Sequential attributes sampling: Inspection error effects and compensation

Abstract

Sequential sampling represents the logical limit in lot-by-lot multiple acceptance sampling. Sequential plans are generally developed in order to fit a desired operating characteristic curve. The basic premise is that items are observed one at a time and classified as good or bad. Following each sampled item, and based upon the current cumulative results a decision is made to accept the lot, reject the lot, or sample another item from the lot. Inspection error severely distorts the operating characteristic performance measure of a sequential sampling plan. Yet, we continue to design sequential plans under the assumption of perfect assessment, even though the fact that inspection errors are common is well documented. This paper examines and illustrates the effects of error on the sequential sampling OC curve. These effects are developed mathematically beginning with Wald's formulation of the sequential probability ratio. The results are computerized and a typical sequential plan is analyzed under several type 1 and type 2 inspection error pairs to determine the resulting OC curves. Additionally, a method of sampling plan design is developed which compensates for the effects of known inspection error. That is, it provides the complete sampling plan which, iffollowed in an error prone environment, yields the OC curve actually desired. This compensating method of sampling plan design has also been computerized. A copy of the entire program appears in the Appendix at the end of the paper.