Lifetime assessment method for products with dependent competing failures based on copula theory

Based on copula theory and methods, we construct the dependent relationship between the margin distribution functions of the competing failure modes and their joint distribution function through copula function. With the dependent relationship, we study statistical inference method of the life testing with dependent competing failure modes, and found the maximum likelihood estimation (MLE) model for the parameter estimations to evaluate the lifetime of the products. The results and analysis of case studies prove that sample size, proportion of censored samples, proportion of failure samples with masked failure mode, and copula model types have great impact on the accuracy of the lifetime assessment of the products with dependent competing failure modes. And with appropriate test data and right copula modes, method developed in this paper has very good accuracy for the lifetime assessment with dependent competing failure modes. It provides an effective and accurate way to solve the problems of statistical inference of life testing with dependent competing failure modes, and also an accurate way of lifetime assessment for products.

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