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The purpose of this study is to develop a joint production, maintenance and quality control strategy involving a periodic preventive maintenance policy.

The proposed integrated policy is defined and modeled mathematically.

The paper focuses on finding simultaneously the optimal values of the preventive maintenance period, the buffer stock size, the sample size, the sampling interval and the control chart limits, such that the expected total cost per time unit is minimized.

The paper attempts to integrate in a single model the three main aspects of any manufacturing system: production, maintenance and quality. The considered system consists of one machine subject to a degradation process that directly affects the quality of products. The process and product quality control is carried out using an “x-bar” control chart. In the proposed model, a preventive maintenance action is performed every α inspections of product quality in order to reduce the shift rate to the “out-of-control” state. A corrective maintenance action is undertaken once the control limits are exceeded. In order to palliate perturbations caused by the stopping of the machine to undergo maintenance actions, a buffer stock is built up to ensure the continuous supply of the subsequent machine. The main goal of this work is to develop a model that captures the underlying link between the preventive maintenance policy, the buffer stock size and the parameters of an “x-bar” control chart used to control the quality of the product. Numerical experiments and a study of the effects of the input parameters variation on the obtained results are performed.

The existing models that simultaneously consider maintenance, inventory and control charts consist of a condition-based maintenance (CBM) policy. Periodic preventive maintenance (PM) has not been considered in such models. The proposed integrated model is original, in that it links production through buffer stocks, quality through a control chart and maintenance through periodic preventive maintenance (different practical settings and modeling approach than when CBM is used). Hence, this paper addresses practical situations where, for economic or technical reasons, only systematic periodic preventive maintenance is possible.

The purpose of this paper is to deal with the problem of integration of production and maintenance policies. In this context, the authors consider production systems made of parallel machines producing a single product over a finite horizon made of equal periods for which a forecasted demand is known. The authors investigate the impact of switching production in case of failure of any given machine.

A mathematical model is first developed to find an optimal production plan which minimizes the average total storage, shortage and production costs. Then, using this optimal production plan and taking into account the influence of the production rate on the degradation of each machine, optimal preventive maintenance (PM) policies are proposed for the situations with and without switching.

Optimal production rates are determined for each production period and for each machine. Optimal PM periods are also computed for each machine.

Usually, in manufacturing systems, the production rate of a machine influences its failure rate. In case a machine fails, it takes a random time to repair it during which production is lost. The paper attempts to propose a switching policy (SP) according to which the lost production is compensated by all the other machines. The effects of the SP coupled with the PM strategy are shown through a numerical example.

Contrarily to previous works, the authors consider more realistic settings with a non-negligible random time for repairing failed machines. In order to compensate the lost production during the repair of a failed machine, a SP is proposed to transfer the load uniformly to all the other machines. As a result, those machines will produce at a higher production rate and will consequently have their failure rate increased. It will therefore be essential to determine an optimal PM schedule knowing that durations of these activities are not negligible. It is shown that the simultaneous implementation of periodic PM and load transfer in case of failure is the most economical integrated strategy.

This paper deals with a particular type of leasing contracts according to which an equipment is leased for free with the condition for the lessee to purchase a predetermined minimum quantity of consumables during each leasing period. Maintenance actions are performed by the lessor and borne by him. Imperfect preventive maintenance is carried out every t time units throughout the leasing period. Minimal repairs are performed following equipment failures. At the end of the leasing period, an overhaul which restores the equipment to “as good as new” state is performed. The equipment is leased many times during its life cycle. The purpose of this paper is to determine the values of the decision variables for the lessor, which are the preventive maintenance (PM) period and the minimum quantity of consumables to be sold to ensure profit.

A mathematical model is developed to express the expected maintenance cost per time unit incurred by the lessor as well as his expected profit over the equipment life cycle. The optimal PM period minimizing the maintenance cost is determined first. Then, given the corresponding minimum maintenance cost, the minimum quantity of consumables (the lessor's break-even point) to be purchased by the lessee is computed. A numerical example and a sensitivity study are presented, and the obtained results are discussed.

The outcome of this work is supposed to help the lessors determining two key values to be included in each leasing contract, namely: (1) the periodicity according to which they will commit to perform preventive maintenance actions such that their average total cost of maintenance is minimized, (2) the minimum quantity of consumables that the lessee must commit to purchasing during the leasing period. This quantity must be between the break-even point and the maximum quantity associated with the capacity of the equipment.

Practically, the objective of this work is first to determine the optimal strategy to be adopted by the lessor in terms of effort relating to PM and second to determine the minimum quantity of consumables that the lessee must purchase during the leasing period such as profit is insured for the lessor.

This type of leasing (for free) has not been addressed in the literature particularly when considering maintenance strategies.

The purpose of this paper is to present a decision model for second-hand products to determine the optimal upgrade level, warranty period and preventive maintenance (PM) effort level which maximize the total expected profit generated by the dealer considering any given past age of the product and the effect of the sales volume.

A mathematical model is developed to derive the optimal triplet: upgrade level, warranty period and PM effort level, which maximize the total expected profit generated by the dealer for any second-hand product with a given past age. Numerical experimentations have been conducted to investigate the effectiveness of the proposed model and to explore the interactions among the model variables.

Numerical experimentations including a sensitivity analysis have been conducted on the model key parameters. The obtained results show that performing PM actions during the warranty period helps the dealers to provide extended warranty for older second-hand products without spending a significant effort on upgrade actions and therefore increase the volume of sales. Also, the interaction between the PM level and the profit margin threshold is demonstrated. Finally, the effect of the sales volume function parameters (the price and warranty elasticity parameters) on the optimal solution is characterized.

Given the complexity of the profit function to be maximized involving a considerable number of decision variables with different nature, the authors limited the study to the case where the past age of the second-hand product is known.

The proposed model aims to provide second-hand product dealers with a modeling framework that enables them to have a realistic estimation of the generated profit by integrating the marketing and engineering key parameters of the second-hand product.

Most of the existing literature dealing with the reliability improvement of second-hand products does not take into account the fact that a realistic estimation of the total profit generated by the dealer requires the consideration of the sales volume. The latter is closely related to the marketing parameters characterized by the warranty period length and the second-hand product selling price. The proposed model introduces the effect of the total sales volume on the total expected profit. The authors also introduce the concept of discrete upgrade levels for a better control of the restoration degree. The authors study the impact of warranty and price elasticity parameters on the optimal solution and the resultant interaction with the customer purchase decision and consequently the sales volume.

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.

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.

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.

The purpose of this paper is to determine a nearly optimal inspection sequence for a series system consisting of two components subject to gradual deterioration and whose failures are not self-announcing and can be detected only through inspection.

The problem is tackled in the context of condition-based maintenance (CBM) with a maintenance model in the class of the control-limit policies for which the maintenance decision is made following inspection by comparison of the deterioration level to critical thresholds. A mathematical model is developed to express the total expected cost per time unit as a function of the inspection instants.

For any given series system composed of two components with known critical deterioration threshold levels, and for any given set of costs related to inspection, inactivity due to failure, and preventive and corrective replacements of each component, a nearly optimal inspection sequence of the system is derived such as the total expected cost is reduced.

Due to the complexity of the cost model with the inspection instants (×1, ×2, ×3, …) being the decision variables, it has not been possible to derive the optimal solution. A quasi-optimal sequence of inspection times is derived along with the corresponding total average cost per time unit.

In many practical situations in which CBM is implemented, a tradeoff between inspection costs and inactivity and replacement costs has to be balanced when determining the intervals between successive inspections at which the degradation level of the components should be assessed and compared to predetermined critical threshold levels. Inspecting too often would increase inspection costs but in the same time it would also increase the probability to avoid a failure and end up with a preventive replacement, whereas not inspecting often enough would increase the probability to end up with a failure increasing replacement and inactivity costs.

While the inspection problem has been largely treated for single component systems, inspection policies become much more complex when considering multi-component systems. A two-component series system is considered in this paper.

The purpose of this study is to propose and model an inspection and preventive maintenance policy for randomly failing systems that alternate operating and idle periods according to their mission profile.

A maintenance policy is defined and modeled mathematically. The paper focuses on finding the age T for inspection which maximizes the stationary availability of the system.

Except for the case of only self‐announcing failures, there always exists a finite optimal strategy T*. Two sufficient conditions for the uniqueness of such an optimum are also derived.

Many productive systems alternate operating and inactive periods, their failures may be self‐announcing or not self‐announcing (detected only through inspection). This paper presents a maintenance strategy for such systems in order to maximize their stationary availability. The proposed strategy suggests submitting the system to inspection when its age reaches T units of time.

This paper states a general expression of the system stationary availability which is considered as the performance criterion. Conditions of existence and uniqueness of an optimal strategy are developed.

The purpose of this paper is to study the evolution of a system stationary availability and determine the optimal preventive maintenance period, which maximises it in a context where preventive and corrective maintenance actions are imperfect and have non‐negligible durations.

The quasi‐renewal process approach and a (p, q) rule are respectively used to model corrective and preventive maintenance. Considering the durations of the preventive and corrective maintenance actions as well as their respective efficiency extents, a mathematical model and a numerical algorithm are developed in order to compute the system stationary availability.

It has been proven that for any given situation regarding the system, the repair and preventive maintenance efficiency extents, and the downtime durations for preventive and corrective maintenance, there is necessarily a finite optimal period T* of preventive maintenance which maximises the system stationary availability. A sufficient condition for the uniqueness of the optimal solution has also been derived. Numerical examples illustrated how preventive and corrective maintenance efficiency extents affect simultaneously the system optimal availability.

The study considers a general industrial framework where preventive and corrective maintenance actions are imperfect. In fact, neither the best‐qualified technicians nor the most suitable tools or spare parts are found to carry out maintenance actions. In such a context for a large variety of technical systems, when implementing preventive maintenance policies one should take into account the efficiency extents of maintenance actions as well as their durations in order to evaluate and optimise the system availability. The paper provides maintenance managers with a decision model allowing not only the computation and optimisation of system availability, but also the investigation of how preventive and corrective maintenance efficiency extents affect simultaneously the system optimal availability. The proposed model also allows one to find to what extent corrective actions ineffectiveness should be tolerated without having an important availability loss.

The paper proposes a modified formulation of the quasi‐renewal process taking into account the non‐negligible duration of corrective maintenance actions and periodic preventive maintenance. A new numerical algorithm is also developed in this context to compute the quasi‐renewal function that it is impossible to find in closed form. This allowed the computation and optimisation of system stationary availability.

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.

The proposed integrated policy is defined and modeled mathematically.

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.

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 numerical example.

The paper proposes an integrated model that links EMQ, quality and an age‐based preventive maintenance policy. It is shown that performing preventive maintenance yields reduction in inventory‐ and quality‐related costs.

The authors consider a system which is a part of a complex equipment (e.g. aircraft, automobile, medical equipment, production machine, etc.), and which consists of N independent series subsystems. The purpose of this paper is to determine simultaneously the system design (reliability) and its preventive maintenance (PM) replacements periodicity which minimize the total average cost per time unit over the equipment useful life, taking into account a minimum required reliability level between consecutive replacements.

The problem is tackled in the context of reliability-based design (RBD) considering at the same time the burn-in of components, the warranty commitment and the maintenance strategy to be adopted. A mathematical model is developed to express the total average cost per time unit to be minimized under a reliability constraint. The total average cost includes the cost of acquiring and assembling components, the burn-in of each component, preventive and corrective replacements performed during the warranty and post-warranty periods. A numerical procedure is proposed to solve the problem.

For any given set of input data including components reliability, their cost and the costs of their preventive and corrective replacements, the system design (reliability) and the periodicity of preventive replacement during the post-warranty period is obtained such as the system’s total average cost per time unit is minimized. The obtained results clearly indicate that a decrease in the number of PM actions to be performed during the post-warranty period increases the number of components to be added at each subsystem at the design stage.

Given that the objective function (cost rate function) to be minimized is non-linear and involves several integer variables, it has not been possible to derive the optimal solution. A numerical procedure based on a heuristic approach has been proposed to solve the problem finding a nearly optimal solution for a given set of input data.

This paper offers to manufacturers a comprehensive approach to look for the most economical combination of the reliability level to be given to their products at the design stage, on one hand, and the PM policy to be adopted, on the other hand, given the offered warranty and service for the products and reliability requirements during the life cycle.

While the RBD problem has been largely treated, most of the published works have focussed on the development or the improvement of solving techniques used to find the optimal configuration. In this paper the authors provide a more comprehensive approach that considers simultaneously RBD, the burn-in and warranty periods, along with the maintenance policy to be adopted. The authors also consider the context of products whose component failures cannot be rectified through repair actions. They can only be fixed by replacement.