Setting test limits under prescribed consumer loss

Abstract

In inspection of manufactured parts inaccuracies of the measurement process compel to use test limits which are more strict than the given specification limits. To avoid violation of the prescribed bound γ on the consumer loss, in practice overly conservative informal approaches are used leading to a loss of yield. In this paper approximations are derived for which γ is realized with high precision. The expressions involved are sufficiently simple and explicit to allow extension to the more realistic case where the parameters of the underlying distributions need to be estimated. Various criteria are presented to measure the closeness of the resulting stochastic consumer losses to γ. Some attention is devoted to the sampling schemes involved.