A Competing Risks Model With Multiply Censored Reliability Data Under Multivariate Weibull Distributions

A competing risks model is composed of more than one failure mode that naturally arises when reliability systems are made of two or more components. A series system fails if any of its components fail. As these components are all part of the same system, they may be correlated. In this paper, we con...

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Bibliographic Details
Published in:IEEE transactions on reliability Vol. 68; no. 2; pp. 462 - 475
Main Authors: Fan, Tsai-Hung, Wang, Yi-Fu, Ju, She-Kai
Format: Journal Article
Language:English
Published: New York IEEE 01.06.2019
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Component reliability
Computer simulation
Data models
Economic models
Expectation–maximization (EM) algorithm
Exponential distribution
Failure modes
Failure times
Fans
Marshall–Olkin Weibull distribution
masked data
Mathematical models
Maximum likelihood estimates
Maximum likelihood estimation
Mean time to failure
multiply censored life test
Multivariate analysis
Parameter estimation
Quantiles
Reliability
series system
Silicon
Statistical analysis
Statistical inference
Weibull distribution
ISSN:0018-9529, 1558-1721
Online Access:Get full text
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Summary:A competing risks model is composed of more than one failure mode that naturally arises when reliability systems are made of two or more components. A series system fails if any of its components fail. As these components are all part of the same system, they may be correlated. In this paper, we consider a competing risks model with <inline-formula><tex-math notation="LaTeX">k</tex-math></inline-formula> failure modes and whose lifetimes follow a joint <inline-formula><tex-math notation="LaTeX">k</tex-math></inline-formula>-variate Marshall-Olkin Weibull distribution, when the data are multiply censored. Normally, each observation contains the failure time as well as the failure mode. In practice, however, it is common to have masked data in which the component that causes failure of the system is not observed. We apply the maximum likelihood approach via expectation-maximization algorithm, along with the missing information principle, to estimate the parameters and the standard errors of the maximum likelihood estimates. Statistical inference on the model parameters, the mean time to failure, and the quantiles of the failure time of the system as well as of the components are all developed. The proposed method is evaluated by a simulation study and also applied to two two-component real datasets successfully.
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ISSN:0018-9529
1558-1721
DOI:10.1109/TR.2019.2907518