Stochastic Analysis of a Cold Standby System with Priority to Preventive Maintenance over Repair


S.C. Malik, Sudesh K. Barak, M.S. Barak

Author affiliation

1 Department of Statistics, M.D. University Rohtak (Haryana)-124001
2 Department of Mathematics, I.G. University, Rewari (Haryana) -122502


A stochastic model is developed for a two-unit cold standby system under the aspect of priority to preventive maintenance over repair. The units are identical having two modes- operative and complete failure. There is a single server who visits the system immediately to carry out the repair activities. Server conducts preventive maintenance of the operative unit after a pre-specific time ‘t’. However, repair of the unit is done by the server at its complete failure. Priority is given to maintenance of one unit over repair of the other unit. The random variables associated with failure time, the rate by which unit undergoes for preventive maintenance and repair time are statistically independent. The failure time and time by which unit goes for preventive maintenance follow exponential distribution while the distributions for maintenance and repair times are taken as arbitrary with different probability density functions. Several measures of system effectiveness are obtained using semi-Markov process and regenerative point technique. Graphs are drawn to depict the behavior of MTSF, availability and profit function giving arbitrary values to various parameters and costs.


cold standby system; maximum operation time; preventive maintenance; repair; priority and stochastic analysis