The Distribution of Observed Defectives in Attribute Acceptance Sampling Plans Under Inspection Error

Abstract

The Type B Operating Characteristic curve in attributes acceptance sampling is simply the probability of lot acceptance versus process fraction defective. The binomial mass function is appropriate for assessing this acceptance probability. Articles on inspection error in attributes acceptance sampling frequently assume the marginal distribution of the number of observed defectives in the sample is binomial with the true fraction defective replaced by the apparent fraction defective. This assumption, however, has been questioned and it is the object of this paper to show explicitly that the existing literature is quite correct. Following this development, additional results are presented which may be useful to others performing research in this area.