The following
x
and
S
charts based on
n  4
have shown statistical control:

Limits
x
Chart
S
Chart
UCL 710 18.08
Central line 700 7.979
LCL 690 0

a) Estimate the process parameters.
b) If the specifications are at
705 15 
, and the process output is normally distributed,

estimate the fraction nonconforming.
c) For the
x
chart, find the probability of a type I error, assuming

is constant.

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

subsequent sample.
e) Find the average run length for the shift in part (d).