Abstract
A commonly used definition of a repairable system (Ascher and Feingold 1984) states that this is a system which, after failing to perform one or more of its functions satisfactorily, can be restored to fully satisfactory performance by any method other than replacement of the entire system. In order to cover more realistic applications, and to cover much recent literature on the subject, we need to extend this definition to include the possibility of additional maintenance actions which aim at servicing the system for better performance. This is referred to as preventive maintenance (PM), where one may further distinguish between condition based PM and planned PM. The former type of maintenance is due when the system exhibits inferior performance while the latter is performed at predetermined points in time.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
10.6 References
Aalen OO, (1988) Heterogeneity in survival analysis. Statistics in Medicine 7:1121–1137.
Andersen P, Borgan O, Gill R, Keiding, N, (1993) Statistical Models Based on Counting Processes. Springer, New York.
Ascher H, Feingold H, (1984) Repairable Systems — Modeling, inference, misconceptions and their causes. Marcel Dekker, New York.
Bedford T, Cooke RM, (2001) Probabilistic Risk Analysis: Foundations and Methods; Cambridge University Press: Cambridge.
Bhattacharjee M, Arjas E, Pulkkinen, U, (2003) Modeling heterogeneity in nuclear power plant valve failure data. In: Mathematical and Statistical Methods in Reliability (Lindqvist BH, Doksum KA, eds.) World Scientific Publishing, Singapore, pp 341–353.
Brown M, Proschan F, (1983) Imperfect repair. Journal of Applied Probability 20:851–859.
Cook RJ, Lawless JF, (2002) Analysis of repeated events. Statistical Methods in Medical Research 11:141–166.
Cooke RM, (1993) The total time on test statistics and age-dependent censoring. Statistics and Probability Letters 18:307–312.
Cooke RM, (1996). The design of reliability databases, Part I and II. Reliability Engineering and System Safety 51:137–146 and 209–223.
Crowder MJ, (2001) Classical competing risks. Chapman & Hall/CRC, Boca Raton.
Crowder MJ, (2004) Competing risks. In: Encyclopedia of actuarial science (Teugels JL, Sundt B, eds.) Wiley, Chichester, pp. 305–313.
Crowder MJ, Kimber AC, Smith RL, Sweeting TJ, (1991) Statistical Analysis of Reliability Data. Chapman & Hall, Great Britain.
Doyen L, Gaudoin O, (2006) Imperfect maintenance in a generalized competing risks framework. Journal of Applied Probability 43:825–839.
Follmann DA, Goldberg MS, (1988) Distinguishing heterogeneity from decreasing hazard rate. Technometrics 30:389–396.
Hokstad P, Frøvig AT, (1996) The modelling of degraded and critical failures for components with dormant failures. Reliability Engineering and System Safety 51:189–199.
Hougaard P, (1984) Life table methods for heterogeneous populations: Distributions describing the heterogeneity. Biometrika 71:75–83.
Langseth H, Lindqvist BH, (2003) A maintenance model for components exposed to several failure mechanisms and imperfect repair. In: Mathematical and Statistical Methods in Reliability (Lindqvist BH, Doksum KA, eds.). World Scientific Publishing, Singapore, pp 415–430.
Langseth H, Lindqvist BH, (2006) Competing risks for repairable systems: A data study. Journal of Statistical Planning and Inference 136:1687–1700.
Lawless JF, (1987) Regression methods for Poisson process data. Journal of American Statistical Association 82:808–815.
Lindqvist BH, (2006) On the statistical modelling and analysis of repairable systems. Statistical Science 21:532–551.
Lindqvist BH, Amundrustad H, (1998) Markov models for periodically tested components. In: Safety and Reliability. Proceedings of the European Conference on Safety and Reliability-ESREL’ 98 (Lydersen S, Hansen GK, Sandtorv HA). AA Balkema, Rotterdam, pp 191–197.
Lindqvist BH, Langseth H, (2005) Statistical modelling and inference for component failure times under preventive maintenance and independent censoring. In: Modern Statistical and Mathematical Methods in Reliability (Wilson A, Limnios N, Keller-McNulty S, Armijo Y). World Scientific Publishing, Singapore, pp. 323–337.
Lindqvist BH, Elvebakk G, Heggland K, (2003) The trend-renewal process for statistical analysis of repairable systems. Technometrics 45:31–44.
Lindqvist BH, Støve B, Langseth H, (2006) Modelling of dependence between critical failure and preventive maintenance: The repair alert model. Journal of Statistical Planning and Inference 136:1701–1717.
Meeker WQ, Escobar LA, (1998) Statistical methods for reliability data. Wiley, New York.
Nelson W, (1995) Confidence limits for recurrence data — applied to cost or number of product reapair. Technometrics 37:147–157.
Peña EA, (2006) Dynamic modelling and statistical analysis of event times. Statistical Science 21:487–500.
Proschan F, (1963) Theoretical explanation of observed decreasing failure rates. Technometrics 5:375–383.
Rausand M, Høyland A, (2004) System reliability theory: Models, statistical methods, and applications. 2nd ed. Wiley-Interscience, Hoboken, N.J.
Ross SM, (1983) Stochastic Processes. Wiley, New York.
Taylor HM, Karlin S, (1984) An introduction to stochastic modeling. Academic Press, Orlando.
Vaupel JW, Manton KG, Stallard E, (1979) The impact of heterogeneity in individual frailty on the dynamics of mortality. Demography 16:439–454.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag London Limited
About this chapter
Cite this chapter
Lindqvist, B.H. (2008). Maintenance of Repairable Systems. In: Complex System Maintenance Handbook. Springer Series in Reliability Engineering. Springer, London. https://doi.org/10.1007/978-1-84800-011-7_10
Download citation
DOI: https://doi.org/10.1007/978-1-84800-011-7_10
Publisher Name: Springer, London
Print ISBN: 978-1-84800-010-0
Online ISBN: 978-1-84800-011-7
eBook Packages: EngineeringEngineering (R0)