Copulas Arisen from Degradation-Based Time-to-Failure Models

Symmetry

Mohamed Kayid¹  Lolwa Alshagrawi¹ 

[1] Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia;

关键词: copula function;    degradation;    failure time;    dependence;   

DOI  :  10.3390/sym14040785

来源: DOAJ

【 摘 要 】

There are a variety of degradation models in the literature, each with a certain effect of random variation around the mean degradation path on the time-to-failure of the device being degraded. To assess the dependence that the random variation around the mean degradation path exerts on the resulting time-to-failure, this paper presents copula functions for time-to-failure-based degradation models with respect to two well-known degradation models, namely, the multiplicative degradation model and the additive degradation model. The implied copula functions for the case of the multiplicative degradation model have explicit forms. The implied copula functions are proved to be symmetric in the case of deterministic effect of degradation on failure, but the copulas obtained when failure is affected uncertainly by degradation are asymmetric. Necessary and sufficient conditions for the implicit copula functions to be symmetric are given.

【 授权许可】

Unknown