A process that is in statistical control has an estimated mean value of 180 and an estimated

Question:

A process that is in statistical control has an estimated mean value of 180 and an estimated standard deviation of 26.

a. Based on subgroups of size 4, what are the control limits for the X and R charts?

b. Suppose that a shift in the mean occurs so that the new value of the mean is 162.

What is the probability that the shift is detected in the first subgroup after the shift occurs?

c. On average, how many subgroups would need to be sampled after the shift occurred before it was detected?

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