A control chart for the number of nonconforming piston rings is maintained on a forging process with np = 16.0. A sample of size 100 is taken each day and analyzed.

(a) What is the probability that a shift in the process average to np = 20.0 will be detected on the first day following the shift? What is the probability that the shift will be detected by at least the end of the third day?
(b) Find the smallest sample size that will give a positive lower control limit.

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np = 16.0; n = 100; p = 16/100-016 UCL = np + 3Vnp(1-5) = 16 + 3(161-0. 16) = 27.00 LCL np-3np 1-p)-16-316(1-0.16) 5.00