X bar and R charts with N = 9 are used to monitor a normally distributed quality characteristic. The control chart parameters are, X bar Chart UCL=814 Center line = 800

LCL = 786

R Chart

UCL = 61.23

CL = 29.70

LCL = 0

a) Both charts exhibit control. What is the probability that a shift in the process mean to 790 will be detected on the first sample following the shift?

(b) For the x chart in (a), find the out-of-control Average Run Length.