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.

Transcribed Image Text:

Chart s Chart UCL= 18.08 LCL = 0 UCL = 710 Center line 700 Center line 7.979 LCL= 690