Question

An office supply company ordered a lot of 400 printers. When the lot arrives the
company inspector will randomly inspect 12 printers. If more than three printers in the
sample are non-conforming, the lot will be rejected. If fewer than two printers are nonconforming, the lot will be accepted. Otherwise, a second sample of size 8 will be
taken. Suppose the inspector finds two non-conforming printers in the first sample and
two in the second sample. Also AQL and LTPD are 0.05 and 0.10 respectively. Let
incoming quality be 4%.
(i) What is the probability of accepting the lot at the first sample?
(ii) What is the probability of accepting the lot at the second sample? 

08 Sep 2023
Answer :
Word Count : 676

To find the probability of accepting the lot at the first and second samples, we can use the concept of acceptance sampling based on the given Acceptable Quality Level (AQL) and Lot Tolerance Percent Defective (LTPD).

Let's calculate the probabilities step by step:

(i) Probability of Accepting the Lot at the First Sample:

In this case, the company inspector randomly inspects 12 printers. If more than three printers in the sample are non-conforming, the lot will be rejected. If fewer than two printers are non-conforming, the lot will be accepted. So, we need to calculate the probability of having 0, 1, or 2 non-conforming printers in the first sample.

We can use the binomial probability formula for this:

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Related Questions

At a call centre, callers have to wait till an operator is ready to take their call. To monitor this process, 5 calls were recorded every hour for the 8-hour working day. The data below shows the waiting time in seconds:

Time Sample Number
1 2 3 4 5
9 a.m 8 9 15 4 11
10 7 10 7 6 8
11 11 12 10 9 10
12 12 8 6 9 12
1 p.m. 11 10 6 14 11
2 7 7 10 4 11
3 10 7 4 10 10
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Time                                     Sample Number

 

9 a.m
10
11
12
1 p.m.
2
3
4

     1 2 3 4 5
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11
12
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10
8		 9
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7
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11		 15
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6
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10
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6
9
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