lec10.3 - 238 Lecture 23: CHAPTER 10: STATISTICAL QUALITY...

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238 Lecture 23: CHAPTER 10: STATISTICAL QUALITY CONTROL Control Charts for Variables – Cont’d (Section 10.2, page 757) Recall: Control charts used for continuous variables are called variables control charts . ( X chart, R chart, and the S chart.) Control charts used for binary or count variables are called attribute control charts. ( p chart for binary variables, c chart for count variables.) Last class, we constructed the R chart (sample range) and X chart (sample mean). Here was our summary: Summary Control Chart Performance A point will occasionally plot outside the 3 limits even when the process is in control. This is called a false alarm . It can also happen The steps in using the R chart and X chart are Choose rational subgroups. Compute the R chart. Determine the special causes for any out-of-control points. Re-compute the R chart, omitting samples that resulted in out-of-control points. Once the R chart indicates a state of control, compute the X chart, omitting samples that resulted in out-of-control points on the R chart. If the X chart indicates that the process is not in control, identify and correct any special causes. Continue to monitor X and R.
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239 that a process that is not in control may not exhibit any points outside the control limits, especially if it is not observed for a long enough time. This is called a failure to detect. We obviously want these errors to occur as infrequently as possible, so we have a means of calculating how frequent these errors occur with a quantity called the average run length (ARL) . Summary Example: A process has mean 3 and standard deviation 1 . Samples of size n=4 are taken. If a special cause shifts the process mean to a value of 3.5, find the ARL. The average run length (ARL) is the number of samples that will be observed, on the average, before a point plots outside the control limits. If p is the probability that any given point plots outside the control limits, then p ARL 1
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240 The S chart The S chart is an alternative to the R chart. Both the S chart and R chart are used to control the variability in a process.
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241
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lec10.3 - 238 Lecture 23: CHAPTER 10: STATISTICAL QUALITY...

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