Eric Châtelet

New method to minimize the preventive maintenance cost of series -parallel systems

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 Matlabs 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.

New methods to minimize the preventive maintenance cost of series–parallel systems using ant colony optimization

This article is based on a previous study made by Bris, Châtelet and Yalaoui [Bris R, Chatelet E, Yalaoui F. New method to minimise the preventive maintenance cost of series–parallel systems. Reliab Eng Syst Saf 2003;82:247–55]. They use genetic algorithm to minimize preventive maintenance cost problem for the series–parallel systems. We propose to improve their results developing a new method based on another technique, the Ant Colony Optimization (ACO). The resolution consists in determining the solution vector of system component inspection periods, TP. Those calculations were applied within the programming tool Matlab. Thus, highly interesting results and improvements of previous studies were obtained.

Bi-objective optimization algorithms for joint production and maintenance scheduling: application to the parallel machine problem

This paper deals with the joint production and maintenance scheduling problem according to a new bi-objective approach. This method allows the decision maker to find compromise solutions between the production objectives and maintenance ones. Reliability models are used to take into account the maintenance aspect of the problem. The aim is to simultaneously optimize two criteria: the minimization of the makespan for the production part and the minimization of the system unavailability for the maintenance side. Two decisions are taken at the same time: finding the best assignment of n jobs to m machines in order to minimize the makespan and deciding when to carry out the preventive maintenance actions in order to minimize the system unavailability. The maintenance actions numbers as well as the maintenance intervals are not fixed in advance. Two evolutionary genetic algorithms are compared to find an approximation of the Pareto-optimal front in the parallel machine case. On a large number of test instances (more than 5000), the obtained results are promising.

Reliability allocation problem in a series–parallel system

Abstract In order to improve system reliability, designers may introduce in a system different technologies in parallel. When each technology is composed of components in series, the configuration belongs to the series–parallel systems. This type of system has not been studied as much as the parallel–series architecture. There exist no methods dedicated to the reliability allocation in series–parallel systems with different technologies. We propose in this paper theoretical and practical results for the allocation problem in a series–parallel system. Two resolution approaches are developed. Firstly, a one stage problem is studied and the results are exploited for the multi-stages problem. A theoretical condition for obtaining the optimal allocation is developed. Since this condition is too restrictive, we secondly propose an alternative approach based on an approximated function and the results of the one-stage study. This second approach is applied to numerical examples.

Optimization of maintenance policy using the proportional hazard model

The evolution of system reliability depends on its structure as well as on the evolution of its components reliability. The latter is a function of component age during a systems operating life. Component aging is strongly affected by maintenance activities performed on the system. In this work, we consider two categories of maintenance activities: corrective maintenance (CM) and preventive maintenance (PM). Maintenance actions are characterized by their ability to reduce this age. PM consists of actions applied on components while they are operating, whereas CM actions occur when the component breaks down. In this paper, we expound a new method to integrate the effect of CM while planning for the PM policy. The proportional hazard function was used as a modeling tool for that purpose. Interesting results were obtained when comparison between policies that take into consideration the CM effect and those that do not is established.

A practical comparison of methods to assess sum-of-products

Abstract Many methods have been proposed in the literature to assess the probability of a sum-of-products. This problem has been shown computationally hard (namely #P-hard). Therefore, algorithms can be compared only from a practical point of view. In this article, we propose first an efficient implementation of the pivotal decomposition method. This kind of algorithms is widely used in the Artificial Intelligence framework. It is unfortunately almost never considered in the reliability engineering framework, but as a pedagogical tool. We report experimental results that show that this method is in general much more efficient than classical methods that rewrite the sum-of-products under study into an equivalent sum of disjoint products. Then, we derive from our method a factorization algorithm to be used as a preprocessing method for binary decision diagrams. We show by means of experimental results that this latter approach outperforms the formers.

Integrating production, inventory and maintenance planning for a parallel system with dependent components

Abstract This paper deals with the problem of integrating preventive maintenance and tactical production planning, for a production system composed of a set of parallel components, in the presence of economic dependence and common cause failures. Economic dependence means that performing maintenance on several components jointly costs less money and time than on each component separately. Common cause failures correspond to events that lead to simultaneous failure of multiple components due to a common cause. We use the β-factor model to represent common cause failures. This means that we assume two possible causes for system failure: the independent failure of single components, and the simultaneous common cause failure of all components. The suggested preventive maintenance is a T-age group maintenance policy in which components are cyclically renewed all together. Furthermore, between the periodic group replacements, minimal repairs are performed on failed components. We are given a set of products that must be produced by this parallel system in lots during a specified finite planning horizon. The objective is to determine an integrated lot-sizing and preventive maintenance strategy of the system that will minimize the sum of preventive and corrective maintenance costs, setup costs, holding costs, backorder costs and production costs, while satisfying the demand for all products over the entire horizon. Numerical examples are used to illustrate the proposed approach.

Joint redundancy and imperfect preventive maintenance optimization for series–parallel multi-state degraded systems

Abstract This paper formulates a joint redundancy and imperfect preventive maintenance planning optimization model for series–parallel multi-state degraded systems. Non identical multi-state components can be used in parallel to improve the system availability by providing redundancy in subsystems. Multiple component choices are available in the market for each subsystem. The status of each component is considered to degrade with use. The objective is to determine jointly the maximal-availability series–parallel system structure and the appropriate preventive maintenance actions, subject to a budget constraint. System availability is defined as the ability to satisfy consumer demand that is represented as a piecewise cumulative load curve. A procedure is used, based on Markov processes and universal moment generating function, to evaluate the multi-state system availability and the cost function. A heuristic approach is also proposed to solve the formulated problem. This heuristic is based on a combination of space partitioning, genetic algorithms (GA) and tabu search (TS). After dividing the search space into a set of disjoint subsets, this approach uses GA to select the subspaces, and applies TS to each selected sub-space.

Connecting a population dynamic model with a multi-period location-allocation problem for post-disaster relief operations

In this study, we propose a mathematical model and heuristics for solving a multi-period location-allocation problem in post-disaster operations, which takes into account the impact of distribution over the population. Logistics restrictions such as human and financial resources are considered. In addition, a brief review on resilience system models is provided, as well as their connection with quantitative models for post-disaster relief operations. In particular, we highlight how one can improve resilience by means of OR/MS strategies. Then, a simpler resilience schema is proposed, which better reflects an active system for providing humanitarian aid in post-disaster operations, similar to the model focused in this work. The proposed model is non-linear and solved by a decomposition approach: the master level problem is addressed by a non-linear solver, while the slave subproblem is treated as a black-box coupling heuristics and a Variable Neighborhood Descent local search. Computational experiments have been done using several scenarios, and real data from Belo Horizonte city in Brazil.

An efficient process to reduce infrastructure vulnerabilities facing malevolence

Abstract In daily life, we are all used to frequent ‘systems’: public transports, industrial parks, shopping areas, stadiums or many others. And with the exponential increase of technologies, we are now living in a kind of ‘open World’ within which goods, persons or information are moving increasingly faster. The consequence is an amazing new way of life and also a number of new threats for our society. To insure the security of all citizens, and also of infrastructures, national skills or anything else, we need to secure our systems efficiently. To do so, we need appropriate tools to accurately analyze vulnerabilities in order to counter all kinds of malevolence. After giving an overview of different methods linked to that problem, we will explain our process to analyze the vulnerabilities of a complex infrastructure and what points are fundamental to take into account facing human aggressions.