Two stage reliability tests for new series systems

Abstract

We want to do acceptance testing of newly minted series systems, all of whose component failure distributions are identical Gamma distributions with unknown shape and scale parameters. The criterion is the equilibrium mean time between failure (MTBF) of the systems. We derive a two stage acceptance testing procedure, and show that as the number of systems in the first stage test tends to infinity, the OC-Curve, derived from this two stage testing procedure, tends in probability to the nominal OC-Curve, derived for a single stage procedure assuming the shape parameter to be known. Also, we have performed a simulation study of small first stage test size properties that confirms our limiting results and gives some guidance on how to choose the number of systems for the first stage test.