A
aablet
Can anyone help explain below question on CQE primer chapter X ( Statistical applications) ?
10.9 A process is in control at X -bar bar = 100, R bar = 7.3 with n=4. If the process level shifts to 101.5, with the same R bar, what is the probability that next X bar point will fall outside the old control limit?
A. 0.016 B. 0.029 C. 0.122 D. 0.360
Correct answer is A but I couldn't figure out how to get this,
This is how I calculated :
Old control limits:
UCL = 100 + 0.729 x 7.3 = 105.32
LCL = 100 - 0.729 x 7.3 = 94.68
sigma = Rbar / D2 = 7.3/2.059 = 3.55
Zu = UCL- X bar / sigma = (105.32-101.5)/3.55 = 1.076
Zl = LCL - X bar / sigma = ( 94.68-101.5) /3.55 = -1.921
Based on standard normal table for Z value, Zu + Zl = 0.112 which is not any of the options.. ( close to C but not exactly)
I would really appreciate if anyone can point out where I did wrong.. Thank you!
10.9 A process is in control at X -bar bar = 100, R bar = 7.3 with n=4. If the process level shifts to 101.5, with the same R bar, what is the probability that next X bar point will fall outside the old control limit?
A. 0.016 B. 0.029 C. 0.122 D. 0.360
Correct answer is A but I couldn't figure out how to get this,
This is how I calculated :
Old control limits:
UCL = 100 + 0.729 x 7.3 = 105.32
LCL = 100 - 0.729 x 7.3 = 94.68
sigma = Rbar / D2 = 7.3/2.059 = 3.55
Zu = UCL- X bar / sigma = (105.32-101.5)/3.55 = 1.076
Zl = LCL - X bar / sigma = ( 94.68-101.5) /3.55 = -1.921
Based on standard normal table for Z value, Zu + Zl = 0.112 which is not any of the options.. ( close to C but not exactly)
I would really appreciate if anyone can point out where I did wrong.. Thank you!
