Selection of Minimum Sample Size Tightened-Normal-Tightened Sampling Inspection Schemes

Abstract

Acceptance sampling schemes are frequently used when finished products or materials are supplied by the producer for making decisions about individual lots or group of lots by examining sample information of such products or material. A sampling scheme is a set of plans that are usually specified by certain parameters such as sample size(s) and acceptance number(s). The tightened-normal-tightened (TNT) sampling scheme is a scheme that incorporates two single sampling plans called normal and tightened sampling plans, having the same sample size, but with different acceptance numbers along with the rules for switching between the plans. The determination of parameters of a sampling scheme for specified requirements on its operating characteristic curve providing protection to the producer and consumer is termed as designing of the scheme. This paper presents an iterative procedure for designing TNT schemes for two specified points on the operating characteristic curve, namely, acceptable quality level and limiting quality level associated with the producer's risk and the consumer's risk, respectively. Tables providing the parameters of the schemes for various values of acceptable quality level and limiting quality level under the conditions of binomial and Poisson distributions are developed and presented. The efficiency of such schemes over the schemes developed by the unity value approach is demonstrated with illustrations.