An economic basis with inspector accuracy considerations for design of a multi-level continuous sampling plan

Although multi-level continuous sampling plans have been in use since 1943, no economic basis for choice of the parameters of a multi-level continuous sampling plan has been developed. Furthermore, recent research has shown that the conventional basis for design of these plans, specification of an Average Outgoing Quality Limit (AOQL), is often invalid if the inspector is capable of committing errors. The objective of this dissertation is establishment of an economic basis with inspector accuracy considerations for design of a multi-level continuous sampling plan. The effects of both Type A inspector errors, which occur when the inspector rejects a non-defective item, and Type B inspector errors, which occur when the inspector accepts a defective item, are incorporated to determine the probability of an inspector accepting or rejecting an item of product. The operation of the multi-level continuous sampling plan is modeled as a Markov process. The steady state probabilities determined from the Markov transition matrix are used in calculation of the Average Fraction Inspected (AFI). A method for calculation of AFI is presented in this dissertation which is computationally more efficient than any method presented in the literature. A computer program utilizing this computational procedure was used to generate tables of values of AFI for specified system parameters.