Optimal preventive maintenance in a production inventory system

We consider a production inventory system that produces a single product type, and inventory is maintained according to an (S, s) policy. Exogenous demand for the product arrives according to a random process. Unsatisfied demands are not back ordered. Such a make-to-stock production inventory policy is found very commonly in discrete part manufacturing industry, e.g., automotive spare parts manufacturing. It is assumed that the demand arrival process is Poisson. Also, the unit production time, the time between failures, and the repair and maintenance times are assumed to have general probability distributions. We conjecture that, for any such system, the down time due to failures can be reduced through preventive maintenance resulting in possible increase in the system performance. We develop a mathematical model of the system, and derive expressions for several performance measures. One such measure (cost benefit) is used as the basis for optimal determination of the maintenance parameters. The model application is explained via detailed study of 21 variants of a numerical example problem. The optimal maintenance policies (obtained using a numerical search technique) vary widely depending on the problem parameters. Plots of the cost benefit versus the system characteristic parameters (such as, demand arrival rate, failure rate, production rate, etc.) reveal the parameter sensitivities. The results show that the actual values of the failure and maintenance costs, and their ratio are significant in determining the sensitivities of the system parameters.     

Optimal inspection policies with predictive and preventive maintenance

A model is proposed to study the inspection and maintenance policy of systems whose failures can be detected only by periodic tests or inspections. Using predictive techniques, the time of the system failure can be predicted for some failure modes. If the system is found failed in an inspection, a corrective maintenance action is carried out. If the system is in a good condition but the predictive test diagnoses a failure in the period until the next inspection, then the system is replaced. The cost rate function is obtained for general distribution function of the signal time of a future failure and for one specific distribution function recently proposed. An algorithm is presented to find the optimal time between inspections and predictive tests and the optimal system replacement times for an age replacement policy. Numerical experiments illustrate the model.     

Simultaneous determination of preventive maintenance and replacement policies in a queue-like production system with minimal repair

This paper addresses the joint effects of preventive maintenance and replacement policies on a queue-like production system with minimal repair at failures. We consider a policy which calls for a preventive maintenance operation whenever N parts have been processed. If a failure occurs and at least K preventive maintenance operations have been carried out, the system is replaced by a new one. Otherwise, a failure is handled by minimal repair. An analytical model is developed and the argument of renewal–reward theory is used to provide long-run expected profit per unit time for a given maintenance and replacement policy. Numerical examples are given to provide some managerial insights.     

Optimal inspection policies in a serial production system including scrap rework and repair: An MILP approach

The allocation of inspection effort problem for aerial systems is formulated as a 0-1 mixed integer linear programming problem. This formulation permits any combination of scrap, rework, or repair at each station and allows the problem to be solved using standard MILP software packages. Moreover electronic spread-sheets may be used to easily calculate the relevant coefficients. An additional advantage of this approach when compared with the traditional dynamic programming approach is the ease with which the basic model may be modified. For example, it is shown how the model may easily be modified to include both a material and a production constraint and to select between various material suppliers. Sensitivity analysis is also easily performed with this approach. This model is then used to show that the optimal inspection policy is dependent on whether a production or a material requirement is used.     

Optimal policies of a two-echelon serial inventory system with general limited capacities

We study optimal policies of capacitated two-echelon serial inventory systems under periodic review. For a system with smaller downstream capacity, we fully characterise the optimal policy as a further modified echelon base stock policy using an intuitive backward induction. The key lies in the magnitude relation between the initial upstream stock level and the downstream capacity. For a system with smaller upstream capacity, we demonstrate that the optimal policy is of a more complex structure where there can be at most four/five target levels up to which the upstream/downstream echelon tries to produce/order. The numbers of levels and their values depend on the length of remaining horizons and the amount of initial upstream inventories. We also specify these potential target levels and then suggest a way to simplify the search of optimal solutions.     

Optimal buffer inventory and preventive maintenance for an imperfect production process

In this paper we present a model to determine the optimal length of continuous production periods between maintenance actions and the optimal buffer inventory to satisfy demand during preventive maintenance or repair of a manufacturing facility. We include in the model the possibility of imperfect production. We consider that the duration and cost of the maintenance action depend on the state of the production facility.     

Joint production,setup and preventive maintenance policies of unreliable two-product manufacturing systems

This article addresses the problem of joint optimisation of production, setup and maintenance activities of unreliable manufacturing system producing two products. Given the complexity of the problem in a dynamic and stochastic environment, the literature has treated the problem separately by considering each axis individually (setup, production and maintenance) or by combining two axes simultaneously (production-setup, production-maintenance). Following the trend of scientific research advances that supports the fact that an integrated control leads to best performances, the main objective of this paper is to provide a control policy that will simultaneously combine the production, the setup and the preventive maintenance activities. To tackle the problem, an experimental resolution approach using combined continuous/discrete event simulation models is considered. The aim is to accurately imitate the production system behaviour, and to optimise the control policy parameters which minimise the total cost incurred. An in-depth study of the effects of the system parameter variation on the performance of the studied policies is performed in order to draw meaningful conclusions and to illustrate the robustness of the proposed resolution approach.     

Effect of maintenance policies on the just-in-time production system

Using simulation, experimental design, and regression analysis, mathematical models are developed here to describe the effect that maintenance policy, machine unreliability, processing time variability, ratio of preventive maintenance time to processing time, ratio of minimal repair time to preventive maintenance time, and production line size have on various measures of performance, namely total production line output and production line variability of the just-in-time production system. The analysis of the data shows that under different situations, different maintenance policies do not have the same effect on the production line performance. The following conclusions were obtained; when the number of production machines is low (five machines or less), and/or when the ratio of minimal repair time to preventive maintenance time is high, maintenance policy III leads to a higher performance than maintenance policy II. Otherwise maintenance policy II, which is more sensitive to the change of the ratio of minimal repair time to preventive maintenance time, leads to a higher performance. The results of the study can be utilized in choosing a maintenance policy as a function of the production process parameters. Once a policy is chosen, the practitioner can select the most important factors to control under that policy in order to minimize the machine idle time, maximize the production process reliability, improve productivity, and therefore increase the production line performance.     

Optimal production and pricing policies in a combined make-to-order/make-to-stock system

In this paper, we consider a production system which is capable to produce two types of products. The first type of products is make-to-order, while the second type is make-to-stock whose demand is satisfied by the on-hand inventory. The demand arrival rates of both types of products are price-sensitive. The excess demand that cannot be satisfied immediately is either backlogged or lost. The system costs include the holding costs of product inventories and shortage costs of unsatisfied demand. The objective is to maximise the total discounted profit over an infinite planning horizon by coordinating the production process and pricing decisions. By analysing the properties of objective functions, we characterise the optimal control policy by two switch curves and the optimal price is also given for different ordering and inventory levels. We also explore the monotonicity of both switch curves which will reduce the computation effort. Numerical experiments are conducted to demonstrate the use of the switch curves in managing the production system and illustrate that compared with the static pricing policy, the optimal integrated price and inventory control policy can result in a significant profit improvement in the make-to-order/make-to-stock system that is much higher than in a single-product system.     

Optimal maintenance policies in incomplete repair models

We consider an incomplete repair model, that is, the impact of repair is not minimal as in the homogeneous Poisson process and not “as good as new” as in renewal processes but lies between these boundary cases. The repairs are assumed to impact the failure intensity following a virtual age process of the general form proposed by Kijima. In previous works field data from an industrial setting were used to fit several models. In most cases the estimated rate of occurrence of failures was that of an underlying exponential distribution of the time between failures. In this paper, it is shown that there exist maintenance schedules under which the failure behavior of the failure-repair process becomes a homogeneous Poisson process.     

Considerations in the use of optimal preventive maintenance policies

Designing products which require maintenance always involves compromises between reliability and maintainability. Both scheduled and preventive maintenance (PM) should be considered in the design phases of a product so that the design can include features to ease the maintenance task. In addition, many design decisions based on Failure Modes and Effects Criticality Analysis (FMECA), Pareto criticality rankings, etc., could and should be strongly influenced by the potential for using preventive maintenance. A component that has a major negative impact on system reliability (because of its life distribution) could become much less consequential if appropriate PM policies are implemented. This paper describes the use of an easy-to-implement analysis procedure to assist a designer or systems analyst in making the reliability/maintainability tradeoff.     

Optimal locations of on-line and off-line rework stations in a serial production system

The production rate and product quality are two vital concerns for any manufacturing industry. Number of defective items reduces production rate and increases unit production cost. Moreover, if nonconforming items reach to the customers then manufacturer’s goodwill may drastically go down. Thus, quality inspection is treated as an inherent part of manufacturing. In this research, an N-stage serial production line with an inspection station at the end of it is considered to make decisions concerning this issue. On detecting a defective item at the end of the line it is scrapped or repaired at regular workstation or is sent to an off-line rework station for repair. Assuming each workstation produces a single type of defect a unit cost function is developed for alternative decisions on each type of defect. In order to minimise the unit cost of production and determine an appropriate decision for individual defect types, a fractional mixed integer nonlinear programming is formulated. After transformation to a mixed integer linear programming problem it is solved optimally. A small problem from garments industry is described in detail to show the solution procedure with a branch and bound method. Empirical tests with up to 40 workstations are permed to show the efficiency of the solution process.     

Control-limit preventive maintenance policies for components subject to imperfect preventive maintenance and variable operational conditions

This paper develops two component-level control-limit preventive maintenance (PM) policies for systems subject to the joint effect of partial recovery PM acts (imperfect PM acts) and variable operational conditions, and investigates the properties of the proposed policies. The extended proportional hazards model (EPHM) is used to model the system failure likelihood influenced by both factors. Several numerical experiments are conducted for policy property analysis, using real lifetime and operational condition data and typical characterization of imperfect PM acts and maintenance durations. The experimental results demonstrate the necessity of considering both factors when they do exist, characterize the joint effect of the two factors on the performance of an optimized PM policy, and explore the influence of the loading sequence of time-varying operational conditions on the performance of an optimized PM policy. The proposed policies extend the applicability of PM optimization techniques.     

基于机会维修策略的预防性维修优化模型研究

为了利用系统内故障部件维修的机会,考虑部件之间在维修方面存在的相关性情况,提出了将机会维修信息融入系统预防性维修的优化模型．该模型在比较按机会预防性维修和按计划预防性维修期望效益的基础上,以系统内故障时机为优化变量、部件维修费用率最小化为目标进行系统预防性维修优化,使确定部件在不同的故障来源时机可提前预防性维修的阈值．最后通过算例,表明不同故障的机会维修阈值对部件预防性维修效果的影响差异,为系统预防性维修决策提供有力的支持．     

Optimal maintenance policies during the post-warranty period

This paper develops the optimal periodic preventive maintenance policies following the expiration of warranty. We consider two types of warranty policies to discuss such optimum maintenance policies: renewing warranty and non-renewing warranty. From the user's perspective, the product is maintained free of charge or with prorated cost on failure during the warranty period. However, the users will have to repair or replace the failed product at their own expenses during the post-warranty period. Given the cost structure to the user during the cycle of the product, we derive the expressions for the expected maintenance costs for the periodic preventive maintenance following the expiration of warranty when applying two types of warranty policies and obtain the optimal number and the optimal period for such post-warranty maintenance policies by minimizing the expected long-run maintenance cost per unit time. Explicit solutions for the optimal periodic preventive maintenance are presented for illustrative purposes.     

Critical machines preventive maintenance policies for group technology shops

This study develops a set of preventive maintenance policies, based on the idea of critical machines, for use in group technology shops. These policies designated certain machines in the shop as critical. When a critical machine breaks down, it is repaired and preventive maintenance is applied to a block of machines (either the remaining machines in the cell, the other machines of the same type or all of the remaining machines in the shop). Simulation of a complex group technology shop was used to compare twelve definitions of criticality and three preventive maintenance conditions. The definition of criticality was not found to be a major cause of performance differences between shops, since in many cases, the same machines were critical by any definition. The application of preventive maintenance to all machines in the shop when a critical machine had failed led to the best shop performance, indicating that the reduction in machine interference caused by doing so was more important than the unique features of group technology.     

Dependability and performance stochastic modelling of a two-unit repairable production system with preventive maintenance

In this paper, a two-unit multistate repairable production system is considered in which preventive maintenance (PM) is implemented in order to improve its dependability and performance. A general model is provided for the production system using a semi-Markov process, for examining system’s limiting behaviour. Apart from combining redundancy with PM, we introduce scenarios like imperfect and failed maintenance which are usually met in real life production systems. For the proposed model, we calculate the availability, the mean time to failure and the total operational cost and we formulate optimisation problems settled with respect to the system’s inspection times. The main aim of our work is to determine the optimal inspection times and consequently the optimal PM policies to be adopted in order to optimise system’s dependability and performance.     

Intelligent dynamic control policies for serial production lines

Heuristic production control policies such as CONWIP, kanban, and other hybrid policies have been in use for years as better alternatives to MRP-based push control policies. It is a fact that these policies, although efficient, are far from optimal. Our goal is to develop a methodology that, for a given system, finds a dynamic control policy via intelligent agents. Such a policy while achieving the productivity (i.e., demand service rate) goal of the system will optimize a cost/reward function based on the WIP inventory. To achieve this goal we applied a simulation-based optimization technique called Reinforcement Learning (RL) on a four-station serial line. The control policy attained by the application of a RL algorithm was compared with the other existing policies on the basis of total average WIP and average cost of WIP. We also develop a heuristic control policy in light of our experience gained from a close examination of the policies obtained by the RL algorithm. This heuristic policy named Behavior-Based Control (BBC), although placed second to the RL policy, proved to be a more efficient and leaner control policy than most of the existing policies in the literature. The performance of the BBC policy was found to be comparable to the Extended Kanban Control System (EKCS), which as per our experimentation, turned out to be the best of the existing policies. The numerical results used for comparison purposes were obtained from a four-station serial line with two different (constant and Poisson) demand arrival processes.     

Optimal periodic preventive maintenance policy for leased equipment

For leased equipment the lessor incurs penalty costs for failures occurring over the lease period and for not rectifying such failures within a specified time limit. Through preventive maintenance actions the penalty costs can be reduced but this is achieved at the expense of increased maintenance costs. The paper looks at a periodic preventive maintenance policy which achieves a tradeoff between the penalty and maintenance costs.     

Studies on optimum preventive maintenance policies for general repair result

In this paper we consider that a unit is repaired preventively after it has operated for time T. After repair, the unit is not as good as a new one, but is equivalent to one which has been used for a period of time. If we let Y indicate such a period of time, then Y is a random variable related to the time for which the unit has already operated. Hence, under the same repair condition as above, we obtain the unit's renovation degree distribution of Y after the unit is repaired preventively at time kT (k = 2, 3, …). Further, using the method of leading variables, we obtain the mean number of times the unit has broken down from time (k − 1)T to time kT (k = 1, 2, …). Finally, considering an objective function with a bound condition and using the Lagrange multipliers method, we obtain an optimal preventive maintenance time T, for which the minimum total repair cost is achieved.