(Answered) Question samples of n 5 units are taken from a process

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Question: Samples of n = 5 units are taken from a process every hour. The x‾ and R values for a particular quality characteristic are determined. After 25 samples have been collected, we calculate x‾= 20 and R‾= 4.56.

a) What are the three-sigma control limits for x‾ and R?

b) Both charts exhibit control. Estimate the process standard deviation.

c) Assume that the process output is normally distributed. If the specifications are 19 ± 5, what are your conclusions regarding the process capability?

d) If the process mean shifts to 24, what is the probability of not detecting this shift on the first subsequent sample?

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