Abstract
A one-shot device is a unit that performs its intended function only once. Actual lifetimes of such kind of devices cannot be observed. One can only observe if a failure occurred before or after a certain inspection time so the data is either left- or right-censored. Since one-shot devices are highly reliable products, accelerated life testing is commonly used to induce early failures. There are often more than one dependent failure modes causing the device to fail. Copula models have become one of the most popular tools for modeling dependence. In this paper, we provide statistical inference for modeling the dependence structure between failure modes in one-shot devices under constant stress accelerated life testing using copulas with Weibull marginals. The point estimates of the unknown parameters for the Weibull distribution along with the dependence parameter estimate are obtained using two estimation methods; the maximum likelihood estimation and the inference function for margins. Also, interval estimates are constructed using the asymptotic and bootstrap methods. The basic bootstrap and the studentized-t bootstrap intervals are obtained. Moreover, the survival probabilities are predicted under normal conditions. Numerical analysis including simulated data and a real life data are conducted to study the performance of the estimates.
Published Version
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