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High availability requirement is essential for series repairable systems, such as power plants, power grids, and automated production lines in addition to the requirement of long life. A backorder occurs when a component of this system fails, while the on-hand stock of the component is zero. The remaining working components in the series system are no longer in operation because of the backorder-induced system downtime, and these working components are considered to be in a switch-OFF state. Ignoring the switch-OFF effect can cause large errors in the evaluation of operational availability for a critical system group of multiple independent repairable systems. This paper focuses on the availability modeling of a system group that consists of N two-component repairable systems and considers the switch-OFF state of the working components. We analyze how a backorder of one component affects the number of other components being in operation by considering the joint state of the available repairable systems and spares. We formulate the spare inventory replenishment process for the two-component system group as two groups of continuous time Markov chains (CTMCs) with and without the switch-OFF effect. Then, we derive the state transition rates of the switch-OFF effect caused by another component backorder. Finally, we present the algorithm of availability of instantaneous and steady states for the system group based on the CTMCs considering the switch-OFF effect. The presented availability model is for system groups that consist of multiple independent repairable systems and extends the system availability model by incorporating the switch-OFF effect on the number of components in operation. This paper provides a solution of availability considering the switch-OFF effect of component and makes possible for two-component repairable systems to achieve higher availability with lower spares stock level.

Availability Modeling of Two-Component Repairable Systems Subject to Switch-Off