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A Stochastic Failure Model with Dependent Competing Risks and its Applications to Condition-Based Maintenance

Part of: Special processes Applications

Published online by Cambridge University Press:  30 January 2018

Ji Hwan Cha  and
Inma T. Castro
Ji Hwan Cha*
Affiliation:
Ewha Womans University
Inma T. Castro*
Affiliation:
University of Extremadura
*
∗ Postal address: Department of Statistics, Ewha Womans University, Seoul, 120-750, Korea. Email address: [email protected]
∗∗ Postal address: Department of Mathematics, University of Extremadura, 10003 Cáceres, Spain. Email address: [email protected]
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Abstract

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In this paper a stochastic failure model for a system with stochastically dependent competing failures is analyzed. The system is subject to two types of failure: degradation failure and catastrophic failure. Both types of failure share an initial common source: an external shock process. This implies that they are stochastically dependent. In our developments of the model, the type of dependency between the two kinds of failure will be characterized. Conditional properties of the two competing risks are also investigated. These properties are the fundamental basis for the development of the maintenance strategy studied in this paper. Considering this maintenance strategy, the long-run average cost rate is derived and the optimal maintenance policy is discussed.

Keywords

Dependent competing risksdegradation processcatastrophic failureexternal shock processbaseline failure rate functioncondition-based maintenance

MSC classification

Primary: 60K10: Applications (reliability, demand theory, etc.)
Secondary: 62P30: Applications in engineering and industry
Type
Research Article
Information
Journal of Applied Probability , Volume 52 , Issue 2 , June 2015 , pp. 558 - 573
Copyright
© Applied Probability Trust 

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