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The Lorenz Transform approach to the Optimal Repair-Cost limit remplacement Policy with Imperfect Repair

Published online by Cambridge University Press:  15 August 2002

T. Dohi ,
F. S. Othman ,
N. Kaio  and
Sunji Osaki
T. Dohi
Affiliation:
Department of Industrial and Systems Engineering, Hiroshima University, 4-1 Kagamiyama 1 Chome, Higashi-Hiroshima 739-8527, Japan; osaki@gal.sys.hiroshima-u.ac.jp.
F. S. Othman
Affiliation:
Department of Industrial and Systems Engineering, Hiroshima University, 4-1 Kagamiyama 1 Chome, Higashi-Hiroshima 739-8527, Japan; osaki@gal.sys.hiroshima-u.ac.jp.
N. Kaio
Affiliation:
Department of Economic Informatics, Hiroshima Shudo University, 1-1-1 Ozukahigashi, Asaminami-ku, Hiroshima 731-3195, Japan.
Sunji Osaki
Affiliation:
Department of Industrial and Systems Engineering, Hiroshima University, 4-1 Kagamiyama 1 Chome, Higashi-Hiroshima 739-8527, Japan; osaki@gal.sys.hiroshima-u.ac.jp.
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Abstract

In this paper, we consider a repair-cost limit replacement problem with imperfect repair and develop a graphical method to determine the optimal repair-cost limit which minimizes the expected cost per unit time in the steady-state, using the Lorenz transform of the underlying repair-cost distribution function. The method proposed can be applied to an estimation problem of the optimal repair-cost limit from empirical repair-cost data. Numerical examples are devoted to examine asymptotic properties of the non-parametric estimator for the optimal repair-cost limit.

Keywords

Repair-cost limitimperfect repairLorenz transformnonparametric estimationmaintenance policy.
Type
Research Article
Information
RAIRO - Operations Research , Volume 35 , Issue 1 , January 2001 , pp. 21 - 36
Copyright
© EDP Sciences, 2001

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References

Bergman, B., Age Replacement, On and the Total Time on Test Concept. Scand. J. Statist. 6 (1979) 161-168.
Bergman, B. and Klefsj, B. ö, The Total Time on Test Concept and Its Use in Reliability Theory. Oper. Res. 32 (1984) 596-607. CrossRef
Chandra, M. and Singpurwalla, N.D., Relationship between Some Notions Which Are Common to Reliability and Economics. Math. Oper. Res. 6 (1981) 113-121. CrossRef
Dohi, T., Matsushima, M., Kaio, N. and Osaki, S., Nonparametric Repair-Limit Replacement Policies with Imperfect Repair. European J. Oper. Res. 96 (1996) 206-273.
T. Dohi, H. Koshimae, N. Kaio and S. Osaki, Geometrical Interpretations of Repair-Cost Limit Replacement Policies. International Journal of Reliability, Quality and Safety Engineering 4 (1997) 309-333.
Drinkwater, R.W. and Hastings, N.A.J., Economical Replacement Model, An. Oper. Res. Quarterly 18 (1967) 121-138. CrossRef
Gastwirth, J.L., General De, Afinition of the Lorenz Curve. Econometrica 39 (1971) 1037-1039. CrossRef
Goldie, C.M., Convergence Theorems for Empirical Lorenz Curves and Their Inverses. Adv. in Appl. Probab. 9 (1977) 765-791. CrossRef
Hastings, N.A.J., The Repair Limit Replacement Method. Oper. Res. Quarterly 20 (1969) 337-349. CrossRef
Kaio, N. and Osaki, S., Optimum Repair Limit Policies with Cost Constraint. Microelectronics and Reliability 21 (1981) 597-599. CrossRef
Klefsj, B. ö, Reliability Interpretations of Some Concepts from Economics. Naval Res. Logist. Quarterly 31 (1984) 301-308. CrossRef
L.M. Lee, Reliability: Probabilistic Models and Statistical Methods. Prentice-Hall, New Jersey (1985).
Lorenz, M.O., Methods of Measuring the Concentration of Wealth. J. Amer. Statist. Assoc. 9 (1893) 209-219.
Love, C.E., Rodger, R. and Blazenko, G., Repair Limit Policies for Vehicle Replacement. INFOR 20 (1982) 226-237.
Love, C.E. and Guo, R., Utilizing Weibull Failure Rates in Repair Limit Analysis for Equipment Replacement/Preventive Maintenance Decisions. J. Oper. Res. Soc. 47 (1996) 1366-1376. CrossRef
Nakagawa, T. and Osaki, S., Optimum Ordering Policies with Lead Time for an Operating Unit. RAIRO Oper. Res. 12 (1978) 383-393. CrossRef
Nguyen, D.G. and Murthy, D.N.P., Note, A on the Repair Limit Replacement Policy. J. Oper. Res. Soc. 31 (1980) 1103-1104. CrossRef
Nguyen, D.G. and Murthy, D.N.P., Optimal Repair Limit Replacement Policies with Imperfect Repair. J. Oper. Res. Soc. 32 (1981) 409-416. CrossRef
Park, K.S., Cost Limit Replacement Policy under Minimal Repair. Microelectronics and Reliability 23 (1983) 347-349. CrossRef
Perez-Ocon, R., Gamiz-Perez, M.L. and Ruiz-Castro, J.E., Study, A of Different Aging Classes via Total Time on Test Transform and Lorenz Curves. Appl. Stochastic Models Data Anal. 13 (1998) 241-248. 3.0.CO;2-D>CrossRef
T.G. Pham and N. Turkkan, The Lorenz and the Scaled Total-Time-on-Test Transform Curves: A Unified Approach. IEEE Trans. Reliability R-43 (1994) 76-84.