Question

Q19. If the AQL=0.02, LQL=0.15, alpha=0.1, and beta=0.2 in an acceptance sampling plan for a company, What is the best approximate value of sample size n and acceptance number c

Answer 1

We have given that-

AQL = 0.02 , LQL = 0.15 , = 0.1 and = 0.2

Now we have to find out the best approximate value of sample size n and acceptance number c.

With c = 0 & at n = 5

At AQL = 0.02

This is the maximum n to meet the condition.

At LQL = 0.15

Unfortunately, this is greater than 0.2. Thus, c = 0 does not work.

(We could have done this step by noting that-

&

While for the condition, it must be greater than or equal to 10 for the beta condition.)

With c = 1,we can have up to n = 26 and meet the requirement that-

P (0 or 1 failures at AQL = 0.02 with n trials) 0.9

The smallest n such that -

P (0 or 1 failures with n trails at LQL = 0.15) = 0.2 is n=19.

In excel,

binom.dist(1,19,0.15,1) = 0.1985

Incidentally, P(0 or 1 failures at AQL = 0.02 with 19 trials) is binom.dist(1,19,0.02,1) = 0.945384 0.9

Thus, our smallest sample size meeting this conditions is n = 19 with c = 1.