A competing risk model for dependent and imperfect condition–based preventive and corrective maintenances

Abstract

This article develops a model for dependent and imperfect condition–based preventive and corrective maintenance actions. The approach is based on the combination of the intensity proportional repair alert, a competing risks-based model and the generalized renewal process. Typically, intensity proportional repair alert can identify either how preventive actions may modify the distribution of the time between critical failures or how corrective events may change the frequency of preventive maintenances, but this method fails to analyze the effectiveness of the maintenance actions because they are treated as being perfect. On the other hand, generalized renewal process is able to capture the quality of maintenance, classifying it as perfect, minimal or imperfect depending on the value of a rejuvenation parameter. However, generalized renewal process cannot distinguish how different types of maintenance influence each other as intensity proportional repair alert does. Therefore, the intensity proportional repair alert–generalized renewal process hybrid approach is proposed here to fill this gap. This article also develops the maximum likelihood estimators for the proposed model as well as a Monte Carlo–based algorithm to estimate the expected number of preventive and corrective maintenances over time. The proposed model is validated through two example applications for which the intensity proportional repair alert–generalized renewal process model results show close agreement with the failure datasets.

Keywords

Competing risks generalized renewal process dependent and imperfect maintenances

Get full access to this article

View all access options for this article.

References

Kijima

Sumita

. A useful generalization of renewal theory: counting processes governed by non-negative Markovian increments. J Appl Probab 1986; 23: 71–88.

Krivtsov

. A Monte Carlo approach to modelling and estimation of the generalized renewal process in repairable system reliability analysis. College Park, MD: University of Maryland, 2000.

Yañez

Joglar

Modarres

. Generalized renewal process for analysis of repairable systems with limited failure experience. Reliab Eng Syst Safe 2002; 77: 167–180.

Pham

Wang

. Imperfect maintenance. Eur J Oper Res 1996; 94: 425–438.

Clements-Croome

. A novel repair model for imperfect maintenance. IMA J Manag Math 2006; 17: 235–243.

Percy

Kearney

Kobbacy

KAH

. Hybrid intensity models for repairable systems. IMA J Manag Math 2010; 21: 395–406.

Crowder

. Classical competing risks. London: Chapman & Hall/CRC Press, 2001.

Cooke

. The design of reliability data bases, part II: competing risk and data compression. Reliab Eng Syst Safe 1996; 51: 209–223.

Cooke

Paulsen

. Concepts for measuring maintenance performance and methods for analysing competing failure modes. Reliab Eng Syst Safe 1997; 55: 135–141.

10.

Bunea

Mazzuchi

Sarkani

. Application of modern reliability database techniques to military system data. Reliab Eng Syst Safe 2008; 93: 14–27.

11.

Jiang

. Discrete competing risk model with application to modeling bus-motor failure data. Reliab Eng Syst Safe 2010; 95: 981–988.

12.

Sarhan

Hamilton

Smith

. Statistical analysis of competing risks models. Reliab Eng Syst Safe 2010; 95: 953–962.

13.

Christen

Ruggeri

Villa

. Utility based maintenance analysis using a Random Sign censoring model. Reliab Eng Syst Safe 2011; 96: 425–431.

14.

Ishioka

Nonaka

. Maximum likelihood estimation of Weibull parameters for two independent competing risks. IEEE T Reliab 1991; 40: 71–74.

15.

Keedy

Feng

. Reliability analysis and customized preventive maintenance policies for stents with stochastic dependent competing risk processes. IEEE T Reliab 2013; 62: 887–897.

16.

Park

. Parameter estimation of incomplete data in competing risks using the EM algorithm. IEEE T Reliab 2005; 54: 282–290.

17.

Park

Kulasekera

. Parametric inference of incomplete data with competing risks among several groups. IEEE T Reliab 2004; 53: 11–21.

18.

Pascual

. Accelerated life test planning with independent Weibull competing risks with known shape parameter. IEEE T Reliab 2007; 56: 85–93.

19.

Pascual

. Accelerated life test planning with independent Weibull competing risks. IEEE T Reliab 2008; 57: 435–444.

20.

Pham

Yaping

. A multi-objective optimization of imperfect preventive maintenance policy for dependent competing risk systems with hidden failure. IEEE T Reliab 2011; 60: 770–781.

21.

Sarhan

Kundu

. Analysis of incomplete data in presence of competing risks among several groups. IEEE T Reliab 2006; 55: 262–269.

22.

Wang

Pham

. Modeling the dependent competing risks with multiple degradation processes and random shock using time-varying copulas. IEEE T Reliab 2012; 61: 13–22.

23.

Langseth

Lindqvist

. A maintenance model for components exposed to several failure mechanisms and imperfect repair. Singapore: World Scientific Publishing Co. Pte. Ltd, 2003.

24.

Brown

Proschan

. Imperfect repair. J Appl Probab 1983; 20: 851–859.

25.

Langseth

Lindqvist

. Competing risks for repairable systems: a data study. J Stat Plan Infer 2006; 136: 1687–1700.

26.

Doyen

Gaudoin

. Imperfect maintenance in a generalized competing risks framework. J Appl Probab 2006; 43: 825–839.

27.

Doyen

Gaudoin

. Classes of imperfect repair models based on reduction of failure intensity or virtual age. Reliab Eng Syst Safe 2004; 84: 45–56.

28.

Cooke

. The total time on test statistic and age-dependent. Stat Probabil Lett 1993; 18: 307–312.

29.

Press

Teukolsky

Vetterling

. Numerical recipes in C: the art of scientific computing. 2nd ed. Cambridge: Cambridge University Press, 2002.

30.

Lins

Moura

MdC

Zio

. A particle swarm-optimized support vector machine for reliability prediction. Qual Reliab Eng Int 2011; 28: 141–158.

31.

Kennedy

Eberhart

Morgan

. Swarm intelligence. San Francisco, CA: Morgan Kaufmann, 2001.

32.

Bratton

Kennedy

. Defining a standard for particle swarm optimization. In: Proceeding of the IEEE swarm intelligence symposium, Honolulu, HI, 1–5 April 2007. New York: IEEE.

33.

Ross

. Simulation. 3rd ed. San Diego, CA: Academic Press, 2002.

34.

Moura

MdC

Zio

Lins

. Failure and reliability prediction by support vector machines regression of time series data. Reliab Eng Syst Safe 2011; 96: 1527–1534.

35.

Wilks

. The large-sample distribution of the likelihood ratio for testing composite hypothesis. Ann Math Stat 1937; 231: 60–62.

36.

DeGroot

Schervish

. Probability and statistics. Boston, MA: Addison-Wesley, 2002.

37.

Droguett

Mosleh

. Time to failure assessment of products at service conditions from accelerated lifetime tests with stress-dependent spread in life. Pesqui Oper 2007; 27: 209–233.