Two stage reliability tests for new series systems (Q1205472)

The paper regards the problem of 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 failures of the systems. The authors 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 procedure, tends in probability to the nominal OC-curve, derived for a single stage procedure assuming the shape parameter to be known. Also, the authors give the results of a simulation study of small first test size properties that confirm their limiting results, and that give some guidance on how to choose the number of systems for the first stage test.