1. A process is monitored for flaws by taking a sample of size 50 each hour and counting the total number of flaws in the sample items. The total number of flaws over the last 30 samples is 658.
a. Compute the center line and upper and lower 3σ control limits.
b. The tenth sample had three flaws. Was the process out of control at that time? Explain.
2. To set up a p chart to monitor a process that produces computer chips, samples of 500 chips are taken daily, and the number of defective chips in each sample isand R.
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The means are X s = 0.058.
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= 5.095, R
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= 0.110, and
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counted. The numbers of defective chips for each of
the last 25 days are as follows:
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a.
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Compute the 3σ limits for the R chart. Is the vari-
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25 22 14 24 18 16 20 27 19 20 22 7 24 26
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ance out of control at any point? If so, delete the
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11 14 18 29 21 32 29 34 34 30 24
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samples that are out of control and recompute X
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b. Compute the 3σ limits for the X chart. On the basis of the 3σ limits, is the process mean in control? If not, at what point is it first detected to be out of control?
c. On the basis of the Western Electric rules, is the process mean in control? If not, when is it first detected to be out of control?
a. Compute the upper and lower 3σ limits for a p chart.
b. At which sample is the process first detected to be out of control?
c. Suppose that the special cause that resulted in the out-of-control condition is determined. Should this cause be remedied? Explain.