Competing failure is an important reliability topic. Thus, the study of the statistical inference of accelerated life testing (ALT) with competing failures is of great significance. In contrast to the previous related studies that assumed that all competing failure modes were cross statistically independent, we study the statistical inference method for ALT considering the statistical dependence of the competing failure modes based on copula theory. With the copula function, we construct the statistically dependent relationship between the margin distributions of the competing failure modes and their joint distribution, and find the maximum likelihood estimation (MLE) model for the parameter estimations. We also present a simple engineering-based multi-dimensional copula construction method applied in the statistical inference for ALT with statistically dependent competing failure modes. The results and analysis of the case studies indicate that the statistical inference models and the multi-dimensional copula construction method derived in this article are not only correct and feasible but have good accuracy and universality. We have provided an effective, universally applicable method for the statistical inference of ALT in situations involving competing failures, statistically independent or dependent, which is of great significance to evaluating a product's lifetime in ALT.
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Zhang et al. (2014) studied this question.