Profit function analysis of system with mixture of warm and cold standby

Abstract

This paper deals with the profit function analysis of a single-server two-unit standby system with two modes of each unit normal (N) and total failure (F). Regarding the standby unit, an interconversion is made repeatedly after a random length of time from warm to cold and cold to warm. Upon failure of the operative unit, the standby unit, if it is warm, starts the operation instantaneously; otherwise the system goes down until the cold standby starts operation. System failure occurs when both units fail totally. Identifying the system at suitable regenerative instants, integral equations are set up and explicit expressions of interest to system designers are obtained to carry out the profit function analysis. The results of two particular cases are also derived.