Availability optimisation for stochastic degrading systems under imperfect preventive maintenance

This paper deals with imperfect preventive maintenance (PM) optimisation problem. The system to be maintained is typically a production system assumed to be continuously monitored and subject to stochastic degradation. To assess such degradation, the proposed maintenance model takes into account both corrective maintenance (CM) and PM. The system undergoes PM whenever its reliability reaches an appropriate value, while CM is performed at system failure. After a given number of maintenance actions, the system is preventively replaced by a new one. Both CM as well as PM are considered imperfect, i.e. they bring the system to an operating state which lies between two extreme states, namely the as bad as old state and as good as new state. The imperfect effect of CM and PM is modelled on the basis of the hybrid hazard rate model. The objective of the proposed PM optimisation model consists on finding the optimal reliability threshold together with the optimal number of PM actions to maximise the average availability of the system. A mathematical model is then proposed. To solve this problem an algorithm is provided. A numerical example is presented to illustrate the proposed maintenance optimisation model.     

An Economic Order Quantity Model with Demand-Dependent Unit Production Cost and Imperfect Production Processes

The classical economic order quantity (EOQ) model assumes that items produced are of perfect quality and that die unit cost of production is independent of demand. Product quality is not always perfect but directly affected by the reliability of the production process used to produce the products. In addition, a relationship between unit production cost and demand may exist under certain circumstances. We propose an EOQ model with demand-dependent unit production cost and imperfect production processes. We formulate this inventory decision problem as a geometric program (GP) and solve it to obtain closed-form optimal solutions. An illustrative example is provided to demonstrate the point that GP has potential as a valuable analytical tool for studying a certain class of inventory control problems. We also discuss the aspect of sensitivity analysis based on the GP approach.     

A cost minimisation model for joint production and maintenance planning under quality constraints

In this paper, integrated planning of production, imperfect maintenance and process inspections in a multi-machine system is investigated. This system consists of parallel machines which deteriorate with time and they may shift from a primarily in-control state to a degraded state with a higher defective rate or to a failed state. Maintenance scheduling corresponds to a discrete time age-based imperfect maintenance with a large number of maintenance alternatives. Process inspections are considered to detect the current state of the system. Detecting a deteriorated condition initiates the quality check of the related sub-lots, rework of defective items and a process adjustment that brings the machine in its normal conditions. Production planning includes a capacitated lot-sizing problem with multiple products. We propose a joint approach that coordinates the decisions of the three functions, where the objective function minimises the total cost. Evaluation of costs and interacting factors is presented and two heuristic methods are proposed to solve the problem. The results of the joint model are compared to a non-integrated method and a sensitivity analysis is conducted.     

考虑缓冲区库存分配的并联系统预防维护策略研究

为提高并联系统生产过程的连续性,提出了考虑缓冲区库存分配的并联系统(3M1B)预防维护模型。首先,考虑并联系统每台设备的故障率与维护率,在并联系统中上下游设备之间建立缓冲区,构建3M1B系统。其次,考虑设备不完美生产的可能性,以缓冲区库存量与设备运行周期为决策变量,以设备最小生产成本率为目标函数建立预防维护模型,求解最佳的预防维护策略与缓冲区库存分配策略。针对此维护模型,采用离散迭代算法与遗传算法进行求解,并比较了2种算法的优劣,结果表明,对于此模型,离散迭代算法优于遗传算法。最后,通过算例验证模型的可行性和有效性。     

Joint optimisation of production,maintenance and quality for batch production system subject to varying operational conditions

This paper considers the integration problem of production, maintenance and quality for a capacitated lot-sizing production system subject to deterioration. The effects of varying operational conditions from batch to batch on system reliability and product quality are modelled by proportional hazards models, resulting in non-monotonic failure rate and defect rate. After each batch production, imperfect preventive maintenance (PM) is determined to mitigate the system deterioration, and inspection is taken to sort nonconforming items in the finished goods. Once the cumulative number of nonconforming items exceeds a predetermined threshold, an overhaul is performed to renew the system. An integrated model for optimising production plan, PM plan and overhaul strategy is developed to minimise the total cost while satisfying all product demands. A genetic algorithm is proposed to solve the integrated model efficiently. Numerical results validate the rationality of the model with varying operational conditions consideration and its applicability in economic benefits.     

Effects of maintenance policy on an imperfect production system under trade credit

The traditional production model development assumed that all products are perfect quality and did not consider maintenance, which is far from reality. In practice, the production process may shift randomly from an in-control state to an out-of-control state during a production run, i.e. process deterioration. This paper considers both preventive maintenance and corrective maintenance which are used to increase the system reliability. The objective of this paper is to determine the optimal production run time and maintenance frequency while minimising the total cost under process deterioration and trade credit. This paper develops a theorem and an algorithm to solve the problem described, provides numerical analysis to illustrate the proposed solution procedure, and discusses the impact of various system parameters. A real case of hi-tech manufacturer is used to verify the model. It predicts a 10.36% decrease in total cost if the preventive maintenance decision is considered.     

A Lagrangian heuristic for minimising risk using multiple heterogeneous metrology tools

Motivated by the high investment and operational metrology cost, and subsequently the limited metrology capacity, in modern semiconductor manufacturing facilities, we model and solve the problem of optimally assigning the capacity of several imperfect metrology tools to minimise the risk in terms of expected product loss on heterogeneous production machines. In this paper, metrology tools can differ in terms of reliability and speed. The resulting problem can be reduced to a variant of the Generalized Assignment Problem (GAP), the Multiple Choice, Multiple Knapsack Problem (MCMKP). A Lagrangian heuristic, including multiple feasibility heuristics, is proposed to solve the problem that are tested on randomly generated instances.     

An integrated EPQ model based on a control chart for an imperfect production process

The notion of quality control is introduced into the classic economic production quantity (EPQ) model. Based on previous research, this paper contributes to an integrated EPQ model combining the concepts of statistical process control and maintenance. An imperfect production process involving three different conditions is considered. A control chart is adopted to monitor the whole process with Taguchi's loss function estimating the quality cost of each condition. A corresponding maintenance policy is planned for the machine depending on what condition it runs in. Thus the proposed EPQ model takes quality-related costs and maintenance-related costs into account other than storage costs and ordering costs already considered in the classic model. The objective of this model is to minimise the total expected production cost per production cycle while simultaneously determining the optimal parameters of control chart design, the interval between sampling, the sample size and the maintenance decision policy. The pattern search method is used to solve the problem using the MATLAB toolbox. In addition, a case study, sensitivity analysis and comparison analysis are presented to demonstrate the application of the model.     

Multi-item reliability dependent imperfect production inventory optimal control models with dynamic demand under uncertain resource constraint

In this paper, imperfect multi-item production inventory models are considered over a finite time horizon with known dynamic demands. The production rates are functions of time which are taken as control variables. In the production process, reliability plays an important role to improve the quality of products and to decrease the defective rate. The said defective units are partially or fully reworked. The unit production cost is a function of production rate and also dependent on raw material cost, development cost due to reliability and wear-tear cost. There is a constraint on the total production cost termed as budget constraint which is crisp/imprecise/random in nature. The objective of the present investigation is to fix the optimum reliabilities of the production system to have maximum return. Thus, the models are formulated as optimal control problems for the maximisation of profit and solved using Hamiltonian (Pontryagin’s Maximum Principle), fixed-final time and free-final state system, Kuhn–Tucker conditions and Generalised Reduced Gradient Method. Several particular cases are derived from the general model. The models are illustrated numerically and graphically and some managerial decisions are derived.     

Reliability modeling of multi‐state degraded repairable systems and its applications to automotive systems

In this paper, we presented a continuous‐time Markov process‐based model for evaluating time‐dependent reliability indices of multi‐state degraded systems, particularly for some automotive subsystems and components subject to minimal repairs and negative repair effects. The minimal repair policy, which restores the system back to an “as bad as old” functioning state just before failure, is widely used for automotive systems repair because of its low cost of maintenance. The current study distinguishes with others that the negative repair effects, such as unpredictable human error during repair work and negative effects caused by propagated failures, are considered in the model. The negative repair effects may transfer the system to a degraded operational state that is worse than before due to an imperfect repair. Additionally, a special condition that a system under repair may be directly transferred to a complete failure state is also considered. Using the continuous‐time Markov process approach, we obtained the general solutions to the time‐dependent probabilities of each system state. Moreover, we also provided the expressions for several reliability measures include availability, unavailability, reliability, mean life time, and mean time to first failure. An illustrative numerical example of reliability assessment of an electric car battery system is provided. Finally, we use the proposed multi‐state system model to model a vehicle sub‐frame fatigue degradation process. The proposed model can be applied for many practical systems, especially for the systems that are designed with finite service life.     

Optimal decision of an economic production quantity model for imperfect manufacturing under hybrid maintenance policy with shortages and partial backlogging

Considering the characteristics of the stochastic shift of the machine state and the uncertainty of the product quality of production, in this paper, we develop an optimisation decision of economic production quantity model for an imperfect manufacturing system under hybrid maintenance policy with shortages and partial backlogging. We assume that the production process is imperfect stemming from the machine reliability and the probability of out-of-control, a hybrid maintenance policy combined of emergency maintenance and preventive maintenance is executed during each production run. Three decision models based on the scenarios of machine breakdown and repair time are developed. The optimal production quantity and maintenance inspection number during each production run are solved with minimising the expected average cost of the system. Numerical examples are used to demonstrate the effectiveness and feasibility of the model. Sensitivity analysis is conducted to analyse the impacts of key parameters on the optimal decision. Some implications related to the effective and economical execution of maintenance policy for practitioners are derived.     

A bi-objective optimization approach for the maintenance planning of networked systems

Networked systems, such as telecommunications, transportation, and power transmission, are critical for the economic development and social well-being of a society and are required to keep the prescribed demand continuously satisfied. Therefore, when planning maintenance actions for such a system, the adverse influence on its reliability caused by the unavailability of the components in the process of being maintained needs to be taken into account. To deal with this problem, we propose a new bi-objective optimization approach to determine the Pareto optimal maintenance plans for a networked system, simultaneously maximizing its reliability within the concerned planning horizon and minimizing the total maintenance cost. Both perfect and imperfect maintenance actions are considered. The proposed approach can well balance the influence of maintenance actions on a networked system's reliability during their implementation and after being completed and, thus, can help ensure its reliability of continuously satisfying the prescribed demand.     

Using 0/1 mixed integer linear programming to solve a reliability-centered problem of power plant preventive maintenance scheduling

The problem of power plant preventive maintenance scheduling is studied in this paper. A reliability perspective is considered. This problem consists of ascertaining which generating units must halt production to be examined regularly for safety. It is very important because a failure in a power station may cause a general breakdown in an electric network. The main consequence is that the electricity demand of customers will not be satisfied in such cases. Therefore, reliability is the key point used in the methodology presented. The problem is approached under the operations research perspective as an optimization issue. 0/1 mixed integer linear programming is used to solve the model reached. An application study is included. The model is put to use in a real power plant setting, representative of the Spanish one. The result obtained is a schedule that allows the efficient organization of preventive maintenance over a specific time horizon.     

Integrating run-based preventive maintenance into the capacitated lot sizing problem with reliability constraint

A joint model for integrating run-based preventive maintenance (PM) into the capacitated lot sizing problem (CLSP) is proposed, in which the production system is subject to deterioration with usage and PM operations are implemented to restore the system. In this model, both production and PM operations are restricted by the system's maximum capacity, and the system reliability has to be maintained above a threshold value throughout the planning horizon. By linearisation of the reliability constraints, the problem is formulated as a mixed-integer linear programming. An explanatory example is given to illustrate the advantage of the joint model comparing with the interval-based PM policy in terms of system's overall cost. A three-stage heuristic is proposed to solve this integrated model, which includes a Lagrangian-based heuristic for the CLSP. The numerical experiments are conducted to evaluate the performance of the developed heuristics and the computational results show that the heuristics can provide good feasible solutions for the corresponding models. The discussion of the results is finally given in detail.     

Preventive maintenance policy of single‐unit systems based on shot‐noise process

This paper develops reliability and maintenance models for a single‐unit system subject to hard failures under random environment of external shocks. Motivated by the observations of shot‐noise process in practice, the impact of shock damage on system failure behavior is characterized by random hazard rate increments. To remove such negative impact, imperfect preventive repair is performed periodically, and preventive replacement is performed after several repairs. Considering the joint effects of both random shocks and imperfect repair on the system hazard rate, we derive recursive equations for the system reliability function. Furthermore, we investigate the optimal maintenance policy that minimizes the expected cost per unit time of the system. The applicability of the reliability and maintenance model is validated by a case study on a wind turbine system.     

不完备生产与条件维护策略下的生产批量决策研究

构建了不完备生产与条件维护下的生产批量模型,采用威布尔分布的曲线分布宽度描述可靠性的退化性,考虑了曲线分布宽度为等比数列和等差数列2种模型,利用报酬更新理论求解了期望平均总成本的最小值。结果表明,第1种模型的期望平均总成本要高于设备不具有退化性的期望平均总成本,前者的条件维护的阈值、最优生产批量和维护次数都比后者的少;第2种模型的期望平均总成本总体要低于设备不具有退化性的期望平均总成本,前者的条件维护的阈值比后者的少,而前者的维护次数和最优生产批量都比后者的多。研究还发现,公比和公差是影响期望平均总成本的最重要因素,需求是影响条件维护的可靠性阈值的最重要因素。本文的相关启示可为管理者提供决策参考依据。     

Selective maintenance optimisation for series-parallel systems alternating missions and scheduled breaks with stochastic durations

This paper deals with the selective maintenance problem for a multi-component system performing consecutive missions separated by scheduled breaks. To increase the probability of successfully completing its next mission, the system components are maintained during the break. A list of potential imperfect maintenance actions on each component, ranging from minimal repair to replacement is available. The general hybrid hazard rate approach is used to model the reliability improvement of the system components. Durations of the maintenance actions, the mission and the breaks are stochastic with known probability distributions. The resulting optimisation problem is modelled as a non-linear stochastic programme. Its objective is to determine a cost-optimal subset of maintenance actions to be performed on the components given the limited stochastic duration of the break and the minimum system reliability level required to complete the next mission. The fundamental concepts and relevant parameters of this decision-making problem are developed and discussed. Numerical experiments are provided to demonstrate the added value of solving this selective maintenance problem as a stochastic optimisation programme.     

具有成组约束的柔性同序加工车间的排序算法

针对轮胎模具的生产调度特点,研究了具有成组约束的两阶段柔性同序加工车间(FF2)的调度问题,建立了目标函数为最小化最大完成时间的调度数学模型,基于Johnson准则提出一种新的启发式算法,并应用企业的实际算例,说明了数学模型和求解方法的可靠性和有效性。     

The supplier–buyer integrated production-inventory model with random yield

This paper revisits the traditional supplier–buyer integrated production-inventory model which deals with the problem of a manufacturer (supplier) supplying a product to a retailer (buyer) serving the consumer market with constant stationary demand. The product is manufactured in batches at a finite rate. The supplier's production batch is depleted by the buyer's replenishment orders at periodic intervals. The buyer's inventory is then consumed by the market demand at a fixed rate. The problem is the simultaneous computation of the manufacturer's production lot-size and the buyer's replenishment order quantity, i.e. the integrated production-inventory policy parameters. The key characteristic considered in this paper is that the manufacturing process is imperfect, and, hence, there are defective items in each production lot. As a result, each replenishment order shipped to the buyer includes defective products and the non-defective percentage in each such shipment is random. Considering the case where the supplier replenishes the buyer via equal-sized shipments, we develop an analytical expression of the total expected cost for the supplier–buyer system under consideration, with and without a considerable inspection time. We first examine the case where the inspection time is negligible, and then we present a generalisation to consider the inspection time explicitly. Our goal is to model the impact of random yield on the system performance. Our findings are useful for computing the integrated production-inventory policy parameters while considering the supply uncertainty due to an imperfect manufacturing process. Through numerical examples, we quantify the impact of supply with random yield on the system performance and illustrate its relationship with the demand and production rate.     

Determining the optimal lot size for the finite production model with random defective rate,the rework process,and backlogging

This paper considers the effects of the reworking of defective items on the economic production quantity (EPQ) model with backlogging allowed. The classic EPQ model assumes that manufacturing facility functions perfectly during a production run. However, due to process deterioration or other factors, the production process may shift and produce imperfect quality items. In this study, a random defective rate is considered, and when regular production ends, the reworking of defective items starts immediately. Not all of the defective items are reworked, a portion of them are scrap and are discarded. Repairing and holding cost per reworked item and disposal cost per scrap item are included in the proposed mathematical modelling and analysis. The renewal reward theorem is utilized to deal with the variable cycle length, and the optimal lot size that minimizes the overall costs for the imperfect quality EPQ model is derived where backorders are permitted.