Bayesian reliability analysis for copula based step-stress partially accelerated dependent competing risks model

Abstract

The reliability of high-reliable and long-lifespan products in the presence of competing risks are commonly derived based on a known acceleration model and a latent independent competing risks model. For the cases with unknown acceleration models and dependent competing risks, this paper proposes a copula based partially accelerated competing risks model using a tampered random variable transformation. The reliability function and dependence structure of the partially accelerated competing risks data are derived between the real lifetime and the accelerated lifetime of each failure cause. In consideration of the parametric constraints and complicated joint posterior distribution, Hamiltonian Monte Carlo method within MCMC procedures is utilized to obtain Bayesian estimation of model parameters and reliability characteristics by defining unconstrained parameters using a specific transformation function. A simulation study is conducted to investigate the estimation performance, showing that the transformation forms have little influence on the point estimation of model parameters, and the constrained parametric Bayesian estimation method is efficient to evaluate the reliability for the proposed model. Finally, a real data set from a light-emitting diode partially accelerated life test is presented for further illustration of Bayesian reliability analysis.