Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-11T01:19:41.021Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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.