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This investigation is concerned with an M/G/1 machine interference problem with imperfect switchover of standbys, in which an unreliable repairman maintains a group of machines. An unreliable repairman means that the repairman is typically subject to unpredictable breakdowns. The time between two consecutive breakdowns follows an exponential distribution, and recovery time of the unreliable repairman follows a general distribution. The lifetime of operating/standby machines and the repair time of failed machines are exponentially and generally distributed, respectively. Using the method of supplementary variable, the stationary probability distribution is obtained. We develop some performance measures and system reliability indices. Furthermore, the cost effectiveness maximization is also discussed. Finally, a cost model is proposed to find the optimal numbers of operating and standby substations, which minimize the average cost per unit time. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the steady-state availability of a repairable system with standby switching failure. The repairable system configuration includes the primary and standby components, where an unreliable server is responsible to repair or monitor the failed ones. The time-to-failure and time-to-repair of the components follow exponential and general distribution, respectively. The server subjects to active breakdown when it is repairing. The time-to-breakdown of the server is also assumed to be exponentially distributed. When the primary components fail, the standby components replace the primary components successfully with probability 1− q . The repair time of the failed components and the repair time of the breakdown server are generally distributed. Further, we frame a practical model with three different repairable system configurations. We use supplementary variable method and integro-differential equations to obtain the steady-state availability of these three different repairable system configurations. Finally, we compare the cost/benefit ratio among the three configurations given the distribution parameters, and to the cost of the primary and standby components. [ABSTRACT FROM AUTHOR]

• A multi-criteria replacement policy under cumulative damage models is discussed. • The mean cist rate is formulated. • The optimal replacement policy is presented theoretically. • Numerical examples are provided. This paper investigates an extended replacement policy for a two-unit system subject to shocks and cumulative damage. As a shock occurs, the system suffers two types of effects: type I shock-effect is rectified by a minimal repair and type II shock-effect is removed by a corrective replacement. The probability of type II shock depends on the number of shocks from the last replacement. Each type I shock causes a minor failure of unit 1 and some damage to unit 2. These damages to unit 2 are additive and the system fails when the total damage exceeds a critical level L. A replacement policy (T, m, l) is considered in which the system is preventively replaced at age T or at the m th type I shock or at the time which the total damage to unit 2 exceeds a pre-specified level l ; and is correctively replaced either at the first type II shock or when the total damage to unit 2 exceeds a failure level L , whichever occurs first. The optimal policy that minimizes the expected cost rate is determined analytically. The proposed model extends several existing results. Our replacement policy is more general, flexible, and applicable in the real situations. [ABSTRACT FROM AUTHOR]

• A multi-criteria replacement policy under cumulative damage models is discussed. • The concept of replacement last is analyzed in detail. • The optimal replacement policy is presented theoretically. • An algorithm for searching the optimal replacement policy is presented. • Numerical examples are provided. −In this study, we discuss a preventive replacement policy under cumulative damage models that include the concept of replacement last. The system is subject to two types of shocks (represented by type 1 shock and type 2 shock) whose probabilities depend on age. Each type 1 shock leads to an amount of additive damage to the system and also causes a minor failure of the system, which can be rectified by a minimal repair. The system will have a catastrophic failure as long as the accumulated damage exceeds a failure level threshold L. Meanwhile, type 2 shock will cause catastrophic failure of the system. The system is replaced preventively at age τ or the n -th type 1 shock or the time instant when the accumulated damage exceeds a pre-specified level k (but less than L), whichever occurs last, and is replaced correctively at the first type 2 shock or the time which the accumulated damage exceeds L , whichever occurs first. The average cost rate is developed and the optimal replacement policy is discussed analytically and computed numerically. [ABSTRACT FROM AUTHOR]