New method to minimize the preventive maintenance cost of series – parallel systems R. Bris a , E. Cha ˆtelet b, * , F. Yalaoui c a Department of Applied Mathematics, Technical University of Ostrava, Czech Republic b System Modelling and Dependability Laboratory, University of Technology of Troyes, 12 rue Marie Curie BP 2060, 10010, Troyes Cedex, France c Industrial Systems Optimization Laboratory, University of Technology of Troyes, 12 rue Marie Curie BP 2060, 10010, Troyes Cedex, France Received 15 January 2003; revised 23 April 2003; accepted 26 June 2003 Abstract General preventive maintenance model for input components of a system, which improves the reliability to ‘as good as new,’ was used to optimize the maintenance cost. The cost function of a maintenance policy was minimized under given availability constraint. An algorithm for first inspection vector of times was described and used on selected system example. A special ratio-criterion, based on the time dependent Birnbaum importance factor, was used to generate the ordered sequence of first inspection times. Basic system availability calculations of the paper were done by using simulation approach with parallel simulation algorithm for availability analysis. These calculations, based on direct Monte Carlo technique, were applied within the programming tool Matlab. A genetic algorithm optimization technique was used and briefly described to create the Matlab’s algorithm to solve the problem of finding the best maintenance policy with a given restriction. Adjacent problem, which we called ‘reliability assurance,’ was also theoretically solved, concerning the increase of the cost when asymptotic availability value conforms to a given availability constraint. q 2003 Elsevier Ltd. All rights reserved. Keywords: Preventive maintenance; Cost; Availability; Optimization; Reliability; Monte Carlo 1. Introduction The evolution of system reliability depends on its structure as well as on the evolution of the reliability of its elements. The latter is a function of the element age on a system’s operating life. Element ageing is strongly affected by maintenance activities performed on the system. Preventive maintenance (PM) consists of actions that improve the condition of system elements before they fail. PM actions such as the replacement of an element by a new one, cleaning, adjustment, etc. either return the element to its initial condition and the element becomes ‘as good as new’ or reduce the age of the element. In some cases, the PM activity does not affect the state of the element but ensures that the element is in operating condition. In this case the element remains ‘as bad as old.’ Optimizing the policy of preliminary planned PM actions is the subject of much research activities. In the past, the economic aspects of preventive and corrective maintenance have been extensively studied for monitored components in which failures are immediately detected and subsequently repaired. Far less attention has been paid to the economics of systems in which failures are dormant and detected only by periodic testing or inspections. Such systems are especially common in industrial safety and protection systems. For these kind of systems, both the availability evaluation models and the cost factors assess- ment differ considerably from those of monitored com- ponents [1]. This paper develops availability and cost models for systems with periodically inspected and maintained com- ponents subjected to some maintenance strategy. The aim of our research is to optimize, for each component of a system, the maintenance policy minimizing the cost function, with respect to the availability constraint such as AðtÞ $ A 0 ; for all t; 0 , t # T M ; and a given mission time T M : A genetic algorithm (GA) is used as an optimization technique. GA is used to solve the above-mentioned 0951-8320/$ - see front matter q 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0951-8320(03)00166-2 Reliability Engineering and System Safety 82 (2003) 247–255 www.elsevier.com/locate/ress * Corresponding author. Tel.: þ 33-3-25-71-56-34. E-mail address: chatelet@utt.fr (E. Cha ˆtelet).