Question: Consider the control chart for individuals with 3-sigma limits. (a) Suppose that a shift in the process mean of magnitude occurs. Verify that the

Consider the control chart for individuals with 3-sigma limits.

(a) Suppose that a shift in the process mean of magnitude σ occurs. Verify that the ARL for detecting the shift is ARL = 43.9.

(b) Find the ARL for detecting a shift of magnitude 2σ in the process mean.

(c) Find the ARL for detecting a shift of magnitude 3σ in the process mean.

(d) Compare your responses to parts (a), (b), and (c) and explain why the ARL for detection is decreasing as the magnitude of the shift increases.

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