Nidhal Rezg

Design of a live and maximally permissive Petri net controller using the theory of regions

This paper addresses the forbidden state problem of Petri nets (PN) with liveness requirement and uncontrollable transitions. The proposed approach computes a maximally permissive PN controller, whenever such a controller exists. The first step, based on a Ramadge-Wonham-like reasoning (1989), determines the legal and live maximal behavior the controlled PN should have. In the second step, the theory of regions is used to design control places to add to the original model to realize the desired behavior. Furthermore, necessary and sufficient conditions for the existence of control places realizing the maximum permissive control are given. A parameterized manufacturing application of significant state space is used to show the efficiency of the proposed approach.

Joint optimization of preventive maintenance and inventory control in a production line using simulation

This paper proposes an integrated method for preventive maintenance and inventory control of a production line, composed of n machines (n ≥ 1) without intermediate buffers. The machines are subject to failures and an age-dependent preventive maintenance policy is used. Approximate analytical results are proposed for the one machine case. Simulation software is used to model and simulate the behaviour of the production line of n machines under various maintenance and inventory control strategies. A methodology combining the simulation and genetic algorithms is proposed jointly to optimize maintenance and inventory control policies. Results are compared with the analytical solutions.

Feedback control logic for forbidden-state problems of marked graphs: application to a real manufacturing system

This paper addresses the forbidden-state problem of general marked graphs with uncontrollable transitions. The models need not to be safe nor cyclic. Control requirements are expressed as the conjunction of general mutual exclusion constraints (GMEC) of markings of so-called critical places. Structural properties such as influence paths and influence zones are proposed to perform the worst-case analysis for each GMEC specification with any given initial marking when only uncontrollable transitions are allowed. Efficient solutions are proposed for the determination of the maximal uncontrollably reachable marking of any critical place, and this for many possible, more or less general, configurations of the net structure, even for the case of overlapping paths of critical places. Besides, we demonstrate that these results can be easily extended to unbounded nets and when critical places have negative weights. For the most general case, when analytical solution is not available, a linear programming approach is proposed. The great advantage of the proposed approach over existing methods is emphasized by using it to solve the supervisory control problem of the automated manufacturing system of Atelier Inter-etablissements de Productique Rhone Alpes Ouest (AIP-RAO), Lyon, France.

Modeling and optimizing a joint inventory control and preventive maintenance strategy for a randomly failing production unit: Analytical and simulation approaches

This paper presents a joint optimal inventory control and preventive maintenance strategy for a randomly failing production unit which supplies an assembly line operating according to a just-in-time configuration. The production unit is submitted to a maintenance action as soon as it reaches a certain age T or at failure; whichever occurs first. In order to palliate perturbations caused by breakdowns and by planned maintenance actions both with random durations, a buffer stock is built up to ensure the supply of the assembly line at a constant rate. A mathematical model is developed to evaluate the average cost per time unit of the proposed strategy. Due to the complexity of the mathematical model and to some approximation assumptions, a second approach based on simulation and experimental design is developed. It allows us to simulate the proposed policy and to generate a second order response surface for easy computation of the optimal values of the decision variables which are the age T at which preventive maintenance must be performed, and the buffer stock level h.

Integrated model of preventive maintenance, quality control and buffer sizing for unreliable and imperfect production systems

In this paper, we develop a joint quality control and preventive maintenance policy for a randomly failing production system producing conforming and non-conforming units. The considered system consists of one machine designed to fulfil a constant demand. According to the proportion l of non-conforming units observed on each lot and compared to a threshold value lm, one decides to undertake or not maintenance actions on the system. In order to palliate perturbations caused by the stopping of the machine to undergo preventive maintenance or an overhaul, a buffer stock h is built up to ensure the continuous supply of the subsequent production line. A mathematical model is developed and combined with simulation in order to determine simultaneously the optimal rate, and the optimal size h* which minimize the expected total cost per time unit including the average costs related to maintenance, quality and inventory.

Preventive maintenance of manufacturing systems under environmental constraints

The paper describes a new preventive maintenance approach for manufacturing systems under environment constraints. The manufacturing system under consideration consists of a machine M1 that produces a single product in a Just-in-Time context. To satisfy a constant demand d, the system called upon another machine M2 (the subcontractor), comprising the so-called environment, which produces at a certain rate the same type of product as M1. Both machines are subjected to random failures. Whereas machine M2 is uncontrollable from the maintenance point of view, an age-limit policy is used for preventive maintenance of machine M1. It is proved that the best age to perform preventive maintenance depends on the history of machine M1 and the state of M2. A numerical example is used to illustrate the proposed approach.

Joint optimal inventory control and preventive maintenance policy

This paper investigates an integrated strategy of inventory control and preventive maintenance for a randomly failing production unit subject to a minimum required availability level. The production unit is submitted to a maintenance action as soon as it reaches a certain age m or at failure, whichever occurs first. A buffer stock h is built up at time A from the start of a production cycle in order to allow a continuous supply of the subsequent production unit at a constant rate during repair and preventive maintenance actions whose respective durations are random. A mathematical model and a numerical procedure are developed to find simultaneously the optimal values of the three decision variables (m*, h*, A*) which minimize the total average cost per time unit and satisfy the availability constraint.

Optimal selective renewal policy for systems subject to propagated failures with global effect and failure isolation phenomena

This paper considers a selective maintenance policy for multi-component systems for which a minimum level of reliability is required for each mission. Such systems need to be maintained between consecutive missions. The proposed strategy aims at selecting the components to be maintained (renewed) after the completion of each mission such that a required reliability level is warranted up to the next stop with the minimum cost, taking into account the time period allotted for maintenance between missions and the possibility to extend it while paying a penalty cost. This strategy is applied to binary-state systems subject to propagated failures with global effect, and failure isolation phenomena. A set of rules to reduce the solutions space for such complex systems is developed. A numerical example is presented to illustrate the modeling approach and the use of the reduction rules. Finally, the Monte-Carlo simulation is used in combination with the selective maintenance optimization model to deal with a number of successive missions.

Simultaneous determination of production lot size and preventive maintenance schedule for unreliable production system

Purpose – The purpose of this study is to propose and model an integrated production‐maintenance strategy for unreliable production systems producing conforming and non‐conforming items.Design/methodology/approach – The proposed integrated policy is defined and modeled mathematically.Findings – The paper focuses on finding simultaneously the optimal values of the lot size Q and the age T at which preventive maintenance must be performed. These values minimize the total average cost per time unit over an infinite horizon.Practical implications – The paper attempts to integrate in a single model the three main aspects of any manufacturing system: production, maintenance, and quality. It deals with the lot‐sizing problem for a production system which may randomly shift to an out‐of‐control state and produce non‐conforming units. The system is submitted to an age‐based preventive maintenance policy. The effect of performing preventive maintenance on quality‐ and inventory‐related costs is shown through a nume...

Periodic and sequential preventive maintenance policies over a finite planning horizon with a dynamic failure law

The purpose of this study is to propose and model periodic and sequential preventive maintenance policies for a system that performs various missions over a finite planning horizon. Each mission can have different characteristics that depend on operational and environmental conditions. These proposed preventive maintenance policies are defined and modeled mathematically. The study of these two policies is based on a dynamic system failure law that takes into account the different missions performed. The first step is to determine the optimal business plan to achieve, i.e. the set of missions to perform in order to maximize the profit of missions minus maintenance costs. Thus, for each plan, we determine the maintenance planning considering two policies. The first preventive maintenance policy is periodic and the objective is to determine the optimal number of preventive maintenance to achieve. For the second policy, namely sequential, we calculate the optimal number of preventive maintenance intervals and the duration of these different intervals.