Analysis of two stage sampling plan with imperfect inspection

Abstract

Acceptance sampling plans used in a typical quality control process, are developed to provide optimal sample size(s) and acceptance (rejection) criterion. In order to apply a sampling plan, a knowledge of acceptable quality level (AQL), a lot tolerance percent defective (LTPD), and the specification of two types of errors (type I and type II) are required. The traditional methods assume that quality control inspectors, inspection tools, and computation processes are free from any errors under normal conditions. However, it has been shown that in practice inspectors, inspection tools as well as computation processes are all erroneous. These errors will have significant impact on sample size(s), decision criterion, average outgoing quality (AOQ), and the operating characteristics curve (OC Curve). The impact of imperfect inspection on AOQ, sample size(s), and OC curves for a two stage sampling plan are presented in this paper. In a two stage sampling plan, the decision to reject or accept a lot is made through two tandem stages of the inspection process. The first stage inspection is performed at the low level component, where m components constitute a single item. An acceptance decision for a single item is made based on the observed number of defects (non-conformities), while an acceptance decision of a given lot depends on the number of defective (non-conforming) items. A simulation program has been developed to investigate the sensitivity of AOQ and OC curves when one or both types of errors (type I and type II) deviate from their specified levels. The computational experiments show that inspection errors cause the discrepancies between the computed values and the specified values. The analysis of simulation results leads us to conclude that, when inspection errors are present, the traditional sampling plans without inclusion of inspection errors are misleading and incorrect.