Consider a situation where a given process goes out of control but the relevant control charts do not indicate so. Assume that the process variation remains constant but the mean shifts from μ to μ + kv­, where k is a fixed constant.

a. Provided that k = 1.5 and n = 5, what is the mean number of subsamples required for X to rise above the upper control limit?

b. Provided that k = 1.5 and n = 9, what is the mean number of subsamples required for X to rise above the upper control limit?

c. Provided that k = 2.0 and n = 5, what is the mean number of subsamples required for X to rise above the upper control limit?