Single sampling plans for inspection by variables under a variance component situation

International Standard ISO 3951 (1989), being based on the Military Standard MIL-STD-414 (1957), specifies an acceptance sampling system of single sampling plans for inspection by variables, under the assumptions that X, the quality characteristic of items in a lot, is (approximately) normally distributed with unknown mean and known or unknown variance and that the measurement error in measuring X is negligible. The acceptance sampling procedure determines the acceptability of a lot from an estimate of the fraction of nonconformimg items in the lot, i.e. the fraction of items with x less than or equal to UL where UL is an upper specification limit (or x greater than or equal to LL where LL is a lower specification limit). In this paper the acceptance procedure is extended to the case where the quality characteristic X is a performance characteristic of the items, and these items can be used repeatedly so that X takes a value for each repetition of use. In this situation the variance of X consists of two components, one describing the variation of X under repeated use of an item, the other one the variation between the mean values of the performance characteristic of different items. The paper considers the cases of known and of unknown components of variance, and gives an example.