Stochastic modeling of non-identical redundant systems with priority, preventive maintenance, and Weibull failure and repair distributions

The ever-increasing demand of automation in appliances and economic constraints in purchasing capacity of consumers motivate to analyse the non-identical redundant system. For this analysis, a stochastic model has been designed for a non-identical redundant system having two units: one operative and other cold standby. Each unit has two possible states: either operative or failure. Original unit gets priority for repair over repair and preventive maintenance of duplicate unit. The repairs, preventive maintenance, and switches used to shift standby unit into operation are perfect. All failure and repair time random variables are arbitrary distributed. The system is observed using SMP and RPT to obtain various characteristics of interest to system designers. At last, some numerical results have been obtained by considering exponential, Rayleigh, and Weibull distributions, and compared with the results obtained by Kumar et al. (Rev Invest Oper 37(3):247–257, 2016a; Cogent Math 3(1):1135721, 2016b).