Question

A control chart for the fraction nonconforming is tobe established using a center line of p = 0.10. Whatsample size is required if we wish to detect a shift inthe process fraction nonconforming to 0.20 withprobability 0.50?​

Answer 1

Answer:

A control chart with 3-sigma limits is to be established for the fraction nonconforming using a centre line of p= 0.1.

a) If the process mean shifts to p1 = 0.2, what sample size is required if we wish to detect this shift on the next sample following the shift with probability at least 0.5, and have the lower control limit positive? Use Poisson tables if normal approximation is not good.

b) For the shift to p1, determine the minimum sample size for the control chart with 3-sigma limits for which the average run length is less than or equal to 5.