Optimum lot inspection based on lognormal reliability tests

Abstract

Improved lognormal reliability test plans are proposed for lot sentencing. A mixed integer nonlinear programming problem is stated and solved in order to find the duration of the reliability test based on lognormal failure count data that minimises the inspection effort. The maximum number of failures tolerated by the decision maker and the necessary number of devices to be tested are also determined. The producer and consumer risks are limited in advanced, whereas the cost function is essentially a linear combination of the required sample size and test time. The minimum-cost test for device reliability demonstration provides the best criterion to decide the acceptability of manufacturing processes and submitted lots. A quick and effective iterative algorithm is suggested to obtain the optimal reliability demonstration test plan. The developed methodology is applied to the production of microelectronic chips, semiconductor lasers and ball bearings for illustrative purposes.