Question

A manufacturer of men’s jeans purchases zippers in lots of 500. The jeans
manufacturer uses single-sample acceptance sampling with a sample size of 10 to
determine whether to accept the lot. The manufacturer uses c = 2 as the acceptance
number. Suppose 3% nonconforming zippers are acceptable to the manufacturer and
8% nonconforming zippers are not acceptable. Find
(i) Probability of accepting a lot of incoming quality 0.04.
(ii) Average outing quality (AOQ), if the rejected lots are screened and all defective
zippers are replaced by non-defectives.
(iii) Average total inspection (ATI). 

08 Sep 2023
Answer :
Word Count : 672

To find the probability of accepting a lot with an incoming quality of 4% (0.04), the average outgoing quality (AOQ), and the average total inspection (ATI) for this acceptance sampling plan, we can use the single-sample acceptance sampling plan with the given parameters:

- Lot size (N): 500 zippers
- Sample size (n): 10 zippers
- Acceptance number (c): 2 nonconforming zippers

(i) Probability of Accepting a Lot with Incoming Quality 0.04 (P(Accept)):

In this case, we want to find the probability of accepting the lot when the incoming quality is 4%. We can use the binomial probability formula:

\small \[ P(X = k) = \binom{n}{k} \cdot p^k \cdot (1 - p)^{n - k} \]

Where:


- \small \(P(X = k)\)  is the probability of having exactly k nonconforming zippers in the sample.


- \small \(\binom{n}{k}\)  is the binomial coefficient, which can be calculated as \\small (\frac{n!}{k!(n-k)!}\).


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