(a) and (b)

Q3: It is known that the process mean (0) is 1.5 microns and the process standard deviation (0) is 0.15 . It is known that 9 test units are taken for examination (sample size n=9 ) every half hour ( h=0.5 hour). The engineers use a control chart for monitoring process mean with center line =0 and 0Ln0 as the upper and lower control limits. They think it is important to detect small shift in process mean early. Thus, they hope the control chart used can give out-of-control signal sooner (average time to signal, ATS 1 =2 hour) when the process mean changes from 1.5 microns to 1.65 microns. (a) Based on the previous statement, The engineers wish the contril chart used has ATS1=2 hour. That means the ARL1= in this case. (3pts) (b) Given your answer in (a), what is the minimum probability that the control chart used would give an out-of-control signal with the ARL1 in (a) when the process mean changes from 1.5 microns to 1.65 microns. The probability should be greater than so that (a) is true. (3pts)