Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-14T05:57:14.775Z Has data issue: false hasContentIssue false
  • English
  • Français

A weak derivative approach to optimization of threshold parameters in a multicomponent maintenance system

Part of: Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Bernd Heidergott
Bernd Heidergott*
Affiliation:
EURANDOM
*
∗ Postal address: EURANDOM, PO Box 513, 5600MB Eindhoven, The Netherlands. Email address: heidergott@eurandom.tue.nl
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider a multicomponent maintenance system controlled by an age replacement policy: when one of the components fails, it is immediately replaced; all components older than a threshold age θ are preventively replaced. Costs are associated with each maintenance action, such as replacement after failure or preventive replacement. We derive a weak derivative estimator for the derivative of the cost performance with respect to θ. The technique is quite general and can be applied to many other threshold optimization problems in maintenance. The estimator is easy to implement and considerably increases the efficiency of a Robbins-Monro type of stochastic approximation algorithm. The paper is self-contained in the sense that it includes a proof of the correctness of the weak derivative estimation algorithm.

Keywords

maintenanceweak derivativesoptimizationsimulation

MSC classification

Primary: 90B25: Reliability, availability, maintenance, inspection
Secondary: 90C31: Sensitivity, stability, parametric optimization
Type
Research Papers
Information
Journal of Applied Probability , Volume 38 , Issue 2 , June 2001 , pp. 386 - 406
Copyright
Copyright © Applied Probability Trust 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

Brémaud, P. and Vázquez-Abad, F. (1994). On the path-wise computation of derivatives with respect to the rate of a point process: the phantom RPA method. Queueing Systems 10, 249–270.CrossRefGoogle Scholar
Cho, D., and Parlar, M. (1991). A survey of maintenance models for multi-unit systems. Eur. J. Operat. Res. 51, 1–23.CrossRefGoogle Scholar
Dekker, R. (1995). Integrating optimization, priority setting, planning and combining of maintenance activities. Eur. J. Operat. Res. 82, 225–240.CrossRefGoogle Scholar
Dekker, R., van der Meer, R., Plasmeijer, R., Wildeman, R., and de Bruin, J. (1998). Maintenance of light standards, a case–study. J. Operat. Res. Soc. 49, 132–143.CrossRefGoogle Scholar
Fu, M., and Hu, J.-Q. (1993). An application of perturbation analysis to a replacement problem in maintenance theory. In Proc. 1993 Winter Simulation Conf., eds Evans, G., Mollaghasemi, M., Russell, E. and Biles, W., pp. 329–337.Google Scholar
Fu, M., and Hu, J.-Q. (1997). Conditional Monte Carlo: Gradient Estimation and Optimization Applications. Kluwer, Boston.CrossRefGoogle Scholar
Kushner, H., and Clark, D. (1978). Stochastic Approximation Methods for Constrained and Unconstrained Systems. Springer, New York.CrossRefGoogle Scholar
L'Écuyer, P. and Vázquez-Abad, F. (1997). Functional estimation with respect to a threshold parameter via dynamic split and merge. Discrete Event Dynamic Systems 7, 69–92.CrossRefGoogle Scholar
Meyn, S., and Tweedie, R. (1993). Markov Chains and Stochastic Stability. Springer, London.CrossRefGoogle Scholar
Pflug, G. (1988). Derivatives of probability measures-concepts and applications to the optimization of stochastic systems. In Discrete Event Systems: Models and Applications (Lecture Notes Control Inf. Sci. 103), eds Varaiya, P. and Kurzhanskii, A. B. Springer, Berlin, pp. 252–274.CrossRefGoogle Scholar
Pflug, G. (1990). On-line optimization of simulated Markovian processes. Math. Operat. Res. 15, 381–395.CrossRefGoogle Scholar
Pflug, G. (1992). Gradient estimates for the performance of Markov chains and discrete event processes. Ann. Operat. Res. 39, 173–194.CrossRefGoogle Scholar
Pflug, G. (1996). Optimization of Stochastic Models. Kluwer, Boston.CrossRefGoogle Scholar
Thorisson, H. (2000). Coupling, Stationarity, and Regeneration. Springer, New York.CrossRefGoogle Scholar
Vázquez-Abad, F., L'Écuyer, P., and Martin, B. (1996). On the linear growth of the split-and-merge simulation tree for a multicomponent age replacement model. In Proc. Discrete Event Systems, eds Smedinga, R., Spathopoulos, M. P. and Kozák, P. IEE, London, pp. 449–455.Google Scholar