# Question: At regular intervals during the last three work shifts technicians

At regular intervals during the last three work shifts, technicians at the Willard Bolt Company have taken a total of 40 samples, each with n 55 bolts. The measurement taken is the bolt diameter, in inches, and the data are listed in file CDB20.

1. Using only the first 20 samples, construct 3-sigma control charts for the mean and range. For each chart, plot all 20 sample means or ranges. Using the mean and range charts together, does the process appear to have been in control when each of these samples was taken? a. If the process was in control for samples 1–20, use the upper and lower control limits from these samples in a second set of control charts that includes all 40 samples. On this basis, was the process in control during the collection of samples 21–40? Use the mean chart and the range chart together in evaluating process control. b. If the process was not in control for each of samples 1–20, assume that an assignable cause has been identified for those that were outside the limits. Use the remaining samples as the basis for UCL and LCL values with which to evaluate samples 21–40.

2. Considering all 40 samples, construct 3-sigma control charts for the mean and range. For each chart, plot all 40 sample means or ranges. Using the mean and range charts together, does the process appear to have been in control when each of these samples was taken?

In general, compared to the charts constructed in part 1, do the sample means and ranges for samples 21–40 fit more easily or less easily into the control limits? Would you expect that they should fit more easily or less easily into the control limits? Why?

3. If your computer statistical package provides additional tests for determining whether a process is in control, carry these out for the entire series of 40 sample means and sample ranges, then interpret the results. Did the computer identify any “out of control” clues that were not caught in part 2?

1. Using only the first 20 samples, construct 3-sigma control charts for the mean and range. For each chart, plot all 20 sample means or ranges. Using the mean and range charts together, does the process appear to have been in control when each of these samples was taken? a. If the process was in control for samples 1–20, use the upper and lower control limits from these samples in a second set of control charts that includes all 40 samples. On this basis, was the process in control during the collection of samples 21–40? Use the mean chart and the range chart together in evaluating process control. b. If the process was not in control for each of samples 1–20, assume that an assignable cause has been identified for those that were outside the limits. Use the remaining samples as the basis for UCL and LCL values with which to evaluate samples 21–40.

2. Considering all 40 samples, construct 3-sigma control charts for the mean and range. For each chart, plot all 40 sample means or ranges. Using the mean and range charts together, does the process appear to have been in control when each of these samples was taken?

In general, compared to the charts constructed in part 1, do the sample means and ranges for samples 21–40 fit more easily or less easily into the control limits? Would you expect that they should fit more easily or less easily into the control limits? Why?

3. If your computer statistical package provides additional tests for determining whether a process is in control, carry these out for the entire series of 40 sample means and sample ranges, then interpret the results. Did the computer identify any “out of control” clues that were not caught in part 2?

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