Control charts for $$ & R have been maintained on a process

and have exhibited statistical control. The sample size is

n$=4.$ the control chart parameters are as follows:

a$)$ Estimate the mean & SD of the process

b$)$ Estimate the natural tolerance limits of the process

c$)$ Suppose the process mean shifts to $630\mathrm{.}00$ while SD

remains constant. What is the probability of an OOC

signal occurring on the first sample following shift.

d$)$ If the USL$=640$ & LSL $=600,$ then calculate the $\%$

defective items produced when $($c$)$ happens.