Abstract
This chapter is concerned with the basic preventive maintenance policies arising in the context of the mathematical maintenance theory. Simple but practically important preventive maintenance optimization models, which involve age replacement and block replacement, are reviewed in the framework of the well-known renewal reward argument. Some variations to these basic models as well as the corresponding discrete time models are also introduced with the aim of the application of the theory to the practice.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Allen, S. G., and D’Esopo, D. A. An ordering policy for repairable stock items. Ope. Res, 16, (1968) 669–674.
Allen, S. G., and D’Esopo, D. A. An ordering policy for stock items when delivery can be expedited. Ope. Res, 16 (1968) 880–883.
Ansell, J., Bendell, A., and Humble, S. Age replacement under alternative cost criteria. Management Sci, 30 (1984) 358–367.
Arrow, K. J., Karlin, S. and Scarf, H. Studies in Applied Probability and Management Science. Stanford University Press (eds.), Stanford, 1962.
Ascher, H. and Feingold, H. Repairable Systems Reliability. Marcel Dekker, N.Y., 1984.
Aven, T. and Jensen, U. Stochastic Models in Reliability. Springer-Verlag, Berlin, 1999.
Barlow, R. E., Engineering Reliability. SIAM, Berlin, 1998.
Barlow, R. E., and Hunter, L. C. Optimum preventive maintenance policies. Ope. Res, 8 (1960) 90–100.
Barlow, R. E., and Hunter, L. C. Reliability analysis of a one-unit system. Ope. Res, 9 (1961) 200–208.
Barlow, R. E., and Proschan, F. Mathematical Theory of Reliability. John Wiley & Sons, N.Y., 1965.
Barlow, R. E., and Proschan, F. Statistical Theory of Reliability and Life Testing: Probability Models. Holt, Rinehart and Winston, N.Y., 1975.
Beichelt, F. A unifying treatment of replacement policies with minimal repair. Naval Res. Logist, 40 (1993) 51–67.
Berg, M., and Cleroux, R. The block replacement problem with minimal repair and random repair costs. J. Stat. Comp. Simul, 15 (1982) 1–7.
Berg, M., and Epstein, B. A modified block replacement policy. Naval Res. Logis. Quart, 23 (1976) 15–24.
Bergman, B. On the optimality of stationary replacement strategies. J. Appl. Prob, 17 (1980) 178–186.
Block, H. W., Borges, W. S., and Savits, T. H. Age-dependent minimal repair. J. Appl. Prob, 22 (1985) 370–385.
Boland, P. J. Periodic replacement when minimal repair costs vary with time. Naval Res. Logist. Quart, 29 (1982) 541–546.
Boland, P. J., and Proschan, F. Periodic replacement with increasing minimal repair costs at failure. Ope. Res, 30 (1982) 1183–1189.
Christer, A. H. Refined asymptotic costs for renewal reward process. J. Opl. Res. Soc, 29 (1978) 577–583.
Christer, A. H. Comments on finite-period applications of age-based replacement models. IMA J. Math. Appl Busin. Indust, 1, (1987) 111–124.
Christer, A. H. and Jack, N. An integral-equation a roach for replacement modelling over finite time horizons. IMA J. Math. Appl. Busin. Indust, 3, (1991) 31–44.
Christer, A. H., Osaki, S., and Thomas, L. C. Stochastic Modelling in Innovative Manufacturing. Lecture Notes in Economics and Mathematical Systems, 445, Springer-Verlag (eds.), Berlin, 1997.
Cleroux, R., Dubuc, S., and Tilquin, C. The age replacement problem with minimal repair and random repair costs. Ope. Res, 27 (1979) 1158–1167.
Cleroux, R., and Hanscom, M. Age replacement with adjustment and depreciation costs and interest charges. Technometrics, 16 (1974) 235–239.
Derman, C., and Sacks, J. Replacement of periodically inspected equipment. Naval Res. Logist Quart, 7 (1960) 597–607.
Dohi, T., Kaio, N. and Osaki, S. Continuous review cyclic inventory models with emergency order. J. Ope. Res. Soc. Japan, 38, 212–229 (1995).
Dohi, T., Kaio, N. and Osaki, S. On the optimal ordering policies in maintenance theory — survey and applications. Applied Stochastic Models and Data Analysis, 14, 309–321 (1998).
Dohi, T., Shibuya, T. and Osaki, S. Models for 1-out-of-Q systems with stochastic lead times and expedited ordering options for spares inventory. Euro. J. Opl. Res, 103,255–272 (1997).
Feller, W. An Introduction to Probability Theory and Its Applications. NY: John Wiley & Sons 1957.
Fox, B. L. Age replacement with discounting. Ope. Res 14 (1966) 533–537.
Gertsbakh, I. B. Models of Preventive Maintenance. North-Holland, Amsterdam, 1977.
Glasser, G. J. The age replacement problem. Technometrics, 9 (1967) 83–91.
Gnedenko, B. V., Belyayev, Y. K. and Solovyev, A. D. Mathematical Methods of Reliability Theory. Academic Press, N.Y., 1969.
Jorgenson, D. W., McCall, J. J. and Radner, R. Optimal Replacement Policy. North-Holland, Amsterdam, 1967.
Kaio, N. and Osaki, S. Optimum ordering policies with lead time for an operating unit in preventive maintenance. IEEE Trans. Reliab, R-27,(1978) 270–271.
Kaio, N. and Osaki, S. Optimum planned maintenance with salvage costs. Int. J. Prod. Res, 16, 249–257 (1978).
Kaio, N. and Osaki, S. Discrete-time ordering policies. IEEE Trans. Reliab, R-28,405–406 (1979).
Kaio, N. and Osaki, S. Optimum planned maintenance with discounting. Int. J. Prod. Res, 18,515–523 (1980).
Kaio, N., and Osaki, S. Review of discrete and continuous distributions in replacement models. Int. J. Sys. Sci, 19 (1988) 171–177.
Karlin, S., and Taylor, H. M. A First Course in Stochastic Processes. NY: Academic Press, 1975.
Karlin, S., and Taylor, H. M. A Second Course in Stochastic Processes. NY: Academic Press, 1981.
McCall, J. J. Maintenance policies for stochastically failing equipment: a survey. Management Sci, 11 (1965) 493–521.
Morimura, H. On some preventive maintenance policies for IFR. J. Ope. Res. Soc. Japan, 12 (1970) 94–124.
Munter, M. Discrete renewal processes. IEEE Trans. Reliab, R-20 (1971) 46–51.
Nakagawa, T. A summary of discrete replacement policies. Euro. J. Opl. Res, 17 (1979) 382–392.
Nakagawa, T. A summary of periodic replacement with minimal repair at failure. J. Ope. Res. Soc. Japan, 24 (1979) 213–228.
Nakagawa, T. Generalized models for determining optimal number of minimal repairs before replacement. J. Ope. Res. Soc. Japan, 24 (1981a) 325–357.
Nakagawa, T. Modified periodic replacement with minimal repair at failure. IEEE Trans. Reliab, R-30 (1981b) 165–168.
Nakagawa, T. Optimal policy of continuous and discrete replacement with minimal repair at failure. Naval Res. Logist. Quart, 31 (1984) 543–550.
Nakagawa, T. Periodic and sequential preventive maintenance policies. J. Appl. Prob, 23 (1986) 536–542.
Nakagawa, T. Modified discrete preventive maintenance policies. Naval Res. Logist. Quart, 33, 703–715 (1986).
Nakagawa, T., and Kowada, M. Analysis of a system with minimal repair and its Application to replacement policy. Euro. J. Opl. Res, 12 (1983) 176–182.
Nakagawa, T. and Osaki, S. Optimum replacement policies with delay. J. Appl. Prob, 11, (1974) 102–110.
Nakagawa, T. and Osaki, S. Analysis of a repairable system which operates at discrete times. IEEE Trans. Reliab, R-25, 110–112 (1976).
Nakagawa, T., and Osaki, S. Reliability analysis of a one-unit system with unrepairable spare units and its optimization applications. Opl. Res. Quart, 27 (1976) 101–110.
Nakagawa, T., and Osaki, S. Discrete time age replacement policies. Opl. Res. Quart, 28 (1977) 881–885.
Ohnishi, M. Optimal minimal-repair and replacement problem under average cost criterion: optimality of (t, T)-policy. J. Ope. Res. Soc. Japan, 40 (1997) 373–389.
Osaki, S. An ordering policy with lead time. Int. J. Sys. Sci, 8, (1977) 1091–1095.
Osaki, S. Stochastic System Reliability Modeling. World Scientific, Singapore, 1985.
Osaki, S. Applied Stochastic System Modeling. Springer-Verlag, Berlin, 1992.
Osaki, S., and Cao, J. Reliability Theory and Applications. World Scientific (eds.), Berlin, 1987.
Osaki, S., and Hatoyama, Y. Stochastic Models in Reliability Theory. Lecture Notes in Economics and Mathematical Systems, 235,Springer-Verlag (eds.), Berlin, 1984.
Osaki, S., Kaio, N. and Yamada, S. A summary of optimal ordering policies. IEEE Trans. Reliab, R-30,272–277 (1981).
Osaki, S., and Nakagawa, T. A note on age replacement. IEEE Trans. Reliab, R-24 (1975) 92–94.
Osaki, S., and Nakagawa, T. Bibliography for reliability and availability of stochastic systems’. IEEE Trans. Reliab. R-25 (1976) 284–287.
Osaki, S., and Yamada, S. Age replacement with lead time. IEEE Trans. Reliab, R-25 (1976) 344–345.
Ozekici, S. Reliability and Maintenance of Complex Systems. NATO ASI Series, Springer (eds.), Berlin, 1996.
Park, K. S. Optimal number of minimal repairs before replacement. IEEE Trans. Reliab, R-28 (1979) 137–140.
Pierskalla, W. P., and Voelker, J. A. A survey of maintenance models: the control and surveillance of deteriorating systems. Naval Res. Logist. Quart, 23 (1976) 353–388.
Phelps, R.I. Replacement policies under minimal repair. J. Opl. Res. Soc, 32 (1981) 549–554.
Phelps, R.I. Optimal policy for minimal repair. J. Opl. Res. Soc, 34 (1983) 425–427.
Ross, S. M. Applied Probability Models with Optimization Applications, San Francisco: Holden-Day, 1970.
Schaeffer, R.L. Optimum age replacement policies with an increasing cost factor. Technometrix, 13 (1971) 139–144.
Segawa, Y., Ohnishi, M., and Ibaraki, T. Optimal minimal-repair and replacement problem with average dependent cost structure. Computers & Math. Appl, 24 (1992) 91–101.
Sherif, Y. S., and Smith, M. L. Optimal maintenance models for systems subject to failure-a review. Naval Res. Logist. Quart, 28 (1981) 47–74.
Shibuya, T., Dohi, T. and Osaki, S. Spare part inventory models with stochastic lead times. Int. J. Prod. Econ, 55,257–271 (1998).
Simon, R. M., and D’Esopo, D. A. Comments on a paper by S. G. Allen and D. A.D’Esopo: An ordering policy for repairable stock items. Ope. Res, 19, (1971) 986–989.
Tahara, A., and Nishida, T. Optimal replacement policy for minimal repair model. J. Ope. Res. Soc. Japan, 18 (1975) 113–124.
Taylor, H. M., and Karlin, S. An Introduction to Stochastic Modeling. NY: Academic Press, 1984.
Thomas, L. C. and Osaki, S. A note on ordering policy. IEEE Trans. Reliab, R-27, (1978) 380–381.
Thomas, L. C. and Osaki, S. An optimal ordering policy for a spare unit with lead time. Euro. J. Opl. Res, 2, (1978) 409–419.
Tilquin, C., and Cleroux, R. Block replacement with general cost structure. Technometrics, 17 (1975) 291–298.
Tilquin, C., and Clerroux, R. Periodic replacement with minimal repair at failure and adjustment costs. Naval Res. Logist. Quart, 22 (1975) 243–254.
Valdez-Flores, C., and Feldman, R. M. A survey of preventive maintenance models for stochastically deteriorating single-unit systems. Naval Res. Logist, 36, 419–446 (1989).
Wiggins, A. D. A minimum cost model of spare parts inventory control. Technometrics, 9 (1967), 661–665.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer Science+Business Media New York
About this chapter
Cite this chapter
Dohi, T., Kaio, N., Osaki, S. (2000). Basic Preventive Maintenance Policies and their Variations. In: Ben-Daya, M., Duffuaa, S.O., Raouf, A. (eds) Maintenance, Modeling and Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-4329-9_7
Download citation
DOI: https://doi.org/10.1007/978-1-4615-4329-9_7
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-6944-8
Online ISBN: 978-1-4615-4329-9
eBook Packages: Springer Book Archive