Repairman Leave Two-unit Cold Standby Repairable System

The two-unit repairable system is a classical model in the mathematical theory ofreliability. Although the mathematical researchers have done much work about it, there waslimited research on repairmen vacations. For the purposes of keeping high workingefficiency or increasing system incomes while repairmen do some subordinate work, it isworth considering repairmen vacations.This paper considers a cold standby repairable system consisting of two units with arepairman. Assuming that the repairman is on single vacation or multiple vacations, theworking life is exponential distribution, and the repair time and vacation time are generaldistributions, by using the Markov renewal process, the total probability decompositiontechnology, Laplace transform and Laplace-Stieltjes transform, some main reliabilityindexes are obtained:(1) The LS transform of the point-wise distribution of time before the first failureF_i(t) and MTTFF;(2) The L transform of the point-wise availability A_i(t) and the steady-stateavailability;(3) The LS transform of the expected failure number during a given (0, t] M_i(t)and the steady-state failure frequency (?)M_i(t)/t;(4) With no vacation some results that are concordant with the related documents areobtained.