Question: Suppose that a process is in control and an X chart is used with a sample size of 4 to monitor the process. Suddenly there

Suppose that a process is in control and an X chart is used with a sample size of 4 to monitor the process. Suddenly there is a mean shift of 1.5σ.

(a) If 3-sigma control limits are used on the X chart, what is the probability that this shift remains undetected for three consecutive samples?

(b) If 2-sigma control limits are in use on the X chart, what is the probability that this shift remains undetected for three consecutive samples?

(c) Compare your answers to parts (a) and (b) and explain why they differ. Also, which limits you would recommend using and why?

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