Reliability analysis for k-out-of-n systems subject to multiple dependent competing failure processes

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

Reliability modeling for planetary gear transmission system considering dependent failure processes

“…An n component system that works if and only if at least k components work is called a k-out-of-n system. 34 Figure 1 34 shows a k-out-of-n system arranged in parallel. As shown in Figure 2, the failure of a system is the result of two dependent yet competing failure modes (soft failure and hard failure) that involve the same random shock process: soft failure is caused jointly by continuous degradation and sudden degradation damage due to random shocks; hard failure is caused by continuous load and abrupt stress due to the same random shocks.…”

“…k-out-of-n system with multiple components, the system remains normal when k parts work simultaneously; when the number of failed components exceeds n-k, the system will fail. [33][34] In literature, [35][36] the actuator of microelectro-mechanical systems (MEMS) is considered as a k-out-of-n system. Researchers have obtained the reliability of the MEMS actuator to determine the vulnerable components in the mechanism by testing actuator failure efficiency under shocks.…”

Dynamic k-out-of-n system with component partnership design with two dependent competing failure processes

“…We consider dynamic k-out-of-n component partnership system where each component may fail due to two competing dependent failure modes, soft failures and hard failures [8,9,13], as depicted in Fig. 2.…”

“…The research extended to the reliability model for kout-of-n system that all components have the same properties and experience two dependent failure processes [13]. For further research, we investigate soft failure process with degradation damages due to a shock process, and catastrophic failures caused by intemperate shock loads on the multi-state k-out-of-n system reliability.…”

A complex multi-state k-out-of-n: G system with preventive maintenance and loss of units

“…Standard and advanced problems of maintenance policies for reliability models have been discussed by Nakagawa (2005). A reliability model and a maintenance policy for a k-out-of-n system, in which all components have the same properties and experience two dependent/correlated failure processes, is developed in Song et al (2012). Coit et al (2015) describe a new kout-of-n system reliability model, appropriate when the minimum number of required components changes dynamically in response to failures, to maximize the utility of the available collection of functioning components.…”