Any help at all will be appreciated with the following question.
Q.) 1. Samples of n = 4 items each are taken from a manufacturing process at regular intervals.
Suppose the process mean u = 200 and the standard deviation o = 10.
a. Find both the 3 sigma control limits and the probability limits (a = 0.002) to control the process mean.
b. Find the average run length and the standard deviation of the run length for both charts (in a.), in the following cases: i) process is in control, ii) process mean shifts to u1 = 209.
c. For both charts in a., what is the required sample size to detect this shift in the process mean on the first or second sample following the shift with the probability >= 0.9? For which of the two charts is the required sample size bigger and why?
d. Assume that the following rule is applied to the control chart with 3 sigma limits constructed in a. The process is declared out of control when either a point plots outside the 3 sigma limits or two consecutive points plot between the two and three sigma control limits on the same side of
the control chart. If the process mean shifts to u1 = 209, what is the probability that the shift will be detected on the first sample following the shift?
I attempted it and here are the answers I got:
a.) 3 sigma: UCL: 215 LCL: 185
Probability limits: 215.45 and 184.55
b.) 1 and 8.69
c.) n> 0.03 !
d.) not sure.
Please correct me where I'm wrong and guide me through this question. If some one can give me the correct answers, I'll get the right solution eventually hopefully.