Question

a) Suppose lots of lightbulbs are created from a continuous production line process, such that a binomial distribution is appropriate for analyzing the sampling plan: Suppose that the sampling plan is to select 3 fuses and test them, with a lot being accepted if none are defective. Criticize this sampling plan. In particular, find the probability of accepting a lot that is 30% defective.

b) For the above situation, suppose we include a RECTIFICATION step for rejected lots. Plot the OC and the AOQ curves for this situation.

Answer 1

Solution:

Given that

A binomial distribution is appropriate for analyzing the sampling plan: Suppose that the sampling plan is to select 3 fuses and test them, with a lot being accepted if none are defective

X~ Binomial (n,p)

Where n = 3 , p = 030 (probability of defective)

P(X) = ⁿC_x p^x (1-p)^n-x

P(Accepting a lot) = P( X =0)  

= ³C₀ 0.30⁰ 0.70³

= 0.343