Reliability Evaluation of a Load-sharing Parallel System with Failure Dependence

• Published in: Communications in statistics. Simulation and computation Vol. 45; no. 9; pp. 3094 - 3113
• Main Authors: Wang, Liying, Zhang, Jie, Chen, Wei, Jia, Xujie
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 20.10.2016; Taylor & Francis Ltd
• Subjects: Availability; Dependence; Failure; Failure dependence; Failure rates; Kernels; Load-sharing parallel system; Markov analysis; Mathematical analysis; Mathematical models; Reliability; Repair time; Semi-Markov process; Stress concentration; Time to the first system failure
• ISSN: 0361-0918; 1532-4141
• DOI: 10.1080/03610918.2014.920880

In a parallel structure load-sharing system, the failure rate of the operating components will usually increase, due to the additional loading induced by the other components' failure. Hence failure dependency exists among components. To quantify the failure dependency, a dependence function is introduced. Under the assumptions that the repair time distributions of components are arbitrary and life times are exponential distributions whose failure rates vary with the number of operating components, a new load-sharing parallel system with failure dependency is proposed. To model the stochastic behavior of the system, the Semi-Markov process induced by it is given. The Semi-Markov kernel associated with the process is also presented. The availability and the time to the first system failure are obtained by employing Markov renewal theory. A numerical example is presented to illustrate the results obtained in the paper. The impact of the failure dependence on the system is also considered.