Modeling the Dependent Competing Risks With Multiple Degradation Processes and Random Shock Using Time-Varying Copulas

We develop s-dependent competing risk model for systems subject to multiple degradation processes and random shocks using time-varying copulas. The proposed model allows for a more flexible dependence structure between risks in which (a) the dependent relationship between random shocks and degradati...

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Bibliographic Details
Published in:IEEE transactions on reliability 2012-03, Vol.61 (1), p.13-22
Main Authors: Wang, Yaping, Pham, Hoang
Format: Article
Language:English
Subjects:
Acceleration
Copula method
Degradation
dependent competing risks
Economic models
Electric shock
Estimating
Fatal
fatal shocks
Joints
Mathematical model
Mathematical models
multiple degradation
Random variables
Reliability
Risk
Studies
System reliability
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Summary:We develop s-dependent competing risk model for systems subject to multiple degradation processes and random shocks using time-varying copulas. The proposed model allows for a more flexible dependence structure between risks in which (a) the dependent relationship between random shocks and degradation processes is modulated by a time-scaled covariate factor, and (b) the dependent relationship among various degradation processes is fitted using the copula method. Two types of random shocks are considered in the model: fatal shocks, which fails the system immediately; and nonfatal shocks, which does not. In a nonfatal shock situation there are two impacts towards the degradation processes: sudden increment jumps, and degradation rate accelerations. The comparison results of the system reliability estimation from both constant and time-varying copulas are illustrated in the numerical examples to demonstrate the application of the proposed model. The modified joint distribution bounds in terms of Kendall's tau and Spearman's rho provide an improvement to Frechet-Hoeffding bounds for estimating the possible system reliability range.
ISSN:0018-9529
1558-1721
DOI:10.1109/TR.2011.2170253