Copyright © 2012 Pearson Education. Chapter 22 Quality Control.

Copyright © 2012 Pearson Education.

Chapter 22

Quality Control

Copyright © 2012 Pearson Education. 22-2

Quality control today is a tool in the larger effort of continual process improvement in both the manufacturing and service industries. In this view, work is a process on which data can be gathered and studied. This study can then lead to improvement in the process.

The process improvement strategy includes understanding the process, collecting the data, assessing the process, eliminating causes of variation, studying the cause and effect of relationships within the process, and implementing changes.

In this chapter we will study some tools used in the assessment of the process data to investigate whether the process has changed, either in its mean or in its variation.


22.1 A Short History of Quality Control

• Walter A. Shewhart was a statistician and engineer working at Bell Laboratories in the early part of the twentieth century. He developed a time plot of a measure of quality which became known as a control chart, or a Shewhart chart, in his honor.

• “Variation from common-cause systems should be left to chance, but special causes of variation should be identified and eliminated.”

Shewhart defined the fundamental rule of statistical process control (SPC) as:



Walter A. Shewhart noticed and defined two distinct sources of variation in manufacturing.

The short-term focus of quality control is to detect and correct the special causes of variation. The long-term focus of continual quality improvement is to reduce the amount of variation from the common causes.

1) Common-cause Variation: Variation due to random fluctuations intrinsic to the process.

2) Special-cause Variation: Variation caused by issues in the process that can be identified. When special-cause variation is present, the process is said to be out of control.



Shewhart’s process was broken down into four distinct stages:

1) Plan: Identify and describe the process, and suggest improvements

2) Do: Implement the changes at a smaller scale.

3) Check: Examine the new process to see if decreased variation occurred.

4) Act: If applicable, implement the improvements on a large scale.



Control and Specification Limits

A control chart is used to determine if an in-control process might change and slip “out of control.”

Control Limits are established to decide when to take action. When points fall outside of the control limits, this signals that the process may have changed and some action is needed.

There are two type of errors that can be made in using a control chart:

• Type I: A false alarm; requiring an unnecessary adjustment to the process

• Type II: A failure to see a change in the process.




Specification Limits are external limits placed on the process based on quality concerns not directly related to how well the parts are produced.

Example: Bolts have a specific diameter range they must fall in in order to work.

Process Capability Studies are used to understand how well the process is working given the specification limits and the actual process parameters (mean and Variance).




The ratio measures the ratio of the entire specification range (both sides of the mean) to 6 times the standard deviation of the actual process variation.

6p

USL LSLC

pC

USL denotes the upper specification limit, LSL denotes the lower specification limit and σ denotes the standard deviation.




Because does not explicitly use the location of the mean it tends to over estimate the potential of the process when the mean is not centered and can be misleading. A measure known as is often used instead. When the process mean and standard deviation are known, is defined as:

pC

min ,3 3pk

USL LSLC

pkCpkC



Example: Potato chips

A potato chip company claims that their bags are filled with 5.0 oz. of chips. Historical data from the bag filing process shows that the standard deviation of the bag weights are 0.1 oz and the mean is 5.02 oz. The quality control team has set the specification limits to 4.75 and 5.25 oz. Determine the values of and .

.833pC

min .766,0.9 .766pkC

pC pkC


22.2 Control Charts for IndividualObservation (Run Charts)

Control Charts for individual observations (sometimes called run charts) are created using measurements made on every product produced to determine if the process has changed or has gone out of control.

The average time between alarms that the process has changed is called the average run length or ARL.

The average time between false alarms for an in-control process is called the in-control ARL.


22.2 Control Charts for IndividualObsevation (Run Charts)

The operating-characteristic (OC) curve describes the ability of any chart in detecting a shift or change in the process.

Shifts are measured in terms of standard deviations. The OC curve gives the probability of detecting a shift of a certain size in the next observation. A level shift is an abrupt change while a gradual change is called a trend.


22.2 Control Charts for IndividualObsevation (Run Charts)

The Western Electric Handbook (WECO, 1956) suggests several rules for deciding whether a process is out of control:

1) One point outside of the 3σ control limits on either side

2) Two out of three consecutive points beyond the 2σ “warning limits”

3) Four out of five consecutive points beyond 1σ from the mean

4) Eight (or seven) points in a row on the same side of the mean

5) Six points in a row increasing (or decreasing)

6) Fourteen points in a row alternatively increasing and decreasing


22.2 Control Charts for IndividualObservation (Run Charts)

Example: A producer of beverage containers wants to ensure that a liquid at 90°C will lose no more than 4°C after 30 minutes. Historical data shows the standard deviation to be 0.2°C. The quality control team has set 3.5°C and 4.5°C as the specification limits. Construct a run chart for the data below and determine if the process is out-of-control.

Container #Temperature

loss (°C)1 3.892 3.713 4.144 4.125 3.746 3.997 4.228 4.029 4.48

10 3.9311 3.8712 3.94


22.3 Control Charts for Measurements: and R ChartsX

X charts are control charts of sample means of periodic samples. These plots have several advantages over run charts.• Less frequent testing is a simple advantage especially when testing can take time or is destructive.

• Sample means have a distribution closer to the normal distribution.

The control limits for the charts are as follows:

3LCLn

3UCLn



XThe chart below shows 25 five-item samples at regular intervals with and .

3 255.7LCLn

3 344.3UCLn

300 33



R charts are control charts of the ranges of periodic samples.

The control limits for the charts are as follows:

32

3R

LCL R dd

3

2

3R

UCL R dd

Where, for k sample:

1 ... kR RR

k

d2 and d3 are found for various sample sizes in Table R.

An alternative to the R chart is the S chart, which uses the standard deviations of samples rather than their ranges.



The R chart below shows 25 samples of size 5 and .

32

3R

LCL R dd

32

3R

UCL R dd

81.32R



To choose an appropriate sample size, quality control monitors examine the operating characteristic curves such as the one below.

Both the process shift and the sample size can be used to find the probability of a Type II error for a next sample.


22.4 Actions for Out-of-Control Processes

For an established manufacturing process there may be an out-of-control action plan (OCAP) in place based on past experience. For a new process for which no such plans exists use the following basic steps to determine the problem.

• Use a team of all those involved in the process to determine the possible causes. Use a cause-and-effect diagram to organize the possible causes.

• Use a series of experiments to test the most probable causes.

• Once the most likely cause is established, correct the problem in hopes of driving the process back into control.

• Restart the monitoring process.


22.5 Control Charts for Attributes: p Charts and c ChartsThe most common type of categorical measurements used in quality control are dichotomous variables (yes/no responses).

Example: A customer service phone call being rated by the customer as either satisfactory or unsatisfactory

A p chart is a control chart of proportions used to monitor the process for changes in proportions of defectives. The control limits for the proportions are as follows:

3pq

LCL pn

3pq

UCL pn


22.5 Control Charts for Attributes: p Charts and c Charts

As with charts there are a variety of alternative rules to WECO to determine if a process is out of control. Minitab, for example, uses the following four:

1) One point outside of the 3σ lines

2) Nine points in a row outside of 1σ on the same side

3) Six increasing or decreasing points in a row

4) Fourteen points in a row that alternate up and down


22.5 Control Charts for Attributes: p Charts and c Charts

A c chart is another option for monitoring dichotomous variables used in the quality control process. Rather than using proportions, the c chart uses the number of defective items in a sample.

The Poisson model is used to determine the probabilities of a certain number of defective products given a low expected value of defects. A Poisson variable has a mean and a standard deviation . Thus the control limits given the standard number of defects c are:

LCL c c UCL c c If the LCL is less than 0 use 0 as the LCL.


22.5 Control Charts for Attributes: p Charts and c ChartsExample: Rope Rope used for climbing is rated to be able to hold a certain weight. The rope fails testing if it snaps when brought to a certain tension. Historically only 1.5% of the tested ropes snap. Suppose a sample of boxes containing 50 ropes are selected at random and tested. a) What is the standard deviation for the sample proportion from

a box of 50.

b) What are the upper and lower 3σ control limits.

c) How many ropes in a box would have to snap for the process to be out of control.

σ =0.017

LCL=0 UCL=.071

4 ropes would have to snap.


22.6 Philosophies of Quality Control

The three common ideas in quality control from statistical thinking are:• All work occurs in a system of interconnected processes.• Variation exists in all processes. • Understanding and reducing variation are keys to success.

Total quality management (TQM) and Six Sigma® are two business improvement approaches.

TQM extends quality control to encompass the total organization.

Six Sigma® focuses more on the identification and elimination of defects or special-cause variations in the business processes.


What Have We Learned?

Understand the principles of quality control.

• A process is in control if the aspects being followed stay within the control limits established for them.

• When a process drifts out of control, it is important to recognize the fact so that adjustments can be made promptly. But we hope to avoid making too many false alarms, so a balance must be found.



Use run charts to track individual observations.

• A level shift flags a sudden change. A trend is a more gradual change.

• The ability of a chart to detect shifts is described by its operating characteristic (OC) curve.

• The Western Electric handbook specified several rules for deciding when a process is out of control.



Use , R, and S charts to track a process by plotting means and ranges or standard deviations of small samples drawn from the process.

X

Understand the basic steps in creating an out-of-control action plan (OCAP).

• The control limits are often based on estimated standard deviations and means. • The S chart is more appropriate than the R chart when samples are moderately large.

1) Organize and prioritize possible causes.

2) Perform experiments to determine the cause.

3) Correct the cause.

4) Restart the monitoring process.



Use p charts and c charts to track processes that have categorical measurements.

• A p chart tracks proportions using control limits based on the standard deviation of a proportion chart.

• A c chart tracks the number of defective items in a process.

Understand the basic philosophies of quality control, such as the Total Quality Management (TQM) and Six Sigma®, and how they are applied to improve business performance and quality.

Copyright © 2012 Pearson Education. Chapter 22 Quality Control.

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