An Expectation Maximization Algorithm to Model Failure Times by Continuous-Time Markov Chains
Joint Authors
Zhao, Dengfu
Chen, Zhiping
Duan, Qihong
Source
Mathematical Problems in Engineering
Issue
Vol. 2010, Issue 2010 (31 Dec. 2010), pp.1-16, 16 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2010-09-21
Country of Publication
Egypt
No. of Pages
16
Main Subjects
Abstract EN
In many applications, the failure rate function may present a bathtub shape curve.
In this paper, an expectation maximization algorithm is proposed to construct a suitable continuous-time Markov chain which models the failure time data by the first time reaching the absorbing state.
Assume that a system is described by methods of supplementary variables, the device of stage, and so on.
Given a data set, the maximum likelihood estimators of the initial distribution and the infinitesimal transition rates of the Markov chain can be obtained by our novel algorithm.
Suppose that there are m transient states in the system and that there are n failure time data.
The devised algorithm only needs to compute the exponential of m×m upper triangular matrices for O(nm2) times in each iteration.
Finally, the algorithm is applied to two real data sets, which indicates the practicality and efficiency of our algorithm.
American Psychological Association (APA)
Duan, Qihong& Chen, Zhiping& Zhao, Dengfu. 2010. An Expectation Maximization Algorithm to Model Failure Times by Continuous-Time Markov Chains. Mathematical Problems in Engineering،Vol. 2010, no. 2010, pp.1-16.
https://search.emarefa.net/detail/BIM-456720
Modern Language Association (MLA)
Duan, Qihong…[et al.]. An Expectation Maximization Algorithm to Model Failure Times by Continuous-Time Markov Chains. Mathematical Problems in Engineering No. 2010 (2010), pp.1-16.
https://search.emarefa.net/detail/BIM-456720
American Medical Association (AMA)
Duan, Qihong& Chen, Zhiping& Zhao, Dengfu. An Expectation Maximization Algorithm to Model Failure Times by Continuous-Time Markov Chains. Mathematical Problems in Engineering. 2010. Vol. 2010, no. 2010, pp.1-16.
https://search.emarefa.net/detail/BIM-456720
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-456720