Question 6 (15 points) A normally distributed quality characteristic, which has mean ,u and standard deviation 0', is monitored with a moving average (MA) control chart. The monitored moving average statistic at r: + rm + EH + EH 4 average of 4 individual observations (11 : 4). time [is dened as ill/If : . For each sample, if is calculated based on the (a) Write out the 3-sign1a Upper control limit using at and afor this MA chart when I> 3 (2 points) (b) Suppose at time t = 10, the process mean shifts from ,u to In + J and the process standard deviation is changes from a" to 20' and then keeps these changes afterwards. Write out the mean and variance of M12, (8 points) ((3) Calculate the probability of M12 plotted above of the Upper 3-sigma control limit obtained in (a) (5 points)