Abstract
In the automotive industry, it is important to know whether the failure of some car parts may be related to the failure of others. This project studies warranty claims for five engine components obtained from a major car manufacturer with the purpose of modeling the joint distributions of the failure of two parts. The one-dimensional distributions of components are combined to construct a bivariate copula model for the joint distribution that makes it possible to estimate the probabilities of two components failing before a given time. Ultimately, the influence of the failure of one part on the operation of another related part can be described, predicted, and addressed. The performance of several families of one-parameter Archimedean copula models (Clayton, Gumbel–Hougaard, survival copulas) is analyzed, and Bayesian model selection is performed. Both right censoring and conditional approaches are considered with the emphasis on conditioning to the warranty period.
Highlights
Studying the reliability of complex engineering systems, one has to account for possible failures of their components
Models Hypothesis 1 (H1) and Hypothesis 4 (H4) were characterized by the lower tail dependence, while Hypothesis 2 (H2) and Hypothesis 3 (H3) were distinguished by upper tail dependence
Applying the Akaike information criterion (AIC) and Bayes information criterion (BIC) as shown in (Shemyakin and Kniazev 2017) demonstrated that the two-parameter classes of Archimedean BB1 copula and Student t-copula provided a better fit than the one-parameter
Summary
Studying the reliability of complex engineering systems, one has to account for possible failures of their components. Copula models of dependence are becoming increasingly popular in such diverse fields as insurance, finance, and health studies because they make it possible to address all three above-mentioned factors of dependence in one general framework (Joe 2014) This framework is provided by modeling the entire joint distribution of individual TTF variables using special classes of copula functions. Copula models have the advantage of being able to address complex non-linear dependence structures going beyond correlation analysis (Embrechts et al 2003) and to model successfully the tails of the joint TTF distribution corresponding to the catastrophic events of cascade failures, playing a special role in engineering system control and risk management.
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