Bayesian Inference for One-Shot Devices with Weibull Dependent Failure Modes Using Copulas

One-shot devices, like airbags, bombs, and fire extinguishers, are reliable products that are extensively destroyed after their use and cannot be used more than once. Assessing the reliability of one-shot devices is challenging since their exact failure times cannot be noted. Instead, the collected data are either right- or left-censored, depending on whether the device passed or failed the test. Accelerated life testing is commonly used to induce more failures of one-shot devices in a reasonable time span. This paper presents Bayesian analysis of one-shot devices with two dependent failure modes. Three Archimedean copulas are used to model the dependence structure among the failure modes, assuming Weibull marginal distributions and a constant stress accelerated life test. A Differential Evolution MCMC algorithm is used to develop the Bayesian point and interval estimates of the model parameters and the reliability under normal operating conditions. The performance of the developed estimates is assessed using a simulation study. The proposed technique is also illustrated using a real data set.