Statistical Quality Control

What is Statistical Quality Control?    Statistics: Statistics means the good amount of data to obtain reliable results. The Science of statistics handles this data in order to draw certain conclusions. Its techniques find extensive applications in quality control, production planning and control, business charts, linear programming etc.Quality: Quality is a relative term and is generally explained with reference to the end use of the product. Quality is thus defined as fitness for purpose.Control: Control is a system for measuring and checking or inspecting a phenomenon. It suggests when to inspect, how often to inspect and how much to inspect, how often to inspect. Control ascertains quality characteristics of an item, compares the same with prescribed quality standards and separates defective item from non-defective ones.Statistical Quality Control (SQC) is the term used to describe the set of statistical tools used by quality professionals. SQC is used to analyze the quality problems and solve them.Statistical quality control refers to the use of statistical methods in the monitoring and maintaining of the quality of products and services.

Statistica1 quality control (SQC) is the term used to describe the set of statistical tools used by quality professionals. Statistical quality control can be divided into two broad categories

1. Statistical process control (SPC) involves inspecting a random sample of the output from a process and deciding whether the process is producing products with characteristics that fall within a predetermined range. SPC answers the question of whether the process is functioning properly or not.

2. Acceptance sampling is the process of randomly inspecting a sample of goods and deciding whether to accept the entire lot based on the results. Acceptance sampling determines whether a batch of goods should be accepted or rejected.

Note: Common causes of variation Random causes that cannot be identified.

Assignable causes of variation Causes that can be identified and eliminated.Objective of Statistical Quality Control: Quality Control is very important for an every company. Quality control includes service quality given to customer, company management leadership, commitment of management, continuous improvement, and fast response, actions based on facts, employee participation and a quality driven culture. The application of statistical techniques to measure and evaluate the quality of a product, service, or process.The main objectives of the quality control module are to control of material reception, internal rejections, clients, claims, providers and evaluations of the same corrective actions are related to their follow-up. These systems and methods guide all quality activities. The development and use of performance indicators is linked, directly or indirectly, to customer requirements and satisfaction, and to management. 

Benefits of Statistical Quality Control1) It provides a means of detecting error at inspection.2) It leads to more uniform quality of production.3) It improves the relationship with the customer.4) It reduces inspection costs. 5) It reduces the number of rejects and saves the cost of material. 6) It provides a basis for attainable specifications. 7) It points out the bottlenecks and trouble spots. 8) It provides a means of determining the capability of the manufacturing process.9) It promotes the understanding and appreciation of quality control.

The Control Chart

Control charts are generally used in a production or manufacturing environment and are used to control, monitor and IMPROVE a process. A control chart is a graphical display of a measured quality characteristic. The measurement is plotted on the vertical axis and the sample (subgroup, subsample or sample number) is recorded on the horizontal axis. A control chart is a graph or chart with limit lines, called control lines. There are basically three kinds of control lines: the upper control limit (UCL), the central line (actual nominal size of product), The lower controls limit (LCL).

The purpose and advantage of drawing a control chart is To detect any changes in the process that would be evident by any abnormal points listed on the

graph from the data collected. A control chart indicated whether the process is in control or not. It warns in time and can make an immediate adjustment to correct the problem bringing the

process back into a "state of control". It ensures product quality level. It provides information about the selection of process and setting up the tolerance limit.

There are two main types of Control Charts.

Quality can be controlled either through actual measurement of dimension, weight or through attributes (as yes or no criteria) for example by using go or not go guage and without caring the actual dimension

The & Control Chart

An & Control Chart is one that shows both the mean value ( X ), and the range ( R ). The Xbar

portion of the chart mainly shows any changes in the mean value of the process, while the R portion shows any changes in the dispersion of the process. This chart is particularly useful in that it shows changes in mean value and dispersion of the process at the same time, making it a very effective method for checking abnormalities within the process; and if charted while in progress, also points out a problem in the production flow in real time mode.

Steps to plot and chart

Let The size of the sample is represented by the letter " n " and the number of subgroups is represented by the letter " N ".

Step1 Find the mean value (Xbar). Use the following formula for each subgroup:

Step 2 Find the range, R. Use the following formula for each subgroup.R = X (largest value) - X (smallest value)

Step 3 - Find the overall mean, or . By using the following formula. .

Step 4 - Compute the average value of the range ( ) by using the following formula.

Step 5 - Compute the Control Limit Lines. Use the following formulas for Xbar and R Control Charts. The coefficients for calculating the control lines are A2, D4, and D3 are located on the bottom of the Work Sheet you are presently using, and presented here:

Control Chart:

Central Line (CL) = .

Upper Control Limit (UCL) = + A2 * .

Lower Control Limit (LCL) = - A2 * .

R Control Chart: Central Line (CL) = R bar figure you calculated.

Upper Control Limit (UCL) = D4 * .

Lower Control Limit (LCL) = D3 * .

Step 6 - Construct the Control Chart. Use graph paper and set the index. Draw in the Control lines CL, UCL and LCL, and label them with their appropriate numerical values. It is recommended that you use a blue or black line for the CL, and a red line for the UCL and LCL. The central line is a solid line. The Upper and Lower control limits are usually drawn as broken lines.

Step 7 - Plot the X bar and R values as computed for each subgroup. Circle any points that lie outside the control limit lines so that you can distinguish them from the others.

P CHARTS it is used for fraction defective of total products.Fraction defective (P) is defined as the ratio of the number of defective produced (d) in a sample divided by the total number of products (n) in that sample.

If is the proportion of defective produced in entire processing or the average fraction defective. It is

given by the following formula

Control chart for fraction defective (P chart)Use P-Charts for quality characteristics that are discrete and involve yes/no or good/bad decisions

Percent of leaking caulking tubes in a box of 48 Percent of broken eggs in a carton

A Production manager for a tire company has inspected the number of defective tires in five random samples with 20 tires in each sample. The table below shows the number of defective tires in each sample of 20 tires.

Sample Sample Size (n) Number Defective

1 20 3

2 20 2

3 20 1

4 20 2

5 20 1

Steps for P chartStep 1: Calculate the Percent defective of Each Sample and the Overall Percent Defective (P-Bar)

Sample Number Defective Sample Size Percent Defective

1 3 20 .15

2 2 20 .10

3 1 20 .05

4 2 20 .10

5 1 20 .05

Total 9 100 .09

Step 2: Calculate the Standard Deviation of P. P chart is based on binomial distribution. The binomial

distribution has the standard deviation which is calculated by the relation.

Step 3: Calculate CL, UCL, LCL

Center line (p bar):

Control limits for ±3σ limits:

The number of defective units cannot be negative so LCL should be taken as 0 if it comes out negative.Step 4: Draw the Chart

Control chart for number of defective (nP chart)

Control chart for percent defective (100P chart)

Instead of fraction defective we can also use the defect ratio in terms of percentage. Percentage defective is 100 times of fraction defective.Percentage defective = 100 × fraction defective = 100P.Using the same notation as in P chart, the standard deviation and control limits are

These charts are applicable under the following condition

nP chart is used when sample size (n) is constant P or 100P chart can be used where sample size is variable.

Comparison of and P charts

P charts

1 These are control chart for variables These are control chart for attributes2 Cost of data collection is higher due to

actual measurementcheaper

3 Sample size are small Large sample size4 The control limits are affected by sample

sizeLess effect as compare to

5 Various chart has to be drawn for various characteristics saparately

Separate charts are not required for each characteristics

6 This method is much superior in diagnosing the cause of variability

Inferior

Control charts for number of defect per unit (C chart)

It is the control chart in which number of defect in a piece or sample is plotted. A defective piece may contain more than one defect, for example a casting may have blow holes and surface cracks.

It control number of defect observed per unit or per sample ( sample size is constant)

It is preffered for large and complex parts.

The control limits are based on poission distribution.

The number of weekly customer complaints is monitored in a large hotel. Develop a three sigma control limits For a C-Chart using the data table.

Week Number of Complaints

1 3

2 2

3 3

4 1

5 3

6 3

7 2

8 1

9 3

10 1

Total 22

Calculate CL, UCL, LCL

Center line (c bar):

=

Control limits for ±3σ limits:

Example of X and R chart

Sample noSample size = 5

X1 X2 X3 X4 X5 RangeR= max-min

1 13 9 12 10 11 11 42 10 11 13 12 14 12 43 16 13 10 11 14 12.8 64 12 14 15 13 16 14 45 11 13 17 14 13 13.6 66 15 13 14 12 10 12.8 57 14 12 13 11 9 11.8 58 10 12 16 13 12 12.6 69 11 13 14 12 15 13 410 16 10 11 12 10 11.8 6

The value of A2, D4 and D3 for n=5 (sample size) A2 = 0.58, D4= 2.11 and D3 = 0

Control Chart:

Central Line (CL) = = 12.54 .

Upper Control Limit (UCL) = + A2 * = 12.54 + 0.58(5) = 15.44

Lower Control Limit (LCL) = - A2 * = 12.54 - 0.58(5) = 9.64

R Control Chart: Central Line (CL) = R bar = 5

Upper Control Limit (UCL) = D4 * = 2.11*5 = 10.55

Lower Control Limit (LCL) = D3 * = 0*5 = 0

R chart

chart

Acceptance Sampling:

It is a process of randomly inspecting the sample of goods deciding, whether to accept or reject the entire lot.

Goal: To accept or reject a batch of items. Frequently used to test incoming materials from suppliers or other parts of the organization prior to entry into the production process.

Used to determine whether to accept or reject a batch of products. Measures number of defects in a sample. Based on the number of defects in the sample the batch is either accepted or rejected. An acceptance level c is specified. If the number of defects in the sample is c the batch is accepted, otherwise it is rejected and subjected to 100% inspection.

Acceptance sampling different from statistical process control is that acceptance sampling is performed before or after the process, rather than during the process. Acceptance sampling before the process involves sampling materials received from a supplier, such as randomly inspecting crates of fruit that will be used in a restaurant, boxes of glass dishes that will be sold in a department store, or metal castings that will be used in a machine shop.

Sampling after the process involves sampling finished items that are to be shipped either to a customer or to a distribution center. Examples include randomly testing a certain number of computers from a batch to make sure they meet operational requirements, and randomly inspecting snowboards to make sure that they are not defective.

It may be wondering why we would only inspect some items in the lot and not the entire lot. Acceptance sampling is used when inspecting every item is not physically possible or would be overly expensive, or when inspecting a large number of items would lead to errors due to worker fatigue. This last concern is especially important when a large number of items are processed in a short period of time. Another example of when acceptance sampling would be used is in destructive testing, such as testing eggs for salmonella or vehicles for crash testing. Obviously, in these cases it would not be helpful to test every item! However, 100 percent inspection does make sense if the cost of inspecting an item is less than the cost of passing on a defective item.

As you will see in this section, the goal of acceptance sampling is to determine the criteria for acceptance or rejection based on the size of the lot, the size of the sample, and the level of confidence we wish to attain. Acceptance sampling can be used for both attribute and variable measures, though it is most commonly used for attributes.

1. Single Sampling Plan: In this plan, a small sample of size (n) is taken randomly and 100% inspection is done on it, if the number of defective part is equal to or less than acceptance number than entire lot is accepted otherwise rejected.

2. Double Sampling Plan: A sample of n unit is taken randomly and number of defective is C1 or less than entire lot is accepted. If number of defective is C2 or more than entire lot is rejected. If the number of defective are between C1 and C2 then another sample of n2 item is taken. If the total number of defective from the two samples together is C3 or less than entire lot is accepted, otherwise rejected.

What is Forecasting? MeaningForecasting is a process of predicting or estimating the future based on past and present data. Forecasting provides information about the potential future events and their consequences for the organization. It may

not reduce the complications and uncertainty of the future. However, it increases the confidence of the management to make important decisions. Forecasting is the basis of premising. Forecasting uses many statistical techniques. Therefore, it is also called as Statistical Analysis.Peculiarities, characteristics or features of forecasting are as follows:-

1. Forecasting in concerned with future events.2. It shows the probability of happening of future events.3. It analysis past and present data.4. It uses statistical tools and techniques.5. It uses personal observations.

Merits, significance or importance of forecasting involves following points:-1. Forecasting provides relevant and reliable information about the past and present events and the likely future events. This is necessary for sound planning.

2. It gives confidence to the managers for making important decisions.3. It is the basis for making planning premises.4. It keeps managers active and alert to face the challenges of future events and the changes in

the environment.Demerits, criticism or limitations of forecasting involves following points:-

1. The collection and analysis of data about the past, present and future involves a lot of time and money. Therefore, managers have to balance the cost of forecasting with its benefits. Many small firms don't do forecasting because of the high cost.

2. Forecasting can only estimate the future events. It cannot guarantee that these events will take place in the future. Long-term forecasts will be less accurate as compared to short-term forecast.

3. Forecasting is based on certain assumptions. If these assumptions are wrong, the forecasting will be wrong. Forecasting is based on past events. However, history may not repeat itself at all times.