Accurately estimating the number of spares for a repairable system

Abstract

Accurately assessing how many spare components are needed to reliably operate a system is an important logistical and systems engineering problem: too many spares is a waste of resources; too few increases the likelihood that the system will fail. A standby system model with constant failure rates is easily developed and solved to provide a useful estimate of the number of spares required to achieve a given level of reliability over a given period of time. However, the model's generalization to more general hazard functions is problematic and gives misleading estimates. Here we examine the number of spares needed to achieve a given level of reliability using the General Sparing Formula for increasing, constant, and decreasing hazard functions. Although the model is simple to use, plausible, and intuitively appealing, its use is not recommended. Given the difficulty of analytically solving a more accurate model, simulation is recommended to determine the required level of sparing to achieve a given level of reliability over the time interval of interest.