Performance Analysis of a Cold Standby System with fault Detection and Arrival Time of Server Subject to Imperfect Coverage

Abstract

The main aim of present paper is to analyse the performance measures of a standby system by using the concept of arrival time of server, repair, imperfect coverage, detection and replacement. A single repair facility is provided to the system as and when required. The repairman takes some time to conduct the repair services. Upon failure of the unit repairman first detect the failed unit to check the feasibility of repair and replacement in case fault is not completely coverage. The repair, replacement, detection and arrival time of the repairman are considered as arbitrary distributed while failure rate is taken as negative exponential distributed. The failure time of the unit is exponentially distributed while the distribution of repair times, replacement time and recovery time of the unit follows arbitrary distribution. Various recurrence relations for reliability, MTSF, availability and profit function are derived using semi-Markov process and regenerative point technique. Graphs for availability and profit function are drawn with respect to failure rate.