Reliability modelling of a parallel-cold standby system with proviso of repair priority

Abstract

Here, reliability modelling of a parallel cold standby system of four units has been done with the provision of priority to repair. Initially, the system has two operative units in parallel mode (called phase-I units) and the other two units are taken as spare in the cold standby (called phase-II units). The phase-I units (main units) are assumed as more efficient than that of the phase-II units (duplicate units). The units in phase-I and phase-II are non-identical but they are identical within the phases. The units in phase-II work simultaneously at the failure of units of phase-I. The priority to repair the units of phase-II has been given over the repair of the units of the phase-I. However, no priority is given for operation of the units of both phases. The repair activities are handled by a single server who attends the system immediately when required. The failure rate of the units follows negative exponential distribution while the distribution for repair time of the phase-I and phase-II units is assumed as arbitrary. Some significant reliability characteristics such as mean sojourn times (MST), transition probabilities, mean time to system failures (MTSF), availability, expected number of repairs (for both phase-I and phase-II units), busy period of the server, expected number of visits of the server and finally the profit function are obtained in steady state by making use of well-known semi-Markov process (SMP) and regenerative point technique (RPT). The graphical representation of these reliability characteristics has been made for arbitrary values of the rates associated with failure and repair times. The application of the present study can be seen in the power distribution system.