14-1 Control Charts for Variation and Mean 705 We will assume that the population standard deviation s is not known as we now consider two of several different types of control charts: 1. R charts (or range charts) used to monitor variation 2. x charts used to monitor means When using control charts to monitor a process, it is common to consider R charts and x charts together, because a statistically unstable process may be the result of increasing variation, changing means, or both. Interpreting Control Charts When interpreting control charts, the following caution is important: CAUTION Upper and lower control limits of a control chart are based on the actual behavior of the process, not the desired behavior. Upper and lower control limits do not correspond to any process specifications that may have been decreed by the manufacturer. When investigating the quality of some process, typically two key questions need to be addressed: 1. Based on the current behavior of the process, can we conclude that the process is within statistical control? 2. Do the process goods or services meet design specifications? In this chapter we address the first question, but not the second; we are focusing on the behavior of the process with the objective of determining whether the process is within statistical control. Also, we should clearly understand the following specific criteria for determining whether a process is in statistical control (or is statistically stable). In this book we will use only the three out-of-control criteria listed above, but some companies use additional criteria such as these: ■ There are at least six consecutive points all increasing or all decreasing. ■ There are at least 14 consecutive points all alternating between up and down (such as up, down, up, down, and so on). DEFINITION A process is not statistically stable or is out of statistical control if one or more of the following out-of-control criteria are satisfied. 1. There is a pattern, trend, or cycle that is obviously not random. 2. There is at least one point above the upper control limit or at least one point below the lower control limit. 3. Run of 8 Rule: There are at least eight consecutive points all above or all below the centerline. (With a statistically stable process, there is a 0.5 probability that a point will be above or below the centerline, so it is very unlikely that eight consecutive points will all be above the centerline or all below it.) Out-of-Control-Criteria he n Don’t Tamper! Nashua Corp. had trouble with its paper-coating machine and considered spending a million dollars to replace it. The machine was working well with a stable process, but samples were taken every so often and, based on the results, unnecessary adjustments were made. These overadjustments, called tampering, caused shifts away from the distribution that had been good. The effect was an increase in defects. When statistician and quality expert W. Edwards Deming studied the process, he recommended that no adjustments be made unless warranted by a signal that the process had shifted or had become unstable. The company was better off with no adjustments than with the tampering that took place. continued
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