow moves.The jumbling of

dots at one point would indicate fumbling or hesitation of the body member. A chrono cycle graph can thus be used to study the motion pattern as well as to compute velocity, acceleration and retardation experienced by the body member at different locations.

The world of sports has used this analysis tool, updated to video, for extensively the purpose of training in the development of from and skill.

Design of Workplace Layout

The design of workplace layout involves the following Detemination of work surface height Design of operator chair (if work is to be done in sitting posture), or allowing the use of antifatigue

mats for standing operator Determination of location of tools, materials, controls, displays and other devices.

We shall consider these briefly.

Work Place Height

This should be decided from the standpoint of comfortable working posture for the operator. Generally, it is equal to the elbow height of operator whether work is done in standing or sitting posture. However, for work involving lifting of heavy parts, it is useful to lower the work surface height by as much as 20 cm. This would reduce the fatigue to the trunk of operator. Similarly, it may be useful to lower the work surface height when work involves usual examination of minute details of fine parts. This would reduce the eye fatigue to the operator. Alternatively, the work surface may be inclined by 15 degrees or so. Work surface height may also be made adjustable in situations where operator is permitted to do work in alternatively sitting and standing postures.

Design of Operator Chair

A seated posture is better than standing posture from the standpoint of stress reduction on the feet and the overall energy expenditure. A well-designed seat should

Provide trunk stabilization so that a good posture is maintained, Permit change of posture and Not unduly press the thigh tissues.

This requires the use of ergonomic considerations and anthropometrics dimensions of operator so that appropriate dimensions are chosen for the following features

1. Seat Height 2. Seat Depth 3. Seat Width 4. Seat Inclination 5. Arm Rests 6. Back Rest 7. Foot Rest

In order that the same seat (or chair) is useable by many operators doing that job, it is necessary to provide adjustability, particularly with respect to seat height.

Standing for long periods of time on a cemented floor is fatiguing. If operator has to work only in standing posture, it is essential to provide resilient anti fatigue floor mats. Such mats allow small muscle contractions in the legs and force the blood to keep circulating.

Determination of location of tools, materials, controls, displays and other devices.

We all know that greater the distance operator moves his body member while doing work, larger is the muscular effort, control and time. This means that all tools, materials, controls, etc need to be located within close reach of the operator. In this context, two areas can be identified normal working area and maximum working area. Figure8 identifies these areas in horizontal and vertical planes.

Within these areas, all tools, materials, controls, displays and other devices must be located on the basis of following principles.

(i) Importance Principle. According to this principle, the most important item or group of items are first located within the normal area in the best position. The next important component item or group of item is then selected and located in the best location within the remaining area. In this way, all the items are located.

(ii) Frequency of Use Principle. According to this principle, the item with the greatest frequency of use has the highest priority for location at the optimum position. From within the remaining items to be located in the remaining area, the same principle can then be applied repetitively.

(iii) Functional Principle. The functional principle of location provides for grouping of items according to their function. For instance, all controls that are functionally related may be grouped together and located at another place.

(iv) Sequence of Use Principle. According to this principle, items are located according to sequence of their use. For illustration, let us consider the case of assembly. As we know, an assembly is made by assembling the sub-assemblies in a certain order. From motion economy or production efficiency point of view, it would be better if sub-assemblies and other items were located in the sequence in which they are to be used in assembly.

Further, for better productivity, it is important that of all tools materials and controls be fixed so that their "search" and " select" is minimized.

Work Study

Definition: Work study may be defined as the analysis of a job for the purpose of finding the preferred method of doing it and also determining the standard time to perform it by two areas of study-method study (motion study) and time study (work measurement).

Role of Work Study in Improving Productivity

In order to understand the role of work study, we need to understand the role of method study and that of time study.

Method study (also sometimes called Work Method Design) is mostly used to improve existing method of doing work although it is equally well applicable to new jobs. When applied to existing jobs, method study aims to find better methods of doing the jobs that are economical and safe, require less human effort, and need shorter make-ready / put-away time. The better method involves the optimum use of best materials and appropriate manpower so that work is performed in well, organized manner leading to utilization, better quality and lower costs.

We can therefore say that through method study we have a systematic way of developing human resource effectiveness, providing high machine and equipment utilization, and making economical use of materials.

Time study, on the other hand, provides the standard time, that is the time needed by worker to complete a job by the specified method. Therefore for any job, the method of doing it is first improved by method study, the new method is implemented as a standard practice and for that job to be done by the new method, and

standard time is established by the use of time study. Standard times are essential for any organisation, as they are needed for proper estimation of

manpower, machinery and equipment requirements daily, weekly or monthly requirement of materials production cost per unit as an input to selling price determination labor budgets worker's efficiency and make incentive wage payments.

By the application of method study and time study in any organization, we can thus achieve greater output at less cost and of better quality, and hence achieve higher productivity.

Work Study and Ergonomics

The work study and the ergonomics are the two areas of study having the same objective: design the work system so that for the operator it is safe, less fatiguing and less time taking.

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>Lecture 2

>Lecture 3 Ei duto copy hoi ni karon website te nei.

Part 2 Quality and Related Concepts

Lecture 1 Introduction

The rapidly increasing global competition over the past decade has led to the emergence of new scenarios for most of the industrial sectors. The industries are now associated with rapid technological changes and product variety proliferation in order to remain competitive. The competitiveness of a company is mostly dependent on its ability to perform well in dimensions such as cost, quality, delivery, dependability and speed, innovation and flexibility to adapt itself to variations in demand.

Aiming at improving organizational performance through the effective use of production capability and

technology, operations strategy such as total quality management (TQM), quality function deployment (QFD), six sigma, business process re-engineering (BPR), just in time (JIT), benchmarking, performance measurement and many others are commonly used. The concept of quality has evolved from mere specifications, controls, inspections, systems, and methods for regulatory compliance to a harmonized relationship with business strategies aimed at satisfying both the internal and external customer. Today, quality and value are, first and above all, givens, and the customer expects them. Quality in the successful organization is fully integrated into all of the business processes and is an extension of everything else that has to happen along the path to success, both for the company and for the people involved.

Quality Definition(s)

As Specified by Joseph Juran, Quality is the fitness of use i.e. it is the value of the goods and services as perceived by the supplier, producer and customer. The measure also pertains to the degree to which products and services conform to specifications, requirements and standards at an acceptable price. Some of the definitions of the term ‘Quality', provided by quality gurus are as follows:

     Quality is fitness for use (JURAN)      Quality is conformance to requirements (CROSBY)  

     the efficient production of the quality that the market expects (DEMING)

     Quality is what the customer says, it is (FEIGENBAUM)

     Quality is the loss that a product costs to the society after being shipped to the customer (TAGUCHI)

     The totality of features and characteristics of a product or services that bear on its ability to satisfy stated or implied needs of the customers (ASQC)

     A quality system is the agreed on company wide and plant wide operating work structure, documented in effective, integrated, technical and managerial procedures for guiding the co-coordinated actions of people, the machines, or the information of company in the best and most practical ways to assume customer quality satisfaction and economical costs of quality. (FEIGENBAUM)

Dimensions of Product Quality

As prescribed by Garvin, the eight dimensions of quality are:

     Performance          (will the product do the intended job?)      Reliability             (how often the product fails?)

     Durability             (how long the product lasts?)

     Serviceability       (how easy is to repair the product?)

     Aesthetics             (what does the product look like?)

     Features                (what does the product do?)

     Perceived quality  (what is the reputation of a company or its products?)

Dimensions of Service Quality

     Reliability      Responsiveness

     Competence

     Courtesy

     Communication

     Credibility

     Security

Three Aspects of Quality (Figure)

The three aspects of quality and their linkages with each other have been depicted in the figure below:

Quality of Design: Consumer's Perspective

The product must be designed to meet the requirement of the customer. The product must be designed right first time and every time and while designing all aspects of customer expectations must be incorporated into the product. The factors need to consider while designing the product are:

Type of product

     Cost      Profit

policy of the company

     Demand

     Availability of the parts

Quality of Conformance: Manufacturer's Perspective

The product must be manufactured exactly as designed. The activities involved at this stage include: defect finding, defect prevention, defect analysis, and rectification.  The difficulties encountered at the manufacturing stage must be conveyed to the designers for modification in design, if any. The two-way communication between designer and manufacturing may help to improve the quality of the product.

Quality of Performance

The product must function as per the expectations of the customer. The two way communication between designers and customer is the key to have a quality product.

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Lecture 2 Evolution of Quality (Figure)

During the early days of manufacturing, an operative's work was inspected and a decision made whether to accept or reject it. The focus was just to accept or reject the products based on the specification. No effort was made on defect prevention.

In the 1920's statistical theory began to be applied effectively to quality control, and in 1924 Shewhart made the first attempt of a modern control chart. His work was later developed by Deming and the early work of Shewhart, Deming, Dodge and Romig constitutes much of what today comprises the theory of statistical process control (SPC). However, there was little use of these techniques in manufacturing companies until the late 1940's.

In the early 1950's, quality management practices developed rapidly in Japanese plants, and become a major theme in Japanese management philosophy, such that, by 1960, quality control and management had become a national preoccupation. 

In 1969, Feigenbaum presented a paper in a conference and the term “total quality” was used for the first time, and referred to wider issues such as planning, organization and management responsibility. Ishikawa presented a paper explaining how “total quality control” in Japan was different, it meaning “company wide quality control”, and describing how all employees, from top management to the workers, must study and participate in quality control. Company wide quality management was common in Japanese companies by the late 1970's.

Total quality management (TQM) came into existence in 1980 by the western world. TQM is now part of a much wider concept that addresses overall organizational performance and recognizes the importance of

processes.

As we move into the 21st century, TQM has developed in many countries into holistic frameworks, aimed at helping organizations achieve excellent performance, particularly in customer and business results.

  

Historical Aspects of Quality

     Edward Deming

–        Postulated Statistical QUALITY Control Principles

–        14 Points of QUALITY Management

–        these Principles successfully adapted by Japanese Manufactures 

     William Crosby

–        Emphasized Humanistic Behavioral Aspects of QUALITY Improvement

–        Becoming More Important Now

     Joseph Juran's QUALITY Trilogy

A. QUALITY Planning

–        Set of QUALITY Goals

–        Set Plans for Operations Based on these Goals 

B. QUALITY Control

–        Responsible for Meeting QUALITY Goals

–        Prevent Adverse Changes

–        Set and Observe

       Performance Measures        Compare with Industry Standards        Benchmarking  

C. QUALITY Improvement

–        Moving from Current Level to the Next Higher Level

–        Organize Teams, Train Operators to identify and Correct QUALITY Problems

Quality Control

Inspection, analysis and action applied to a portion of the product in a manufacturing operation to estimate overall quality of the product and determine what, if any, changes must be made to achieve or maintain the

required level of quality.

Quality control of a product can be viewed as a system which ensures

     Proper Planning      Right Design      Proper equipment      Proper Inspection      Corrective action 

Traditional Concept: Quality Control has been concerned with detecting poor quality in manufacturing products and taking corrective action to eliminate it.

Modern Concept: Quality Control encompasses a broader scope of activities including:

     Robust design      Statistical Proecess Control

Two aspects of quality control

     Off-line quality control      On-line quality control

Off-line quality control encompasses all those activities that are performed before the actual manufacturing of the product or service rendered

On-line quality control activities start from the manufacturing of a product till it goes in the field and also after sale service. The quality tools used in the phase are Statistical Process control and Acceptance Sampling

Importance of Quality Control

     Quality is vital in all areas of business, including the product development and production functions

     Cost of quality is ultimately reduced by investing money up front in quality design and development

     Typical costs of poor quality include downtime, repair costs, rework, and employee turnover

Benefits of Quality Control

A well-established, committed quality system in an organization will render the following benefits

     Improvement in the quality of product      Higher productivity      Cost reduction      Continuous improvement in quality of product

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Lecture 3 Quality Costs

Quality costs components are

     Prevention costs      Appraisal costs

     Internal Failure Costs

     External Failure Costs 

Prevention costs

These costs are incurred in the process of trying to prevent defects and errors from occurring. The costs involved are for

     planning the quality control process      training and educating

     designing the product for quality

     designing the production system for quality

     preventive maintenance 

Appraisal costs (detection costs)

These are the costs of determining the current quality of the production system or inspection and testing through sampling. The costs involved are for

     measuring and testing parts and materials      conducting statistical process control

     receiving inspection

     reporting on quality

Internal Failure Costs

These costs are incurred when defects and errors are found before shipment or delivery to the customer. The costs involved are for

     labor and materials that are scrapped      reworking and retesting to correct defects

     lost profits

External Failure Costs

These are the costs of trying correct defects and errors after receipt by the customer.

The costs involved are for

     quick response to complaints      adjustments to correct the problem

     lost goodwill

     warranties and insurance

     settlements of lawsuits

     product recall

COQ = Prevention Cost + Appraisal Cost + Internal Failure Cost + External Failure Cost

      Cost of Conformance                              Cost of Non-Conformance

 Traditional View of Quality Costs

 Modern/Contemporary View of Quality Costs

Normal Cost of Quality Distribution when Quality System is NOT in Place

Optimum Cost of Quality Distribution when Quality System is in Place

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Lecture 4 Seven Basic Quality Control Tools

     Histograms      Run Charts      Pareto Charts      Flow Charts      Scatter Diagrams      Cause and Effect Diagrams      Control Charts

Histograms

A Histogram is a bar graph used to present frequency data. Histograms provide an easy way to evaluate the

distribution of data over different categories

Steps in making Histogram

     Define Categories for Data      Collect Data, sort them into

the categories      Count the Data for each

category      Draw the Diagram. Each

category finds its place on the x-Axis.

     The bars will be as high as the value for the category

The histogram reveals the following about the process

Centering of the process data: The centering of the data provides information on the process about some mean.

Spread of the data:       Histogram width defines the variability of the process about the mean

Shape of the histogram: Bell or normal shaped histogram is expected. Other than normal or bell shape means something wrong with the process responsible for poor quality.

Limitations ofthe Histograms

The randomness in the data in developing histogram losses the vital information As data are not represented in order, the time-dependent or time-related trends in

the process may not be revealed

RunChart

Run Charts arebetter option over histograms as they overcome the limitations of thehistograms. A run chart represents change in measurement over a sequence ortime. Run charts are used to determine cyclic events and their average values.

Steps in making Run Charts

•  Collect Data

•  Arrange data with time sequence

•  Plot the data in order

•  Interpreting Data

The run chart reveals the following about the process

  Run charts display process performance over time   Trends, cycles, and large variations are clearly visible   An average line may be added to a run chart to clarify movement of the data away from the

process average

Two types of mistake normally people commit while interpreting the run chart

1. cycle or trend exist but actually it is not 2. cycle or trend does not exist but actually they exist

To overcome this problem a thumb rule is to look at the data for a long period of time

Pareto Chart

VILFREDO PARETO an Italian economist provided a golden rule which fits into many managerial situations. The golden rule he noticed is “WEALTH IS CONCENTRATED IN A FEW PEOPLE”. Pareto principle : “The majority of wealth is held by a disproportionately small segment of the population”. This principle is also known as 80 / 20 principle. 80% of the problems are caused by 20% of the causes

JURAN has noticed that this principle applies to quality improvement as well. According to Juran the problems that occur a few are very frequent while other important problems occur seldom. He given the phrase as “Vital few and the trivial many”

Pareto Charts are used to apply the 80/20 rule of Joseph Juran which states that 80% of the problems are the result of 20% of the problems. A Pareto Chart can be used to identify that 20% root causes of problem.

A Perot chart is similar like histogram

Steps in making Pareto Charts

First define categories Sort the data into the

Categories and find out the         frequency of occurrence

of each category

Arrange the categories in descending order

The Pareto Chart of the following problem is given below:

   

Problem Type Frequency Annual Cost on Rs.1000 Cumulative%A 40 20 40

B 20 6 60

C 14 3 74

D 10 2 84

E 8 2 92

F 5 1.5 97

G 3 1.8 100

Flow Chart

A flow chart is way of representing a procedure using simple symbols and arrows. A Flow chart shows the activities in a process and the relationships between them. A Flow chart lets a process be understood easily. It also demonstrate the relationships between the elements of the process.

Steps in making Flow Charts

Determine the Process need to be represented by flow chart

List down the sequence of operation and other details

Start at a certain point and go then step by step

        using flow chart symbols

Write the titles to each element

Scatter Diagram

Scatter diagram is a statistical chart which shows a trend in a series of data. It demonstrates correlations between values.

Steps in making Scatter Diagram

Plot the data points Draw trend line by

fitting a straight line

Upward line shows the positive trend

                       (X increases and Y increases)

Downward line shows the negative trend

(X increases and Y decreases)

Cause and Effect Diagrams (Steps)

A Cause and Effect Diagram shows the relationship between effect and the categories of their causes. The diagram look like a fishbone it is therefore also called fish-bone diagram. Cause and effect diagram enables a team to focus on the content of a problem. It helps to provide a comprehensive picture of the problem and the root causes of the same.

Steps in making Cause and Effect Diagram

Determine the Effect or Problem

Categorize the possible causes

Describe the possible causes

1. Draw an arrow horizontally pointing to an effect

 

2. Draw four or more branches off the large arrow to represent main categories of potential causes. Typical categories are man, machinery, methods, and materials.

3. Secondary causes can be listed on branches off the category branches.

4. Additional causes can be branched off the Secondary causes.

5. Additional Causes, if any, may further be branched off the tertiary causes. The process goes on till

all the possible causes have been explored.

Control Chart

Control charts are statistical tool, showing whether a process is in control or not. It is a graphical tool for monitoring the activities of an ongoing process also referred as Shewhart control charts.

Steps in making control chart

     Define Upper limit, lower limit and Center line      Draw Chart      Plot the data points into chart      Interpret the control chart

Details regarding control chart is given in the next lectures

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Lecture 5 Control Charts (Figure) 

Control charts are statistical tool, showing whether a process is in control or not.  It is a graphical tool for monitoring the activities of an ongoing process also referred as Shewhart control charts. Control charts are used for process monitoring and variability reduction.

Before discussing and calculating the limits etc. of control charts, it is necessary to understand causes of variations present in the system. Variability is an inherent feature of every process.  Production data always have some variability.  

Causes of Variations

Two types of causes are present in the production system

        Special causes:          Variation due to identifiable factors in the production process. Examples of special causes include: wrong tool, wrong production method, improper raw material, operator's skill, wrong die etc. Control of process is achieved through the elimination of special causes. According to Deming, only 15% of the problems are due to the special causes. Special causes or also sometimes referred as Assignable causes

        Common causes:       Variation inherent in the process. Improvement of process is accomplished through the reduction of common causes and improving the system. According to Deming, 85% of the problems are due to the common causes.

Assignable causes are controlled by the use of statistical process charts.

Steps in constructing a control chart

     Decide what to measure or count      Collect the sample data      Plot the samples on a control chart      Calculate and plot the control limits on the control chart      Determine if the data is in control      If non-random variation is present, discard the data (fix the problem) and recalculate the control

limits      When data are with in the control limits we leave the process assuming there are only chance

causes present

A process is in control IF

     No sample points outside control limits      Most points near process average or center line      About equal number of points above and below the center line      Sample point are distributed randomly

 

 

Figure: Control Chart Representing Limits, Special Causes, Common Causes

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Lecture 6 Types of Process Data

Two types of process data:

1.      Variable:  continuous data. Things we can measure. Example includes length, weight, time,

temperature, diameter, etc.

2.      Attribute:  discrete data. Things we count. Examples include number or percent defective items in a lot, number of defects per item etc.

Types of Control Charts: the classification of control charts depend upon the type of data.

1.      Variable charts: are meant for variable type of data. X bar and R Chart, X bar and sigma chart, chart for the individual units

2.      Attribute chats  : are meant for attribute type of data. p chart, np chart, c chart, u chart, U chart 

Control charts for the variable type of data (X bar and R charts)

In the x bar chart the sample means are plotted in order to control the mean value of a variable. In R chart, the sample ranges are plotted in order to control the variability of a variable

Centre line, upper control limit, lower control limit for x bar and R charts are calculated. The formulae used are as following:

  

            = mean of the ith sample

n                = sample size,

Xi               = ith data 

 

 

 Ri               = range of ith  sample

 Xmax(i)         = maximum value of the data in ith sample

 Xmin (i)        = minimum value of the data in ith sample 

 

 

              = mean of g samples 

       (Centre Line for X bar chart) 

              = mean of mean of g samples

g                = number of samples

 

 

    = standard deviation of samples

  =    = estimate of standard deviation of population

d2               = parameter depends on sample size n

      

     (Upper control limit for X bar chart) 

 A2              =            = parameter depends on sample size 

 value of A2 can be directly obtained from the standard tables 

   (Lower control limit for X bar chart)  

 where    (Upper control limit for R chart) 

   where    (Lower control limit for R chart)

Example:

Mean values and ranges of data from 20 samples (sample size = 4) are shown in the table below:

S.N

Mean of

Sample

Range

S.N

Mean of

Sample

Range

S.N

Mean of

Sample

Range

S.N

Mean of

Sample

Range

S.N

Mean of

Sample

Range

1 10 4 5 9 5 9 10 4 13 12 4 17 12 4

2 15 4 6 11 6 10 11 6 14 12 3 18 15 3

3 12 5 7 11 4 11 12 5 15 11 3 19 11 3

4 11 4 8 9 4 12 13 4 16 15 4 20 10 4

Sum of mean of 20 samples =  = 232

Average of mean values of 20 samples =  = 11.6 (Center Line of X bar Chart)

Average of Ranges of 20 samples         =     = 4.15 (Center Line of R Chart)

Upper Control Limit of X bar chart       = 11.6 + A2 4.15 (A2 = 0.729 for sample size 4)

                                                                   = 14.63

Lower Control Limit of X bar chart       = 11.6 - A2 4.15 (A2 = 0.729 for sample size 4)

                                                                   = 8.57

Upper Control Limit of R chart             = D3 4.15 (D3 = 2.282 for sample size 4)

                                                                   = 9.47 9.5

Lower Control Limit of R chart             = D4 4.15 (D4 = 0 for sample size 4)     

                        

 X-Bar Chart

Sample data at S.N 2, 16, and 18 are slightly above the UCL. Efforts must be made to find the special causes and revised limits are advised to calculate after deleting these data.

R Chart

All the data are within the LCL and UCL in R Chart. Hence variability of the process data is not an issue to worry.

Control charts for Attribute type data (p, c, u charts)

p-charts calculates the percent defective in sample. p-charts are used when observations can be placed in two categories such as yes or no, good or bad, pass or fail etc.

c-charts counts the number of defects in an item. c-charts are used only when the number of occurrence per unit of measure can be counted such as number of scratches, cracks etc.

u-chart counts the number of defect per sample. The u chart is used when it is not possible to have a sample size of a fixed size.

For attribute control charts, the estimate of the variability of the process is a function of the process average.

Centre line, upper control limit, lower control limit for c, p, and u charts are calculated. The formulae used are as following:

 p-chart formulae

  = centre line of p chart

Where n is the sample size. Sample size in p chart must be

Sometimes LCL in p chart becomes negative, in such cases LCL should be taken as 0

c-chart formulae

  = centre line of c chart

 

u-chart formulae

    =   

ci =number of defects in ith sample

k = number of samples

ni = size of  ith samples

Example: p-chart

Data for defective CDs from 20 samples (sample size = 100) are shown in the table below: 

Sample No.

No. of Defective CDs = x

Proportion Defective =

x/sample size Sample

No.No. of

Defective CDs = x

Proportion Defective =

x/sample size 1 4 .04 11 6 .06

2 3 .03 12 5 .05

3 3 .03 13 4 .04

4 5 .05 14 5 .05

5 6 .06 15 4 .04

6 5 .05 16 7 .07

7 2 .02 17 6 .06

8 3 .03 18 8 .08

9 5 .05 19 6 .06

10 6 .06 20 8 .08

CL =

p-Chart

Sample data at S.N 16 , 18, and 20  are above the UCL. Efforts must be made to find the special causes and revised limits are advised to calculate after deleting these data. There is important observation that is clearly visible from the data points that there is an increasing trend in the average proportion defectives beyond sample number15 also, data show cyclic pattern. Process appears to be out of control and also there is a strong evidence that data are not from independent source.

Example: c-chart

Data for defects on TV set from 20 samples (sample size = 10) are shown in the table below:           

Sample No. No. of Defects

Sample No.

No. of Defects

Sample No.

No. of Defects

Sample No.

No. of Defects

1 5 6 4 11 6 16 5

2 4 7 5 12 5 17 4

3 5 8 6 13 4 18 6

4 6 9 8 14 7 19 6

5 4 10 7 15 6 20 6

CL =

c-Chart

None of the sample is out of the LCL and UCL. But the chart shows cyclic trend.

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Lecture 7 Process Capability

Process Stability

A process output is considered stable when it consists of only common-cause variation and has the reproducibility over a long period of time. Common-cause variation originates from the basic elements of a manufacturing process. Which are 5 Ms:

     Machine,      Man (operator),      Material,      Method of work, and      Measurement system

UNSTABLE PROCESS

(As mean value and Variance of the process is continuously varying)

STABLE PROCESS

(As mean value and Variance of the process is constant)

The process parameters can not be correctly estimated for an unstable process because of the following reasons.

     No well defined output distribution      Misleading decisions

     No useful estimation of process capability      No useful purpose for process improvement

Process Capability

Prerequisites for process capability is to estimation of process average and process standard deviation.

Process Capability for Bilateral Specification

A process producing a characteristic with a bilateral specification meets the minimum requirement of capability when it is stable, and has no more than 0.135 percent of its output for this characteristic outside either specification limit.

Process Capability for Unilateral Specification

A  process  producing a characteristic with a unilateral specification  meets the minimum requirement of capability  when it is stable, and  has no more  than 0.135 percent of its output for this characteristic outside the single specification limit.

Why Processes Fail?        Process variation (spread) is too large

      Process average is not properly centered       Process average is not properly centered and Process Variation is too large

Measuring Process Capability 

1. Capability Index, Cp For bilateral specification 

     When Process average is equal to nominal value:

             Cp = (USL – LSL) / 6s 

     When process average is not equal to nominal value:

            Cp = Minimum (m - LSL/ 3s   , USL- m / 3s )

2. Capability Index, Cp For unilateral specification 

     In case of USL :

Cp = Maximum (USL- m / 3s   , USL-X / 3s ) 

     In case of LSL :

Cp = Maximum (m-LSL / 3s   , X - USL / 3s )

 

Cp values Capability Ratings

Cp ³ 2.00 Terrific

1.67 £ Cp < 2.00 Excellent

1.33 £ Cp < 1.67 Good

1.00 £ Cp < 1.33 Fair

0.67 £ Cp < 1.00 Poor

 Cp < 0.67 Terrible

Flow Chart for Conducting a Process Capability  

 

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Part 3 CPM/PERT

Lecture 1

Project Management

A project is a well defined task which has a definable beginning and a definable end and requires one or more resources for the completion of its constituent activities, which are interrelated and which must be accomplished to achieve the objectives of the project. Project management is evolved to coordinate and control all project activities in an efficient and cost effective manner. The salient features of a project are:

        A project has identifiable beginning and end points.         Each project can be broken down into a number of identifiable activities which will consume

time and other resources during         their completion.         A project is scheduled to be completed by a target date.         A project is usually large and complex and has many interrelated activities.         The execution of the project activities is always subjected to some uncertainties and risks. 

Network Techniques

The network techniques of project management have developed in an evolutionary way in many years. Up to the end of 18th century, the decision making in general and project management in particular was intuitive and depended primarily on managerial capabilities, experience, judgment and academic background of the managers. It was only in the early of 1900's that the pioneers of scientific management, started developing the scientific management techniques. The forerunner to network techniques, the Gantt chart was developed, during world war I, by Henry L Gantt, for the purpose of production scheduling. The Gantt chart ( Figure 1 ) was later modified to bar chart ( Figure 2 ), which was used as an important tool in both the project and production scheduling. The bar charts, then developed into milestone charts ( Figure 3 ), and next into network techniques (such as CPM and PERT).

Network Construction 

A network is the graphical representation of the project activities arranged in a logical sequence and depicting all the interrelationships among them. A network consists of activities and events.

Activity

An activity is a physically identifiable part of a project, which consumes both time and resources. Activity is represented by an arrow in a network diagram ( Figure 4 ). The head of an arrow represents the start of activity and the tail of arrow represents its end. Activity description and its estimated completion time are written along the arrow. An activity in the network can be represented by a number of ways: (i) by numbers of its head and tail events (i.e. 10-20 etc.), and (ii) by a letter code (i.e. A, B etc.). All those activities, which must be completed before the start of activity under consideration, are called its predecessor activities. All those activities, which have to follow the activity under consideration, are called its successor activities ( Figure 5 ). An activity, which is used to maintain the pre-defined precedence relationship only during the construction of the project network, is called a dummy activity. Dummy activity is represented by a dotted arrow and does not consume any time and resource ( Figure 6 ). An unbroken chain of activities between any two events is called a path.

Event

An event represents the accomplishment of some task. In a network diagram, beginning and ending of an activity are represented as events. Each event is represented as a node in a network diagram. An event does not consume any time or resource. Each network diagram starts with an initial event and ends at a terminal event. Each node is represented by a circle ( Figure 7) and numbered by using the Fulkerson's Rule. Following steps are involved in the numbering of the nodes:

      The initial event, which has all outgoing arrows and no incoming arrow, is numbered as 1.       Delete all the arrows coming out from node just numbered node (i.e. 1). This step will create

some more nodes (at least one) into initial events. Number these events in ascending order (i.e. 2, 3 etc.).

      Continue the process until the final or terminal node which has all arrows coming in, with no arrow going out, is numbered.

An illustration of Fulkerson's Rule of numbering the events is shown in Figure 8 . As a recommendation it must be noted that most of the projects are liable for modifications, and hence there should be a scope of adding more events and numbering them without causing any inconsistency in the network. This is achieved by skipping the numbers (i.e. 10, 20, 30…).

Rules for drawing network diagram

Rule 1: Each activity is represented by one and only one arrow in the network.

Rule 2: No two activities can be identified by the same end events ( Figure 9 ).

Rule 3: Precedence relationships among all activities must always be maintained.

Rule 4: Dummy activities can be used to maintain precedence relationships only when actually required. Their use should be minimized in the network diagram ( Figure 10 ).

Rule 5: Looping among the activities must be avoided( Figure11 ).

CPM and PERT

The CPM (critical path method) system of networking is used, when the activity time estimates are deterministic in nature. For each activity, a single value of time, required for its execution, is estimated. Time estimates can easily be converted into cost data in this technique. CPM is an activity oriented technique.

The PERT (Project Evaluation and Review Technique) technique is used, when activity time estimates are stochastic in nature. For each activity, three values of time (optimistic, most likely, pessimistic) are estimated.  Optimistic time (to) estimate is the shortest possible time required for the completion of activity. Most likely time (tm) estimate is the time required for the completion of activity under normal circumstances. Pessimistic time (tp) estimate is the longest possible time required for the completion of activity. In PERT β-distribution is used to represent these three time estimates. As PERT activities are full of uncertainties, times estimates can not easily be converted in to cost data. PERT is an event oriented technique.

 

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Lecture 2

Calculation of Expected Time and Variance of a Path in PERT

The Expected Time of a chain of activities in series, is the SUM of their expected times, similarly the variance of the path, is the SUM of Variances of activities on the path in Fig below, three activities A,B and C are connected in series, (i.e. from a path). Their time estimates to-tm-tpare given along the activity arrow. The expected time of the path 1-2-3-4 is

As the length of the path ,that is the number of activies connected in series increases,the variance of the path and hence the uncertainty of meeting the expected time increases.

Example:

In the Network of fig below, the PERT time estimates of the activities are written along the activity arrow in the order to-tm-tp. Compute the expected time and variance for each activity. Also compute the expected duration and standard deviation for the following path of the Network

           (a) 10-20-50-80-90

           (b) 10-30-50-70-90

           (c) 10-40-60-80-90

Solution :

The Computation of expected times and variance for different activities are carried in a table given below

Activityi              j

Time Estimates to            tm           tp

Expected Time tE

Variance

10           20 6             9           12 9.00 1.00

10           30 3             5            9 5.33 1.00

10           40 10         14           18 14.00 1.78

20           50 7           10           13 10.00 1.00

20           70 3             4             8 4.5 0.69

30           50  4           10           12 9.33 1.78

40           50   8           11           14 11.00 1.00

40           60  5          10           12 10.00 2.78

50           70 3            4            5 4.00 0.11

50           80 11           15          17 14.67 1.00

60           80 4             8           10 9.17 0.69

70           90 6             7            9 7.67 1.00

80           90 6             9           12 7.17 0.25

 

Network Analysis(CPM) :

In the project network given in figure below , activation and their directions are specified at the activities. Find the critical path and the project duration.

(a) Forward Pass Computations :

ET(j) is the earliest expected time of event j,

ET(i) is the earliest expected time of predecessor activity i,

is the expected time of activity i-j.

(b) Backward Pass Computations :

LT(j) is the latest expected time of event i,

LT(i) is the latest expected time of sucessor event j,

is the expected time of activity i-j.

 

Predecessor Event i

Successor    Event j

Expected time of

activity i-j

ET(i)Earliest expected

Time of the Predecessor

activity i

ET(j)Earliest expected Time of event j

LT(i)Latest

expected time of event i

LT(j)Latest expected

time of sucessor event j

10 7 0 7 0 7

15 12 0 12 7 19

20 17 0 17 5 22

20 15 7 22 7 22

25 9 7 16 21 30

30 11 12 23 19 30

25 5 22 27 25 30

30 8 22 30 22 30

35 10 27 37 30 40

45 15 27 42 35 50

35 10 30 40 30 40

40 8 30 38 35 43

45 10 40 50 40 50

45 7 38 45 43 50

 

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ForcastingLecture 1

Introduction

The growing competition, frequent changes in customer's demand and the trend towards automation demand that decisions in business should not be based purely on guesses rather on a careful analysis of data concerning the future course of events. More time and attention should be given to the future than to the past, and the question 'what is likely to happen?' should take precedence over 'what has happened?' though no attempt to answer the first can be made without the facts and figures being available to answer the second. When estimates of future conditions are made on a systematic basis, the process is called forecasting and the figure or statement thus obtained is defined as forecast.

In a world where future is not known with certainty, virtually every business and economic decision rests upon a forecast of future conditions. Forecasting aims at reducing the area of uncertainty that surrounds management decision-making with respect to costs, profit, sales, production, pricing, capital investment, and so forth. If the future were known with certainty, forecasting would be unnecessary. But uncertainty does exist, future outcomes are rarely assured and, therefore, organized system of forecasting is necessary. The following are the main functions of forecasting:

        The creation of plans of action.         The general use of forecasting is to be found in monitoring the continuing progress of plans based on

forecasts.         The forecast provides a warning system of the critical factors to be monitored regularly because they

might drastically affect the performance of the plan.

It is important to note that the objective of business forecasting is not to determine a curve or series of figures that will tell exactly what will happen, say, a year in advance, but it is to make analysis based on definite statistical data, which will enable an executive to take advantage of future conditions to a greater extent than he could do without them. In forecasting one should note that it is impossible to forecast the future precisely and there always must be some range of error allowed for in the forecast.

Dependent versus Independent Demand

Demand of an item is termed as independent when it remains unaffected by the demand for any other item. On the other hand, when the demand of one item is linked to the demand for another item, demand is termed as dependent. It is important to mention that only independent demand needs forecasting. Dependent demand can be derived from the demand of independent item to which it is linked.

Business Time Series

The first step in making a forecast consists of gathering information from the past. One should collect statistical data recorded at successive intervals of time. Such a data is usually referred to as time series. Analysts plot demand data on a time scale, study the plot and look for consistent shapes and patterns. A time series of demand may have constant, trend, or seasonal pattern ( Figure 1 ) or some combination of these patterns. The forecaster tries to understand the reasons for such changes, such as,

Changes that have occurred as a result of general tendency of the data to increase or decrease, known as

secular movements.

Changes that have taken place during a period of 12 months as a result in changes in climate, weather

conditions, festivals etc. are called as seasonal changes.

Changes that have taken place as a booms and depressions are called as cyclical variations.

Changes that have taken place as a result of such forces that could not be predicted (like flood, earthquake

etc.) are called as irregular or erratic variations.

Lecture 1

Introduction

The growing competition, frequent changes in customer's demand and the trend towards automation demand that decisions in business should not be based purely on guesses rather on a careful analysis of data concerning the future course of events. More time and attention should be given to the future than to the past, and the question 'what is likely to happen?' should take precedence over 'what has happened?' though no attempt to answer the first can be made without the facts and figures being available to answer the second. When estimates of future conditions are made on a systematic basis, the process is called forecasting and the figure or statement thus obtained is defined as forecast.

In a world where future is not known with certainty, virtually every business and economic decision rests upon a forecast of future conditions. Forecasting aims at reducing the area of uncertainty that surrounds management decision-

making with respect to costs, profit, sales, production, pricing, capital investment, and so forth. If the future were known with certainty, forecasting would be unnecessary. But uncertainty does exist, future outcomes are rarely assured and, therefore, organized system of forecasting is necessary. The following are the main functions of forecasting:

        The creation of plans of action.         The general use of forecasting is to be found in monitoring the continuing progress of plans based on

forecasts.         The forecast provides a warning system of the critical factors to be monitored regularly because they

might drastically affect the performance of the plan.

It is important to note that the objective of business forecasting is not to determine a curve or series of figures that will tell exactly what will happen, say, a year in advance, but it is to make analysis based on definite statistical data, which will enable an executive to take advantage of future conditions to a greater extent than he could do without them. In forecasting one should note that it is impossible to forecast the future precisely and there always must be some range of error allowed for in the forecast.

Dependent versus Independent Demand

Demand of an item is termed as independent when it remains unaffected by the demand for any other item. On the other hand, when the demand of one item is linked to the demand for another item, demand is termed as dependent. It is important to mention that only independent demand needs forecasting. Dependent demand can be derived from the demand of independent item to which it is linked.

Business Time Series

The first step in making a forecast consists of gathering information from the past. One should collect statistical data recorded at successive intervals of time. Such a data is usually referred to as time series. Analysts plot demand data on a time scale, study the plot and look for consistent shapes and patterns. A time series of demand may have constant, trend, or seasonal pattern ( Figure 1 ) or some combination of these patterns. The forecaster tries to understand the reasons for such changes, such as,

Changes that have occurred as a result of general tendency of the data to increase or decrease, known as

secular movements.

Changes that have taken place during a period of 12 months as a result in changes in climate, weather

conditions, festivals etc. are called as seasonal changes.

Changes that have taken place as a booms and depressions are called as cyclical variations.

Changes that have taken place as a result of such forces that could not be predicted (like flood, earthquake

etc.) are called as irregular or erratic variations.

PPCLecture 1

Introduction

Production Planning is a managerial function which is mainly concerned with the following important issues:

What production facilities are required? How these production facilities should be laid out in the space available for production? and How they should be used to produce the desired products at the desired rate of production?

Broadly speaking, production planning is concerned with two main aspects: (i) routing or planning work tasks (ii) layout or spatial relationship between the resources. Production planning is dynamic in nature and always remains in fluid state as plans may have to be changed according to the changes in circumstances.

Production control is a mechanism to monitor the execution of the plans. It has several important functions:

Making sure that production operations are started at planned places and planned times. Observing progress of the operations and recording it properly. Analyzing the recorded data with the plans and measuring the deviations. Taking immediate corrective actions to minimize the negative impact of deviations from the plans. Feeding back the recorded information to the planning section in order to improve future plans.

A block diagram depicting the architecture of a control system is shown in Figure1. Important functions covered by production planning and control (PPC) function in any manufacturing system are shown in Table1along with the issues to be covered.

Types of Production Systems

A production system can be defined as a transformation system in which a saleable product or service is created by working upon a set of inputs. Inputs are usually in the form of men, machine, money, materials etc. Production systems are usually classified on the basis of the following:

Type of product, Type of production line, Rate of production, Equipments used etc.

They are broadly classified into three categories:

Job shop production Batch production Mass production 

Job Production

In this system products are made to satisfy a specific order. However that order may be produced-

                    -only once

                    -at irregular time intervals as and when new order arrives

                    -at regular time intervals to satisfy a continuous demand

The following are the important characteristics of job shop type production system:

Machines and methods employed should be general purpose as product changes are quite frequent. Planning and control system should be flexible enough to deal with the frequent changes in product

requirements. Man power should be skilled enough to deal with changing work conditions. Schedules are actually non existent in this system as no definite data is available on the product. In process inventory will usually be high as accurate plans and schedules do not exist. Product cost is normally high because of high material and labor costs. Grouping of machines is done on functional basis (i.e. as lathe section, milling section etc.) This system is very flexible as management has to manufacture varying product types. Material handling systems are also flexible to meet changing product requirements.

Batch Production

Batch production is the manufacture of a number of identical articles either to meet a specific order or to meet a continuous demand. Batch can be manufactured either-

            -only once

            -or repeatedly at irregular time intervals as and when demand arise

            -or repeatedly at regular time intervals to satisfy a continuous demand

The following are the important characteristics of batch type production system:

As final product is somewhat standard and manufactured in batches, economy of scale can be availed to some extent.

Machines are grouped on functional basis similar to the job shop manufacturing. Semi automatic, special purpose automatic machines are generally used to take advantage of the similarity

among the products. Labor should be skilled enough to work upon different product batches. In process inventory is usually high owing to the type of layout and material handling policies adopted. Semi automatic material handling systems are most appropriate in conjunction with the semi automatic

machines. Normally production planning and control is difficult due to the odd size and non repetitive nature of order.

Mass Production

In mass production, same type of product is manufactured to meet the continuous demand of the product. Usually demand of the product is very high and market is going to sustain same demand for sufficiently long time.

The following are the important characteristics of mass production system:

As same product is manufactured for sufficiently long time, machines can be laid down in order of processing sequence. Product type layout is most appropriate for mass production system.

Standard methods and machines are used during part manufacture. Most of the equipments are semi automatic or automatic in nature. Material handling is also automatic (such as conveyors). Semi skilled workers are normally employed as most of the facilities are automatic. As product flows along a pre defined line, planning and control of the system is much easier. Cost of production is low owing to the high rate of production. In process inventories are low as production scheduling is simple and can be implemented with ease.

MRPLecture 1

Introduction

It was discussed in demand forecasting that in the dependent demand situation, if the demand for an item is known, the demand for other related items can be deduced. For example, if the demand of an automobile is known, the demand of its sub assemblies and sub components can easily be deduced. For dependent demand situations, normal reactive inventory control systems (i.e. EOQ etc.) are not suitable because they result in high inventory costs and unreliable delivery schedules. More recently, managers have realized that inventory planning systems (such as materials requirements planning) are better suited for dependent demand items. MRP is a simple system of calculating arithmetically the requirements of the input materials at different points of time based on actual production plan. MRP can also be defined as a planning and

scheduling system to meet time-phased materials requirements for production operations. MRP always tries to meet the delivery schedule of end products as specified in the master production schedule.

MRP Objectives

MRP has several objectives, such as:

Reduction in Inventory Cost: By providing the right quantity of material at right time to meet master production schedule, MRP tries to avoid the cost of excessive inventory.

Meeting Delivery Schedule: By minimizing the delays in materials procurement, production decision making, MRP helps avoid delays in production thereby meeting delivery schedules more consistently.

Improved Performance: By stream lining the production operations and minimizing the unplanned interruptions, MRP focuses on having all components available at right place in right quantity at right time.

MRP System

A simple sketch of an MRP system is shown in figure. It can be seen from the figure that an MRP system has three major input components:

Master Production Schedule (MPS): MPS is designed to meet the market demand (both the firm orders and forecasted demand) in future in the taken planning horizon. MPS mainly depicts the detailed delivery schedule of the end products. However, orders for replacement components can also be included in it to make it more comprehensive.

Bill of Materials (BOM): BOM represents the product structure. It encompasses information about all sub components needed, their quantity, and their sequence of buildup in the end product. Information about the work centers performing buildup operations is also included in it.

Inventory Status File: Inventory status file keeps an up-to-date record of each item in the inventory. Information such as, item identification number, quantity on hand, safety stock level, quantity already allocated and the procurement lead time of each item is recorded in this file.

After getting input from these sources, MRP logic processes the available information and gives information about the following:

Planned Orders Receipts: This is the order quantity of an item that is planned to be ordered so that it is received at the beginning of the period under consideration to meet the net requirements of that period. This order has not yet been placed and will be placed in future.

Planned Order Release: This is the order quantity of an item that is planned to be ordered and the planned time period for this order that will ensure that the item is received when needed. Planned order release is determined by offsetting the planned order receipt by procurement lead time of that item.

Order Rescheduling: This highlight the need of any expediting, de-expediting, and cancellation of open orders etc. in case of unexpected situations.

InventryLecture 1

Introduction

The amount of material, a company has in stock at a specific time is known as inventory or in terms of money it can be defined as the total capital investment over all the materials stocked in the company at any specific time. Inventory may be in the form of,

         raw material inventory          in process inventory

         finished goods inventory

         spare parts inventory

         office stationary etc.

As a lot of money is engaged in the inventories along with their high carrying costs, companies cannot afford to have any money tied in excess inventories. Any excessive investment in inventories may prove to be a serious drag on the successful working of an organization. Thus there is a need to manage our inventories more effectively to free the excessive amount of capital engaged in the materials.

Why Inventories

Inventories are needed because demand and supply can not be matched for physical and economical reasons. There are several other reasons for carrying inventories in any organization.

To safe guard against the uncertainties in prices fluctuations, supply conditions, demand conditions, lead times, transport contingencies etc.

To reduce machine idle times by providing enough inprocess inventories at appropriate locations.

To take advantages of quantity discounts, economy of scale in transportation etc.

To decouple operations i.e. to make one operation's supply independent of another's supply. This helps in minimizing the impact of break downs, shortages etc. on the performance of the down stream operations. Moreover operations can be scheduled independent of each other if operations are decoupled.

 To reduce the material handling cost of semi-finished products by moving them in large quantities between operations.

To reduce clerical cost associated with order preparation, order procurement etc.

Inventory Costs

In order to control inventories appropriately, one has to consider all cost elements that are associated with the inventories. There are four such cost elements, which do affect cost of inventory.

Unit cost: it is usually the purchase price of the item under consideration. If unit cost is related with the purchase quantity, it is called as discount price.

Procurement costs: This includes the cost of order preparation, tender placement, cost of postages, telephone costs, receiving costs, set up cost etc.

Carrying costs: This represents the cost of maintaining inventories in the plant. It includes the cost of insurance, security, warehouse rent, taxes, interest on capital engaged, spoilage, breakage etc.

Stockout costs: This represents the cost of loss of demand due to shortage in supplies. This includes cost of loss of profit, loss of customer, loss of goodwill, penalty etc.

If one year planning horizon is used, the total annual cost of inventory can be expressed as:

Total annual inventory cost = Cost of items + Annual procurement cost + Annual carrying cost  +  Stockout cost

The objective of inventory management team is to minimize the total annual inventory cost. A simplified graphical presentation in which cost of items, procurement cost and carrying cost are depicted is shown in Figure 1 . It can be seen that large values of order quantity Q result in large carrying cost. Similarly, when order quantity Q is large, fewer orders will be placed and procurement cost will decrease accordingly. The total cost curve indicates that the minimum cost point lies at the intersection of carrying cost and procurement curves.

Inventory Operating Doctrine

When managing inventories, operations manager has to make two important decisions:

When to reorder the stock (i.e. time to reorder or reorder point) How much to stock to reorder (i.e. order quantity)

Reorder point is usually a predetermined inventory level, which signals the operations manager to start the procurement process for the next order. Order quantity is the order quantity.

Inventory Modelling

This is a quantitative technique for deriving the minimum cost model for the inventory problem in hand.

Economic Order Quantity (EOQ) Model

This model is applied when objective is to minimize the total annual cost of inventory in the organization. Economic order quantity is that size of the order which helps in attaining the above set objective. EOQ model is applicable under the following conditions.

Demand per year is deterministic in nature Planning period is one year

Lead time is zero or constant and deterministic in nature

Replenishment of items is instantaneous

Demand/consumption rate is uniform and known in advance

No stockout condition exist in the organization

The total annual cost of the inventory is given by the following equation in EOQ model (Figure 2 ):

Economic Production Quantity (EPQ) Model

In EOQ model supply was instantaneous, which may not be the case in all industrial applications. If supply of items is gradual to satisfy a continuous demand, then supply line will be depicted by a slanted line (Figure 3 )

Lecture 2 eta ekhono dey ni.