Question

A large lot of parts arrives at a factory. The quality engineer samples n parts out of the lot and tests them. If the number of parts that do not pass the test is strictly larger than c, then the lot is rejected. Assume the fraction of parts that are defective in the lot is equal to p. (a) Write an expression for the chance that the lot is accepted. (b) Assume n = 100 and c = 3. For values of p = 0.01,0.02,···,0.15, find the chance that the lot is accepted. (c) Draw a graph where the “x” axis (actually p axis) gives the values of p and the “y” axis, the probability that the lot is accepted.

Answer 1

Hee total sampled parts = n and if the number of parts that do not pass the test is larger than c, lot is rejected,

Here the disrribution is binomial distribution with n and probability of success = p

so here

Pr(Lot is accepted) = BINOMDIST(c, n, p, true)

(b) Here n= 100 and c = 3

now for values p = 0.01, 0.02, 0.03,,......0..15

p	P(lot is accepted)
0.01	0.9816
0.02	0.8590
0.03	0.6472
0.04	0.4295
0.05	0.2578
0.06	0.1430
0.07	0.0744
0.08	0.0367
0.09	0.0173
0.1	0.0078
0.11	0.0034
0.12	0.0015
0.13	0.0006
0.14	0.0002
0.15	0.0001