Reliability of a retrial system with mixed standby components and Bernoulli vacation

Abstract

ABSTRACT This paper studies a retrial system with mixed standby components and a single repairman under Bernoulli vacation schedule. Such a model is motivated by some machine repair systems in practice. The repairman may either go for a vacation of random length with probability or stay idle in system with probability after the completion of a repair. If a component fails, it is repaired at once when the repairman is idle, whereas whether the repairman is busy or vacation, the failed components enter into an orbit. The expressions of steady-state availability, reliability function and the mean time to system first failure are obtained by using vector Markov process and Laplace transform theory. Sensitivity analysis and relative sensitivity analysis are provided. An application example of the intelligent automatic system is demonstrated. Finally, some numerical experiments are conducted to show the impacts of system parameters on reliability indexes. The results presented in the paper may be useful for machine repair system engineers.