Reliability assessment for consecutive-[formula omitted]-out-of-[formula omitted]: F retrial systems under Poisson shocks

Abstract

This paper derives reliability indices of a linear consecutive-k-out-of-n: F system with retrial under Poisson shocks. The system fails if and only if at least k consecutive components from n components fail and is maintained by one repairman. When a component fails during the repairman’s unavailability, it will be waiting until the repairmen becomes available. The failure of a component may be caused by its intrinsic characteristics such as ageing and deterioration or extrinsic factors such as shocks. It is assumed that a component will fail once the magnitude of a shock is greater than a threshold. At any time, a component is at one of the three states: working, waiting for repair, and under repair. For some systems, we need to obtain reliability indices for practical use. Hence, this paper uses the Markov chain to model the transition between states and obtains several reliability indices. The parameter sensitivity of the system reliability indices is analysed with numerical experiments.