×

Maintenance scheduling under age replacement policy using proportional hazards model and TTT-plotting. (English) Zbl 0917.90142

Summary: The failure characteristics of a system may depend on the total operating time, operating time since the last repair, failure history, operating conditions or on the values of monitored variables. A reliability based approach which takes into consideration values of monitored variables is suggested for estimating the optimum maintenance (or replacement) time interval for a system or threshold values of monitored variables under the age replacement policy. The maintenance cost equation is formed on the basis of the planned and unplanned maintenance costs and the values of monitored variables. The proportional hazards model is used to identify the importance of monitored variables. The reliability function is estimated considering the values of monitored variables. A Total Time on Test (TTT) plot based on this estimate of the reliability function is used to estimate the optimum maintenance (or replacement) time interval for a system or threshold values of monitored variables. This approach is illustrated with an example.

MSC:

90B25 Reliability, availability, maintenance, inspection in operations research
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Al-Najjar, B., Some problems on the selection of a condition based maintenance technique for mechanical systems, ()
[2] Barlow, R.E.; Proschan, F., Mathematical theory of reliability and life testing, (1965), Wiley New York · Zbl 0132.39302
[3] Barlow, R.E.; Campo, R., Total time on test process and applications to failure data analysis, (), 451-481
[4] Bergman, B., Some graphical methods for maintenance planning, (), 467-471
[5] Bergman, B.; Klefsjö, B., A graphical method applicable to age replacement problems, IEEE transactions on reliability, R-31, 478-481, (1982) · Zbl 0502.90037
[6] Breslow, N.E., Covariance analysis of censored survival data, Biometrics, 30, 89-99, (1974)
[7] Cho, D.I.; Parlar, M., A survey of maintenance models for multi-unit systems, European journal of operational research, 51, 1-23, (1991)
[8] Cox, D.R., Regression models and life-tables, Journal of the royal statistical society B, 34, 187-220, (1972) · Zbl 0243.62041
[9] Cox, D.R.; Oakes, D., Analysis of survival data, (1984), Chapman and Hall London
[10] Dohi, T.; Kaio, N.; Osaki, S., Solution procedure for a repair-limit problem using the TTT concept, IMA journal of mathematics applied in business and industry, 6/1, 101-111, (1995) · Zbl 0826.90053
[11] Kalbfleisch, J.D.; Prentice, R.L., The statistical analysis of failure time data, (1990), Wiley New York · Zbl 0504.62096
[12] Kaplan, E.L.; Meier, P., Non-parametric estimation from incomplete observations, Journal of the American statistical association, 53, 457-481, (1958) · Zbl 0089.14801
[13] Klefsjö, B., TTT-transforms — A useful tool when analysing different reliability problems, Reliability engineering, 4, 231-241, (1986)
[14] Kumar, D.; Klefsjö, B., Proportional hazards model: a review, Reliability engineering and system safety, 44, 177-188, (1994)
[15] Kumar, U.; Klefsjö, B.; Granholm, S., Reliability investigation for a fleet of load haul dump machines in a swedish mine, Reliability engineering and system safety, 26, 341-361, (1989)
[16] Love, C.E.; Guo, R., Using proportional hazard modelling in plant maintenance, Quality and reliability engineering international, 7, 7-17, (1991)
[17] Newby, M., A critical look at some point process models for repairable systems, IMA journal of mathematics applied in business and industry, 4, 375-394, (1993) · Zbl 0784.62084
[18] Valdez-Flores, C.; Feldman, R.M., A survey of preventive maintenance models for stochastically deteriorating single-unit system, Naval research logistics, 36, 419-446, (1989) · Zbl 0671.90028
[19] Westberg, U.; Kumar, D., Estimation of the cumulative baseline hazard rate in the proportional hazards model, (), 254-258
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.