The Quality Manager for Widgets,Inc.is concerned about the quality of the lot of several thousand widgets which his company produced this week and is now ready to ship.If he uses an acceptance sampling plan of n = 8 and c = 1,what will be the average outgoing quality (AOQ)for lots with 10% defectives?
A).0813
B).0962
C).1869
D).7318
E).8131

Question

Quizplus · Accepted Answer

AOQ can be calculated using the following formula:

AOQ = P(D)*P(A) + P(D)*P(R)*P(A) + P(D)*P(R)^2*P(A) + ...

where 
P(D) = proportion of defectives in the lot 
P(R) = proportion of good items remaining in the lot after each sampling 
P(A) = proportion of accepted lots

Given n = 8 and c = 1, we can use the single-sampling plan to find out the probability of accepting a lot with 10% defectives.

Using the binomial distribution, 
P(reject) = P(X >= 2) = 1 - P(X = 0) - P(X = 1) 
where P(X = k) = (n choose k)*p^k*q^(n-k)

P(reject) = 1 - P(X = 0) - P(X = 1) 
= 1 - (8 choose 0)*0.1^0*0.9^8 - (8 choose 1)*0.1^1*0.9^7 
= 0.2138

Therefore, P(accept) = 1 - P(reject) = 0.7862

Now, we can substitute these values into the formula for AOQ:

AOQ = P(D)*P(A) + P(D)*P(R)*P(A) + P(D)*P(R)^2*P(A) + ... 
= 0.1*0.7862 + 0.1*0.2138*0.7862 + 0.1*0.2138^2*0.7862 + ... 
= 0.0813

Therefore, the answer is A.