Question: 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

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 - kσ, where k is a fixed constant.

a. Provided that k = 1.0 and n = 4, what is the mean number of subsamples required for X to fall below the lower control limit?

b. Provided that k = 1.0 and n = 8, what is the mean number of subsamples required for X to fall below the lower control limit?

c. Provided that k = 0.5 and n = 4, what is the mean number of subsamples required for X to fall below the lower control limit?

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