Samples f n= 5 units are taken from a process every hour. The x and R values for a particular quality characteristic are determined. After 25 sample have been collected, we calculate x =20 and R = 4.56.
(a) What are the three-sigma control limits for the x and R?
(b) Both charts exhibit control. Estimate the process standard deviation.
(c) Assume that the process output is normally distributed. If he specifications are 19  5, what are your conclusions regarding the process capability?
(d) If the process mean shifts to 24, what is the probability of not detecting this shift on the first subsequent sample?