Statistical analysis of the k/n(G) system with dependent competing failure components influenced by Gumbel-Hougarrd Copula and progressively hybrid censored data

Consider a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>k</mml:mi> <mml:mo>/</mml:mo> <mml:mi>n</mml:mi> <mml:mo>(</mml:mo> <mml:mi>G</mml:mi> <mml:mo>)</mml:mo></mml:math> system, in which the system components are composed of multiple dependent failure mechanisms, and the dependence between the mechanisms is connected by the Gumbel-Hougarrd (GH) Copula. This paper presents a progressively hybrid censored test based on the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>k</mml:mi> <mml:mo>/</mml:mo> <mml:mi>n</mml:mi> <mml:mo>(</mml:mo> <mml:mi>G</mml:mi> <mml:mo>)</mml:mo></mml:math> system. Based on the censored test, the IFM(Marginal inference) method is used to estimate the model parameters and system reliability. Meanwhile, the MH (Metropolis-Hastings) sampling mixed with the Gibbs sampling method is proposed to realize the Bayes estimation of the model parameters and system reliability. Also, under the non-informative prior conditions, the conditional posterior density of the shape parameters of the marginal Weibull distribution is proved to be log-concave. The Monte Carlo simulation results showed that the proposed Bayes method is better than the traditional IFM method. Finally, the model and method proposed in this paper are applied to real data.