706 CHAPTER 14 Statistical Process Control ■ Two out of three consecutive points are beyond control limits that are 2 standard deviations away from the centerline. ■ Four out of five consecutive points are beyond control limits that are 1 standard deviation away from the centerline. For monitoring variation in a process, it might make more sense to use standard deviations, but range charts are quite effective for cases in which the size of the samples (or subgroups) is 10 or fewer. If the samples all have a size greater than 10, the use of an s chart is recommended instead of an R chart. (See Exercise 13.) The following is a summary of notation and the components of the R chart. Monitoring Process Variation: Control Chart for R Objective Construct a control chart for R (or an “R chart”) that can be used to determine whether the variation of process data is within statistical control. Requirements 1. The data are process data consisting of a sequence of samples all of the same size n. 2. The distribution of the process data is essentially normal. 3. The individual sample data values are independent. Notation n = size of each sample or subgroup R = mean of the sample ranges (the sum of the sample ranges divided by the number of samples) Graph Points plotted: sample ranges (each point represents the range for each subgroup) Centerline: R (the mean of the sample ranges) Upper control limit 1UCL2: D4R (where D4 is a constant found in Table 14-2) Lower control limit 1LCL2: D3 R (where D3 is a constant found in Table 14-2) KEY ELEMENTS DEFINITION An R chart (or range chart) is a plot of sample ranges instead of individual sample values. In addition to plotting the values of the ranges, we include a centerline located at R, which denotes the mean of all sample ranges, as well as another line for the lower control limit and a third line for the upper control limit. It is used to monitor the variation in a process. Control Chart for Monitoring Variation: The R Chart
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