Question

Question 5

Suppose a multiple-sampling plan shown in the table below:

Cumulative Sample Size	Acceptance Number	Rejection Number
25	0	2
50	1	3
75	3	5
100	4	7

Describe the circumstances in which the lot will be inspected to the third stage but will not proceed to the fourth stage.

Answer 1

In order to go to next stage, we need 1 defect (any other number results in acceptance or rejection). After the next sample considered, we want that there should be 2 defects in the combined sample to proceed to the third stage. Hence the new sample should have exactly 1 defect. Now we are in stage 3 and have 2 defects in total. The third sample results in proceeding to the fourth stage if the combined sample has 4 defects, i.e the third new sample has 2 new defects. Any other number of defect would result in acceptance or rejection at third stage and hence won't proceed to the fourth stage. Thus the circumstances are:

Exactly 1 defect in the first sample

Exactly 1 defect in the second new sample

The number of defects in the third new sample is different from 2.