# Question: The following x and s charts based on n

The following x and s charts based on n = 4 have shown statistical control:

(a) Estimate the process parameters µ and σ.

(b) If the specifications are at 705 ± 15, and the process output is normally distributed, estimate the fraction nonconforming.

(c) For the chart, find the probability of a type I error, assuming σ is constant. x

(d) Suppose the process mean shifts to 693 and the standard deviation simultaneously shifts to 12. Find the probability of detecting this shift on the x chart on the first subsequent sample.

(e) For the shift of part (d), find the average run length.

(a) Estimate the process parameters µ and σ.

(b) If the specifications are at 705 ± 15, and the process output is normally distributed, estimate the fraction nonconforming.

(c) For the chart, find the probability of a type I error, assuming σ is constant. x

(d) Suppose the process mean shifts to 693 and the standard deviation simultaneously shifts to 12. Find the probability of detecting this shift on the x chart on the first subsequent sample.

(e) For the shift of part (d), find the average run length.

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