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Optimal periodic inspection policy for systems generating environmental damage over a finite time horizon

Lazhar Tlili (University of Tunis El Manar, National Engineering School of Tunis, CEREP, Tunis, Tunisia)
Mehdi Radhoui (University of Carthage, National Engineering School of Carthage, CEREP, Tunis, Tunisia)
Anis Chelbi (University of Tunis, National Higher Engineering School of Tunis, CEREP, Tunis, Tunisia)

Journal of Quality in Maintenance Engineering

ISSN: 1355-2511

Article publication date: 10 October 2016




The authors consider systems that generate damage to environment as they get older and degrade. The purpose of this paper is to develop an optimal condition-based maintenance strategy for such systems in situations where they have a finite operational time requirement. The authors determine simultaneously the optimal number of inspections and the threshold level of environmental damage which minimize the total expected cost over the considered finite time horizon.


The environmental degradation level is monitored through periodic inspections. The authors model the environmental degradation process due to the equipment’s degradation by the Wiener process. A mathematical model and a numerical procedure are developed. Numerical calculations are performed and the influence of the variation of key parameters on the optimal solution is investigated.


Numerical tests indicate that as the cost of the penalty related to the generation of an excess damage to environment increases, inspections should become more frequent and the threshold level should be lowered in order to favor preventive actions reducing the probability to pay the penalty.

Research limitations/implications

Given the complexity of the cost function to be minimized, it is difficult to derive analytically the optimal solution. A numerical procedure is designed to obtain the optimal condition-based maintenance policy. Also, the developed model is based on the assumption that the degradation follows a process with stationary independent increments. This may not be appropriate for all types of degradation processes.

Practical implications

The proposed optimal maintenance policy may be relevant and very useful in the perspective of green operations. In fact, this paper offers to decision-makers a comprehensive approach to implement a green maintenance policy and to rapidly understand the net effect of the maintenance policy with respect to environmental regulation requirements.


The main contribution consists in the modeling and optimization of the condition-based maintenance policy over a finite time horizon. Indeed, existing condition-based maintenance models over an infinite time horizon are not applicable for systems with a finite operational time requirement.



Tlili, L., Radhoui, M. and Chelbi, A. (2016), "Optimal periodic inspection policy for systems generating environmental damage over a finite time horizon", Journal of Quality in Maintenance Engineering, Vol. 22 No. 4, pp. 453-467.



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Copyright © 2016, Emerald Group Publishing Limited

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