An X chart uses samples of size 1. The center line is at

Chapter 15, Problem 59E

(choose chapter or problem)

Problem 59E

An X chart uses samples of size 1. The center line is at 100, and the upper and lower 3-sigma limits are at 112 and 88, respectively.

(a) What is the process σ ?

(b) Suppose that the process mean shifts to 96. Find the probability that this shift is detected on the next sample.

(c) Find the ARL to detect the shift in part (b).

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