A Discussion of All-or-None Inspection Policies

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Abstract
An optimal inspection policy will inspect either every item produced or no item when (a) product characteristics are well modeled as iid and (b) overall inspection cost is a sum of individually and identically determined costs for each of the items encountered. This result is widlsly known for special cases such as iid Bernoulli product characteristics with single-sample lot acceptance-sampling plans. We show that the result holds true much more generally and over a much wider class of inspection plans, even when independent inspection errors are possible. We examine the assumptions that lead to all-or-none optimality and discuss the practil:al meaning of all-or-none results to practitioners. Examples are given to demonstrate that both “other” cost structures and “informative” inspections (i.e., lack of independence) can lead to optimal policies that are not of the all-or-none type.

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