Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-04T18:41:30.909Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Part of: Applications Special processes

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]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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 

References

Aven, T. (1996). Condition based replacement policies — a counting process approach. Reliab. Eng. System Safety 51, 275–281.Google Scholar
Aven, T. and Jensen, U. (1999). Stochastic Models in Reliability. Springer, New York.CrossRefGoogle Scholar
Bogdanoff, J. L. and Kozin, F. (1985). Probabilistic Models of Cumulative Damage. John Wiley, New York.Google Scholar
Castanier, B., Bérenguer, C. and Grall, A. (2003). A sequential condition-based repair/replacement policy with non-periodic inspections for a system subject to continuous wear. Appl. Stoch. Models Business Industry 19, 327–347.CrossRefGoogle Scholar
Cha, J. H. (2001). Burn-in procedures for a generalized model. J. Appl. Prob. 38, 542–553.Google Scholar
Ebrahimi, N. (1997). Multivariate age replacement. J. Appl. Prob. 34, 1032–1040.CrossRefGoogle Scholar
Finkelstein, M. and Cha, J. H. (2013). Stochastic Modeling for Reliability. Shocks, Burn-in and Heterogeneous Populations. Springer, London.Google Scholar
Grall, A., Dieulle, L., Bérenguer, C. and Roussignol, M. (2002). Continuous-time predictive-maintenance scheduling for a deteriorating system. IEEE Trans. Reliab. 51, 141–150.Google Scholar
Kalbfleisch, J. D. and Prentice, R. L. (1980). The Statistical Analysis of Failure Time Data. John Wiley, New York.Google Scholar
Kebir, Y. (1991). On hazard rate process. Naval Res. Logistics 38, 865–876.CrossRefGoogle Scholar
Lehmann, E. L. (1966). Some concepts of dependence. Ann. Math. Statist. 37, 1137–1153.Google Scholar
Liao, H., Elsayed, E. A. and Chan, L.-Y. (2006). Maintenance of continuously monitored degrading systems. Europ. J. Operat. Res. 175, 821–835.Google Scholar
Mi, J. (1994). Burn-in and maintenance policies. Adv. Appl. Prob. 26, 207–221.CrossRefGoogle Scholar
Nakagawa, T. (2005). Maintenance Theory of Reliability. Springer, London.Google Scholar
Park, C. and Padgett, W. J. (2006). Stochastic degradation models with several accelerating variables. IEEE Trans. Reliab. 55, 379–390.CrossRefGoogle Scholar
Sherif, Y. S. and Smith, M. L. (1981). Optimal maintenance models for systems subject to failure—a review. Naval Res. Logistics Quart. 28, 47–74.Google Scholar
Tijms, H. C. (2003). A First Course in Stochastic Models. John Wiley, Chichester.Google Scholar
Valdez-Flores, C. and Feldman, R. M. (1989). A survey of preventive maintenance models for stochastically deteriorating single-unit systems. Naval Res. Logistics 36, 419–446.Google Scholar
Wang, H. (2002). A survey of maintenance policies of deteriorating systems. Europ. J. Operat. Res. 139, 469–489.Google Scholar