A Parallel System with Priority to Preventive Maintenance over Repair Subject to Maximum Operation and Repair Times

Abstract In this work, a stress is given on the evaluation of performance measures of a parallel system under priority with necessary conditions on operation and repair times. The units are identical in nature subject to constant failure. There is a single server who visits the system immediately to rectify the faults whenever occurred in the system. The system undergoes for preventive maintenance after a pre-specific time‘t’ up to which no failure occurs. However, repair of the unit is done at its failure. And, the unit is replaced by new one in case its repair is not possible by the server in a given maximum repair time. The maintenance and repair activities are perfect. Priority is given to preventive maintenance of one unit over repair of the other. The random variables associated with failure, preventive maintenance, repair and replacement times are statistically independent. The failure time and the time by which unit undergoes for preventive maintenance and replacement follow negative exponential distribution, whereas the distributions for preventive maintenance, repair and replacement rates are taken as arbitrary with different probability density functions. The system is observed at suitable regenerative epochs by using semi-Markov process and regenerative point technique. Graphs are drawn to depict the behavior of some important reliability measures giving particular values to the parameters and costs. The profit of the system model has also been evaluated considering different cost policies.