Reliability modelling of a parallel system with maximum operation and repair times

Abstract

A parallel system of two identical units has been analysed under the aspects of maximum operation and repair times. The unit fails directly from normal mode. A single server is called immediately to conduct preventive maintenance of the unit after a pre-specific time 't' (called maximum operation time). The replacement of the unit is made by new one in case its repair is not possible by the server in a given maximum repair time. The unit works as new after preventive maintenance and repair. The distributions of failure time of the unit, the time to which unit undergoes for preventive maintenance and replacement are taken as negative exponential. However, the distributions of preventive maintenance, repair and replacement times are considered as arbitrary with different probability density functions. The expressions for several reliability measures are derived in steady-state using semi-Markov process and regenerative point technique. The graphical behaviour of the MTSF, availability and profit function has been examined giving arbitrary values to various parameters and costs. The profit of the system model has also been obtained considering different costs.