Modeling of The Effect of Corrective and Preventive Maintenance with Bathtub Failure Intensity
Published at : 17 Jan 2014
Volume : IJtech
Vol 4, No 2 (2013)
DOI : https://doi.org/10.14716/ijtech.v4i2.111
Krit, M., Rebaï, A., 2013. Modeling of The Effect of Corrective and Preventive Maintenance with Bathtub Failure Intensity. International Journal of Technology. Volume 4(2), pp. 157-166
| Makrem Krit | Higher Institute of Companies Administration, Gafsa University, Tunisia |
| Abdelwaheb Rebaï | Higher school of Trade, Sfax University, Tunisia |
The aim of this paper is to propose a general model to illustrate the joint effect of corrective and preventive maintenance on repairable systems. The intensity of the failure process without maintenance is characterized in bathtub form. The maintenance effect is expressed by the change induced on the failure intensity before and after maintenance. It takes into account the possibility of dependent maintenance times with different effects. The likelihood functions are derived, so parameter estimations and assessment of the maintenance efficiency are possible. The properties of the parameters estimators have to be theoretically studied. Finally, results are applied to a real maintenance data set.
Bathtub failure intensity, Estimation, Imperfect maintenance, Reliability, Repairable system
Andersen, P.K., Borgan, O., Gill, R.D., 1993. Statistical Models based on Counting Processes, Springer Series in Statistics, Springer-Verlag.
Bedford, T., Mesina, C., 2000. The impact of modeling assumptions on maintenance optimisation, 2nd International Conference on Mathematical Methods in Reliability, MMR 2000, Bordeaux, pp. 171-174.
Bertholon, H., Bousquet, N., Celeux, G., 2004. An Alternative Competing Risk Model to the Weibull Distribution in Lifetime Data Analysis. Technical Report : RR-5265, INRIA Press, Orsay, France.
Bunea, C., Cooke, R.M., Lindqvist Bo., 2002. Competing Risk Perspective over Reliability Data Bases. Conference on Mathematical Methods in Reliability, MMR, Trondheim, Norway, Volume I, pp. 131-134.
Cooke, R., Bedford, T., 2002. Reliability Databases in Perspective. IEEE Transactions on Reliability, Volume 51, pp. 294-310.
Dijoux, Y., 2009. A Virtual Age Model based on a Bathtub Shaped Initial Intensity. Reliability Engineering and System Safety, Volume 94, pp. 982-989.
Dorrepaal, J., 1996. Analysis Tools for Reliability Databases, Postdoctorate Thesis, Delft University of Technology, 1996 also published by Swedish Nuclear Power Inspectorate SKI Report 95-67, Stokholm, Sweden.
Doyen, L., Gaudi, O., 2004. Classes of Imperfect Repair Models based on Reduction of Failure Intensity or Virtual Age. Reliability Engineering and System Safety, Volume 84, pp. 45-56.
Doyen, L., Gaudoin, O., 2005. Modélisation de l'effcacité de la maintenance des systèmes réparables, Rapport du contrat T50L47/F00555/0 entre EDF et le LMC, Institut National Politechnique de Grenoble, France.
Doyen, L., Gaudi, O., 2006. Imperfect Maintenance in a Generalized Competing Risk Framework. J. Appl. Probab.,Volume 43(3), pp. 825–839.
Doyen, L., 2010. Asymptotic Properties of Imperfect Repair Models and Estimation of Repair Efficiency. Naval Research Logistics, Volume 57(3), pp. 296-307.
Doyen, L., Gaudoin, O., 2011. Modelling and Assessment of Aging and Efficiency of Corrective and Planned Preventive Maintenance. IEEE Trans. Reliab., Volume 60(4), pp. 759–769.
Finkelstein, M.S., 2008. Failure Rate Modelling for Risk and Reliability, Springer, London.
Jack, N., 1998. Age-Reduction Models for Imperfect Maintenance, IMA Journal of
Mathematics Applied in Business and Industry, Volume 9, pp. 347-354.
Kijima, M., Tortorella, M., Baxter, L.A., 1996. A Point Process Model for the Reliability of a Maintained System Subject to General Repair. Communications in Statistics -Stochastic Models, Volume 12(1), pp. 37-65.
Kijima, M., Morimura, H., Suzuki, Y., 1988. Periodical Replacement Problem without Assuming Minimal Repair. European Journal of Operational Research, Volume 37, pp. 194-203.
Krit, M., Rebai, A., 2012. An Estimate of Maintenance Efficiency in Brown-Proschan Imperfect Repair Model with Bathtub Failure Intensity. Journal of Industrial Engineering and Management, Volume 5(1), pp. 88-101.
Kwam, P.H., Peña, E.A., 2005. Estimating Load-sharing Properties in a Dynamic Reliability System, J. Am Stat Assoc., Volume 100, pp. 262–272.
Kvam, P.H., Singh, H., Whitaker, L.R., 2002. Estimating Distributions with Increasing Failure Rate in an Imperfect Repair Model. Lifetime Data Analysis; Volume 8, pp. 53-56.
Langseth, H., Lindqvist, B.H., 2003. A Maintenance Model for Components Exposed to Several Failure Mechanisms and Imperfect Repair. Quality, Reliability and Engineering Statistics. World Scientific Publishing.
Langseth, H., Lindqvist, B.H., 2004. A Maintenance Model for Components Exposed to Several Failure Mechanisms and Imperfect Repair, In Mathematical and Statistical Methods in Reliability, Lindqvist BH, Doksum KL (eds). World Scientific: Singapore; pp. 415-430.
Lindqvist, B., 1999. Statistical Modelling and Analysis of Repairable Systems, Statistical and Probabilistic Models in Reliability, Ionescu, D.C. and Limnios N. eds, Birkhauser, Boston, pp. 3-25.
Nakagawa, T.,1986. Periodic and Sequential Preventive Maintenance Policies. Journal of Applied Probability, Volume 23, pp. 536-542.
Peña, E.A., Slate, E.H., González, J.R., 2007. Semiparametric Inference for a General Class of Models for Recurrent Events. J Stat Plan Inference, Volume 137, pp. 1727–1747.