Variance reduction for a replacement process

Abstract

Prediction of replacement requirements for components (such as manufacturing equipment or engines) requires analysis of a replacement process. Unfortunately, unless component lives are exponentially distributed, that analysis requires transform methods, approxima tions, or simulation. Only simulation or approxima tion may be used for prediction of replacement re quirements when the replacement process is complicat ed, when it is subdivided into several periods of time, when replacements are not all new, or when several identical components that operate simulta neously are supplied from the same stock of spares.

This paper shows that in a simulation the use of complementary antithetic random variates in the generation of component lifetimes reduces the vari ance of the sample mean number of replacements in a multiple-component multiple-period replacement process in which the components may be either new or used. Reducing the variance results in more accurate predictions for fixed simulation runtimes or, alter natively, allows shorter runtimes (and hence lower costs) to achieve specified accuracy.