TypeA operating characteristic functions of defects sampling plans

Abstract

Investigations on acceptance sampling have attached rather few attention to defects inspection. As to sampling models and the corresponding operating characteristic (OC) function of single defects sampling plans, generally only typeB (process model) has been considered: sampling from a production process where the OC is conceived as a function of sample sizen, acceptance numberc, and process average number of defects per itemλ. For modern quality control, both the steadily increasing complexity of products and the need for differentiated cost calculation involve a clear demand for defects sampling in its practically most relevant form: lot-by-lot single sampling plans, where the OC (typeA, lot OC) is considered as a function of lot sizeN, sample sizen, acceptance numberc, number of defects in the lotK. The present paper develops two lot OC functions from suitable assumptions on the arrangements of the total numberK of defects over theN elements of the lot. Limiting theorems on these OC functions are used to justify to some extent the customary assumption that the Poisson process OC can serve as an approximation for typeA. The dependence of the OC functions on sample sizen, acceptance numberc, total number of defects in the lotK is described by simple formulae.