No abstract

A new k-out-of-n redundancy system is studied where all components have the same characteristics and experience dependent failure processes due to simultaneous exposure to degradation and shock loads. The k-out-of-n system reliability model is developed and preventive maintenance policy is applied. Some research has been done on a single component or simple system, or systems with independent failure times and failure processes. This new model extends previous research by considering degrading components within a k-out-of-n system with dependent failure processes. Failure times for all components are probabilistically dependent. Each component can fail due to a soft failure process or a hard failure process. The failure processes are mutually competing since either failure process can cause the component to fail. The failure processes are also dependent since the arrival of each shock affects both failure processes for all components. An age replacement policy is applied for this system. Optimal replacement interval is determined by minimizing a cost rate function. Keywords-dependent failure processes; multi-component systems; k-out-of-n system; degradation; random shocks; preventive maintenance NOTATION N(t) number of shock loads that have arrived by time t n number of components in a k-out-of-n system k number of required components in a k-out-of-n system λ arrival rate of random shocks D threshold for catastrophic/hard failure of the component W j size/magnitude of the j th shock load on the component F W (w) cumulative distribution function (cdf) of W j H critical wear degradation failure threshold of the component X(t) wear volume of the component due to continuous degradation at t X S (t) total wear volume of the component at t due to both continual wear and instantaneous damage; Y j damage size contributing to soft failure of the component caused by the j th shock load;y) pdf of the sum of k independent and identically distributed (i.i.d.) Y j variables f T (t) pdf of the failure time, T F T (t) cdf of the failure time, T V periodic replacement interval C(t) cumulative maintenance cost by time t CR(V) average long-run maintenance cost rate E[U] expected value of the renewal cycle length, U

No abstract