The inspection process rejects lots with high fraction defectives. After rejection either you may stop, or you may continue the inspection of all the items in the rejected lot and all defective items are replaced with good items. Such a policy is known as Rectifying Inspection.
In rectifying inspection, all outgoing lots consist of N itellis either accepted ones or rejected ones. Suppose? a lot has inconung fraction defectivef. If it is accepted ( N - n) items remain uninspected. We. therefore, expect,f (N - n) defectives in the accepted lots (;lssunling that the defectives found in the sample are replaced with good ones). In contrast, if it is rejected and hence (100 percent rectified and inspected) there are no defectives. Thus if P,, is the probability that the sanlpling plan will accept the lot,
Outgoing fraction defective =(Pa) (fl (N - n) + (1 - P,,) (0)/NIn rectifying inspection, all outgoing lots consist of N itellis either accepted ones or rejected ones. Suppose? a lot has inconung fraction defectivef. If it is accepted ( N - n) items remain uninspected. We. therefore, expect,f (N - n) defectives in the accepted lots (;lssunling that the defectives found in the sample are replaced with good ones). In contrast, if it is rejected and hence (100 percent rectified and inspected) there are no defectives. Thus if P,, is the probability that the sanlpling plan will accept the lot,
(Pa)( f) ( N N - n ) ) =(Pa)(f)
A plot of ongoing fraction defective against incoming fraction defective ( f ) is generally called the Average (lutgoing Quality (AOQ) curve. Figure 9.7 shows the curve tor silrnpfing plan B ( n = 150, c = 6) o f the earlier examples. This curve has a surprisiilg property th;rl. as,f increases, there conles a point at whiih the outgoing fraction defective actually begins to improve. The reason being that the sanlpling plan rejects most bad lots and they are rectified through 100 percent inspection.
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| AOQ Curve for Sampling Plan B (N = 10,000) |
The most critical incoming fraction defective gives the worst outgoing quallty ()n the average, the value of that critlcal of is not lmportant but the corresponding outgolng tractlo11 defective generally know as Average Outgoing Quality Limit (AOQL) IS extremely useful. No matter what the incoming fraction defective is, the long-run average outgoing fraction defective wlll not be worse than AOQL.
You do not have to deterline AOQL by plotting the AOQ. One can use the following AOQL factor given Table. To get the AOQL simply use the formula
AOQL=AOQL factor[1/n-1/N]
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| AOQL Factor |
Convince youself that you understand the mechanism of determining AOQL by doing tlle following activity.
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