Profit analysis of a two-unit priority standby system subject to degradation

Abstract

This paper deals with the profit analysis of a single-server two-unit (one priority and the other ordinary) cold standby system subject to degradation. Initially the priority (P) unit is operative and the ordinary (O) unit is kept as the cold standby. It is assumed that the P-unit passes through three operative stages (excellent, good and satisfactory) before it fails. The P-unit enters into the total failure (F) mode only from the satisfactory stage, and after repair it enters into the normal (N) mode with any of the ‘excellent’, ‘good’ and ‘satisfactory’ stages with probabilities p1, p2 and p3 , respectively. Identifying the system at suitable regenerative instants, the integral equations are set up and the explicit expressions of interest to system designers are obtained to carry out the profit function analysis. The results are also derived in a particular case.