1. Copyright © Cengage Learning. All rights reserved. 16 Quality Control Methods

2. Copyright © Cengage Learning. All rights reserved. 16.1 General Comments on Control Charts

3. 3 A central message throughout this book has been the pervasiveness of naturally occurring variation associated with any characteristic or attribute of different individuals or objects. In a manufacturing context, no matter how carefully machines are calibrated, environmental factors are controlled, materials and other inputs are monitored, and workers are trained, diameter will vary from bolt to bolt, some plastic sheets will be stronger than others, some circuit boards will be defective whereas others are not, and so on.

4. 4 General Comments on Control Charts We might think of such natural random variation as uncontrollable background noise. There are, however, other sources of variation that may have a pernicious impact on the quality of items produced by some process. Such variation may be attributable to contaminated material, incorrect machine settings, unusual tool wear, and the like. These sources of variation have been termed assignable causes in the quality control literature.

5. 5 General Comments on Control Charts Control charts provide a mechanism for recognizing situations where assignable causes may be adversely affecting product quality. Once a chart indicates an out-of-control situation, an investigation can be launched to identify causes and take corrective action. A basic element of control charting is that samples have been selected from the process of interest at a sequence of time points. Depending on the aspect of the process under investigation, some statistic, such as the sample mean or sample proportion of defective items, is chosen.

6. 6 General Comments on Control Charts The value of this statistic is then calculated for each sample in turn. A traditional control chart then results from plotting these calculated values over time, as illustrated in Figure 16.1. Figure 16.1 A prototypical control chart

7. 7 General Comments on Control Charts Notice that in addition to the plotted points themselves, the chart has a center line and two control limits. The basis for the choice of a center line is sometimes a target value or design specification, for example, a desired value of the bearing diameter. In other cases, the height of the center line is estimated from the data. If the points on the chart all lie between the two control limits, the process is deemed to be in control. That is, the process is believed to be operating in a stable fashion reflecting only natural random variation.

8. 8 General Comments on Control Charts An out-of-control “signal” occurs whenever a plotted point falls outside the limits. This is assumed to be attributable to some assignable cause, and a search for such causes commences. The limits are designed so that an in-control process generates very few false alarms, whereas a process not in control quickly gives rise to a point outside the limits. There is a strong analogy between the logic of control charting and our previous work in hypothesis testing. The null hypothesis here is that the process is in control.

9. 9 General Comments on Control Charts When an in-control process yields a point outside the control limits (an out-of-control signal), a type I error has occurred. On the other hand, a type II error results when an out-of- control process produces a point inside the control limits. Appropriate choice of sample size and control limits (the latter corresponding to specifying a rejection region in hypothesis testing) will make the associated error probabilities suitably small.

10. 10 General Comments on Control Charts We emphasize that “in control” is not synonymous with “meets design specifications or tolerance.” The extent of natural variation may be such that the percentage of items not conforming to specification is much higher than can be tolerated. In such cases, a major restructuring of the process will be necessary to improve process capability. An in-control process is simply one whose behavior with respect to variation is stable over time, showing no indications of unusual extraneous causes.

11. 11 General Comments on Control Charts Software for control charting is now widely available. The journal Quality Progress contains many advertisements for statistical quality control computer packages. In addition, SAS and Minitab, among other general-purpose packages, have attractive quality control capabilities.