Reliability of k/n System with Competing Failures Component Connected by Gumbel-Barnett Copula

The reliability of k/n system with two interrelated competitive failure mechanisms leading to component failure is considered. The competitive correlation is connected by Gumbel-Barnett (GB) Copula with Weibull marginal distributions that have different scale parameters and shape parameters. The effects of GB Copula on the failure rate and reliability of components and k/n system are studied when the shape parameters are equal. We proved that the components have increasing, decreasing and bathtub failure rate in terms of the same shape parameter but different values. The reliability of the k/n (n>1) system is not consistently superior to that of the simple system (i.e., k/n=1/1).Based on progressively Type-II censored samples, the Bayes estimation of the parameters and reliability of the k/n system are discussed, and Monte Carlo experiments are carried out to illustrate proposed methods. Finally, a real-life data is provided to demonstrate the model and method proposed in this paper.