First Emptiness in the Spare Parts Problem for Reparable Components

This paper investigates the probability distribution of time to first emptiness in the spare parts problem for repairable components, where “r” spares are provided initially. Two cases are considered, namely, (i) when the component is constantly used, and (ii) when it is intermittently used. Expressions for the Laplace Transforms and the first two moments of the probability density functions of time to first emptiness are derived.