A control chart with 3-sigma limits is to be established for the fraction nonconformingusing 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 detectthis shift on the next sample following the shift with probability at least 0.5, andhave the lower control limit positive? Use Poisson tables if normal approximation isnot good.

b) For the shift to ??1, determine the minimum sample size for the control chart with3-sigma limits for which the average run length is less than or equal to 5.