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lec10.2

lec10.2 - 227 Lecture 22 CHAPTER 10 STATISTICAL QUALITY...

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227 Lecture 22: CHAPTER 10: STATISTICAL QUALITY CONTROL Control Charts for Variables (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.) We will first take a look at continuous variables: for these data, an R chart or S chart is first used to control the variability in the process, and then an X chart is used to control the process mean. We assume for this section that the measurements follow an approximately normal distribution. Control charts are constructed by taking successive samples from the output of a process, making measurements on the sampled items, and then plotting summary statistics of these results. For each subgroup, a summary statistic is calculated and plotted (on the vertical axis) versus the subgroup number (on the horizontal axis). The statistics used to calculate the charts are x (subgroup mean), R (subgroup range) and S (subgroup standard deviation). The control limits and centerline of a control chart are based on the sampling distribution of the chart statistic. The smaller of the two control limits is called the lower control limit (LCL) and the larger one is called the upper control limit (UCL).

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228 Example plot: Plotted points that fall outside (ie. above the UCL or below the LCL) are interpreted as signals of possible special causes, whereas points within the control limits are usually (but not always) associated with common cause variation, that is, the absence of special causes. Example: U.S. companies commonly use 3-sigma limits to establish control limits. Some other countries (e.g. Great Britain) use control limits that are 3.09 sigmas from the chart’s centerline. a) Using the normal distribution, what is the probability that a single control chart point falls above the UCL in a 3-sigma control chart? b) Using the normal distribution, what is the probability that a single control chart point falls above the UCL in a 3.09-sigma control chart?
229 The difference between the control chart for the mean and the control chart for the variation is quite obvious: one chart is to track the process average and the latter is for the process of variation. Note: One should create the chart for process variation first because its centerline is a key ingredient in calculating the control limits for the chart that monitors the process average. The R chart is based on the sample range. Let’s illustrate with an example.

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lec10.2 - 227 Lecture 22 CHAPTER 10 STATISTICAL QUALITY...

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