A sample size of n = 5 items is taken from a manufacturing process. A quality characteristic is measured, and x-bar and R values are calculated for each sample. The quality characteristic is normally distributed. After 30 samples, we have i=130xi=1500 and i=130Ri=60

a)Compute central lines and 3-sigma trial control limits for the x-bar and R charts.

b)Assume both charts exhibit in control, the estimated process mean, and standard deviation.

c)Suppose mean shifted by 2. If we want the probability of detecting this shift at the first sample equals to 0.9, what control limits do you recommend for the x-bar chart? (Hint: The upper and lower control limits are to be the same distance from the Center Line; and assume the mean shift is large and make appropriate approximations when calculating the type two error if necessary)