The Lorenz transform approach to the optimal repair-cost limit replacement policy with imperfect repair

T. Dohi; F. S. Othman; N. Kaio; Sunji Osaki

RAIRO - Operations Research - Recherche Opérationnelle (2001)

  • Volume: 35, Issue: 1, page 21-36
  • ISSN: 0399-0559

Abstract

top
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.

How to cite

top

Dohi, T., et al. "The Lorenz transform approach to the optimal repair-cost limit replacement policy with imperfect repair." RAIRO - Operations Research - Recherche Opérationnelle 35.1 (2001): 21-36. <http://eudml.org/doc/105236>.

@article{Dohi2001,
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.},
author = {Dohi, T., Othman, F. S., Kaio, N., Osaki, Sunji},
journal = {RAIRO - Operations Research - Recherche Opérationnelle},
keywords = {repair-cost limit; imperfect repair; Lorenz transform; nonparametric estimation; maintenance policy},
language = {eng},
number = {1},
pages = {21-36},
publisher = {EDP-Sciences},
title = {The Lorenz transform approach to the optimal repair-cost limit replacement policy with imperfect repair},
url = {http://eudml.org/doc/105236},
volume = {35},
year = {2001},
}

TY - JOUR
AU - Dohi, T.
AU - Othman, F. S.
AU - Kaio, N.
AU - Osaki, Sunji
TI - The Lorenz transform approach to the optimal repair-cost limit replacement policy with imperfect repair
JO - RAIRO - Operations Research - Recherche Opérationnelle
PY - 2001
PB - EDP-Sciences
VL - 35
IS - 1
SP - 21
EP - 36
AB - 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.
LA - eng
KW - repair-cost limit; imperfect repair; Lorenz transform; nonparametric estimation; maintenance policy
UR - http://eudml.org/doc/105236
ER -

References

top
  1. [1] B. Bergman, On Age Replacement and the Total Time on Test Concept. Scand. J. Statist. 6 (1979) 161-168. Zbl0422.62084MR555079
  2. [2] B. Bergman and B. Klefsjö, The Total Time on Test Concept and Its Use in Reliability Theory. Oper. Res. 32 (1984) 596-607. Zbl0546.62070MR756006
  3. [3] M. Chandra and N.D. Singpurwalla, Relationship between Some Notions Which Are Common to Reliability and Economics. Math. Oper. Res. 6 (1981) 113-121. Zbl0496.90041MR618968
  4. [4] T. Dohi, M. Matsushima, N. Kaio and S. Osaki, Nonparametric Repair-Limit Replacement Policies with Imperfect Repair. European J. Oper. Res. 96 (1996) 206-273. Zbl0917.90138
  5. [5] 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. 
  6. [6] R.W. Drinkwater and N.A.J. Hastings, An Economical Replacement Model. Oper. Res. Quarterly 18 (1967) 121-138. 
  7. [7] J.L. Gastwirth, A General Definition of the Lorenz Curve. Econometrica 39 (1971) 1037-1039. Zbl0245.62082
  8. [8] C.M. Goldie, Convergence Theorems for Empirical Lorenz Curves and Their Inverses. Adv. in Appl. Probab. 9 (1977) 765-791. Zbl0383.60003MR478267
  9. [9] N.A.J. Hastings, The Repair Limit Replacement Method. Oper. Res. Quarterly 20 (1969) 337-349. 
  10. [10] N. Kaio and S. Osaki, Optimum Repair Limit Policies with Cost Constraint. Microelectronics and Reliability 21 (1981) 597-599. 
  11. [11] B. Klefsjö, Reliability Interpretations of Some Concepts from Economics. Naval Res. Logist. Quarterly 31 (1984) 301-308. Zbl0538.90027
  12. [12] L.M. Lee, Reliability: Probabilistic Models and Statistical Methods. Prentice-Hall, New Jersey (1985). MR1320503
  13. [13] M.O. Lorenz, Methods of Measuring the Concentration of Wealth. J. Amer. Statist. Assoc. 9 (1893) 209-219. 
  14. [14] C.E. Love, R. Rodger and G. Blazenko, Repair Limit Policies for Vehicle Replacement. INFOR 20 (1982) 226-237. Zbl0501.90042
  15. [15] C.E. Love and R. Guo, Utilizing Weibull Failure Rates in Repair Limit Analysis for Equipment Replacement/Preventive Maintenance Decisions. J. Oper. Res. Soc. 47 (1996) 1366-1376. Zbl0863.90069
  16. [16] T. Nakagawa and S. Osaki, Optimum Ordering Policies with Lead Time for an Operating Unit. RAIRO Oper. Res. 12 (1978) 383-393. Zbl0402.90047MR516516
  17. [17] D.G. Nguyen and D.N.P. Murthy, A Note on the Repair Limit Replacement Policy. J. Oper. Res. Soc. 31 (1980) 1103-1104. Zbl0444.90042MR603209
  18. [18] D.G. Nguyen and D.N.P. Murthy, Optimal Repair Limit Replacement Policies with Imperfect Repair. J. Oper. Res. Soc. 32 (1981) 409-416. Zbl0452.90031MR612693
  19. [19] K.S. Park, Cost Limit Replacement Policy under Minimal Repair. Microelectronics and Reliability 23 (1983) 347-349. 
  20. [20] R. Perez–Ocon, M.L. Gamiz–Perez and J.E. Ruiz–Castro, A Study of Different Aging Classes v i a Total Time on Test Transform and Lorenz Curves. Appl. Stochastic Models Data Anal. 13 (1998) 241-248. Zbl0913.60076
  21. [21] 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. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.