Probabilistic analysis of a series–parallel repairable system with three units and vacation

Numerical solution of the steady-state probability and reliability of a repairable system with three unites

“…Hu et al discussed a three-unit system with n failure modes and priority and obtained the explicit expressions of the steady-state probabilities of the system in [4]. Moreover, Hu et al studied the steady-state availability and the mean up-time of a series-parallel repairable system consisting of one master control unit, two slave units and a single repairman who operates single vacation in [5]. Recently, Chen studied the three-unit repairable system with preemptive priority to part 1 and single vacation of a repairman in [6].…”

Reliability of a repairable system

“…In the existing literature (e.g., see [9]- [11]), numerical results are often given under the assumption that the repair time distributions of the units are exponential, that is to say µ i (x) are constants. It is not enough to show whether their methods are powerful or not since in this situation it is easy to obtain the reliability indices directly through simple computation.…”

Asymptotic Stability of a Series-Parallel Repairable System Consisting of Three-Unit with Multiple Vacations of a Repairman

“…According to [3], the series-parallel repairable system consisting of three-unit with multiple vacations of a repair-man can be described by the following system of partial differential equations with integral boundary conditions:…”

“…From this point, to study reliability of repairable systems with a repairman who can take a vacation or can do other work is important in terms of theory and practice. Hu et al [3] considered a series-parallel repairable system with three units and multiple vacations of a repairman; they obtained the reliability indices of the system by using the method of supplement variables, the vector Markov progress method and the tool of the Laplace transform. They used the dynamic solution in calculating the availability and the reliability.…”