Economic interpretation of models for the replacement of machines

The purpose of this article is to give an economic interpretation of results derived from mathematical replacement models. It is based on results found in the literature. The conclusion is that the moment of replacement is always determined by the equality of marginal replacement costs to the marginal costs of postponed replacement. This extension gives the models practical applicability by providing an exact decision criterion and a concrete interpretation. In other words: practical decisions are given a theoretical foundation.     

Optimal tool replacement for processes with low fraction defective

Tool wear is a frequent and natural part in many machining processes and is a systematic assignable cause. The fraction of defectives would rise as the tool deteriorates. When the fraction defective reaches a certain level, the tool must be replaced. To minimize the defective parts and the overall tool costs, the optimal tool replacement time needs to be determined. Process capability indices (PCIs) have been effectively used in the manufacturing industry to measure the fraction of defectives. Conventional methods of capability measurement become inaccurate since the process data is contaminated by the assignable cause variation. In order to determine the optimal tool replacement time to maintain maximum product quality, conventional capability calculation must be modified. Considering process capability changes dynamically, an estimator of C_pmk is investigated. We obtain an exact form of the sampling distribution in the presence of a systematic assignable cause. This study provides an effective management policy for optimal tool replacement under low fraction of defectives. To illustrate the application of this procedure, a case study involving the tool wear problem is presented.     

Optimizing Preventive Maintenance Models

We deal with the problem of scheduling preventive maintenance (PM) for a system so that, over its operating life, we minimize a performance function which reflects repair and replacement costs as well as the costs of the PM itself. It is assumed that a hazard rate model is known which predicts the frequency of system failure as a function of age. It is also assumed that each PM produces a step reduction in the effective age of the system. We consider some variations and extensions of a PM scheduling approach proposed by Lin et al. [6]. In particular we consider numerical algorithms which may be more appropriate for hazard rate models which are less simple than those used in [6] and we introduce some constraints into the problem in order to avoid the possibility of spurious solutions. We also discuss the use of automatic differentiation (AD) as a convenient tool for computing the gradients and Hessians that are needed by numerical optimization methods. The main contribution of the paper is a new problem formulation which allows the optimal number of occurrences of PM to be determined along with their optimal timings. This formulation involves the global minimization of a non-smooth performance function. In our numerical tests this is done via the algorithm DIRECT proposed by Jones et al. [19]. We show results for a number of examples, involving different hazard rate models, to give an indication of how PM schedules can vary in response to changes in relative costs of maintenance, repair and replacement. Part of this work was carried out while the first author was a Visiting Professor in the Department of Mechanical Engineering at the University of Alberta in December 2003.     

Reliable tool replacement policy for quality and cost

A tool management model is developed which determines the optimal initial tool setting and tool replacement time in consideration of balancing quality loss, replacement cost, and possible tool failure. A quadratic loss function is employed to characterize the costs resulting from the deviation of part dimension from its target value. The tool reliability function is used to represent the probability of possible tool failure. The model development does not attempt to explain the underlying physics of tool wear and tool failure and does not intend to apply to on-line tool replacement decision. Instead, the present study provides a decision model for management engineers in off-line tool management applications.     

Optimization problems of replacement first or last in reliability theory

This paper takes up age and periodic replacement last models with working cycles, where the unit is replaced before failure at a total operating time T or at a random working cycle Y, whichever occurs last, which is called replacement last. Expected cost rates are formulated, and optimal replacement policies which minimize them are discussed analytically. Comparisons between such a replacement last and the conventional replacement first are made in detail. It is determined theoretically and numerically which policy is better than the other according to the ratios of replacement costs and how the mean time of working cycles affects the comparison results. It is also shown that the unit can be operating for a longer time and avoid unnecessary replacements when replacement last is done. For further studies, expected cost rates of modified models and their applications in a standard cumulative damage model with working cycles are obtained and computed numerically. Finally, case studies on replacement last and first in maintaining electronic systems of naval ships under battle and non-battle statuses are given.     

Last time buy decisions for products sold under warranty

Manufacturers supplying products under warranty need a strategy to deal with failures during the warranty period: repair the product or replace it by a new one, depending on e.g. age and/or usage of the failed product. An (implicit) assumption in virtually all models is that new products to replace the failed ones are immediately available at given replacement costs. Because of the short life cycles of many products, manufacturing may be discontinued before the end of the warranty period. At that point in time, the supplier has to decide how many products to put on the shelf to replace failed products under warranty that will be returned from the field (the last time buy decision). This is a trade-off between product availability for replacement and costs of product obsolescence. In this paper, we consider the joint optimization of repair-replacement decisions and the last time buy quantity for products sold under warranty. We develop approximations to estimate the total relevant costs and service levels for this problem, and show that we can easily find near-optimal last time buy quantities using a numerical search. Comparison to discrete event simulation results shows an excellent performance of our methods.     

Hybrid block replacement and inspection policies for a multi-component system with heterogeneous component lives

Novel replacement policies that are hybrids of inspection maintenance and block replacement are developed for an n identical component series system in which the component parts used at successive replacements arise from a heterogeneous population. The heterogeneous nature of components implies a mixed distribution for time to failure. In these circumstances, a hybrid policy comprising two phases, an early inspection phase and a later wear-out replacement phase, may be appropriate. The policy has some similarity to burn-in maintenance. The simplest policy described is such a hybrid and comprises a block-type or periodic replacement policy with an embedded block or periodic inspection policy. We use a three state failure model, in which a component may be good, defective or failed, in order to consider inspection maintenance. Hybrid block replacement and age-based inspection, and opportunistic hybrid policies will also arise naturally in these circumstances and these are briefly investigated. For the simplest policy, an approximation is used to determine the long-run cost and the system reliability. The policies have the interesting property that the system reliability may be a maximum when the long-run cost is close to its minimum. The failure model implies that the effect of maintenance is heterogeneous. The policies themselves imply that maintenance is carried out more prudently to newer than to older systems. The maintenance of traction motor bearings on underground trains is used to illustrate the ideas in the paper.     

Heuristics for determining economic processing rates in a flexible manufacturing system

In this paper, models are presented for determining economic processing speeds and tool loading to minimize the makespan required to produce a given set of parts in a flexible manufacturing system. Using Taylor's tool life equation, models for determining the optimal processing speeds and the tools to be loaded into finite capacity machine magazines are formulated to minimize the maximum processing time in the system. These problems are evaluated for computational complexity, and several heuristics for obtaining good feasible solutions to the problem are discussed. The quality of the solutions obtained using these heuristics is evaluated by computational experiments against lower bounds established by either relaxations or optimal solutions when possible.     

Asset replacement for an urban railway using a modified two-cycle replacement model

This paper considers the application of capital replacement models at Mass Transit Railway Corporation Limited (MTRCL), Hong Kong. A particular characteristic of the replacement problems considered is that costs relating to existing equipment are generally constant or increasing only slowly. Consequently, replacement is often driven by technical obsolescence, but other criteria are used for informing decisions. The applicability of traditional OR models of replacement is then problematic. We recommend the use of a modified two-cycle replacement model and compare this model to existing capital replacement models. Issues relating to the estimation of delay costs and failure consequences and their influence on the replacement decision are also considered—this is done using a fixed horizon model, which is a special case of the modified two-cycle model. Track points and escalators are used as particular examples. In addition to modelling recommendations, we discuss the management of asset replacement with emphasis on the procedures necessary to ensure that asset replacement requirements are considered appropriately and effectively. The paper treats, in particular, the procedural issues of asset replacement, and the discussion of asset replacement system methodology reflects the current practise at MTRCL, Hong Kong, and developments within that organization through collaboration with academia. The modified two-cycle replacement model is recommended by us for general replacement applications. The asset replacement procedure is presented as an exemplar for business and industry.     

自动化车床最优刀具检测模型研究

针对自动化车床工序最优检测和刀具更换问题进行了探讨.将定期检测和将刀具更换作用于同一工序流程,在只考虑刀具故障条件下,通过概率论和更新过程理论建立了以单位时间内期望费用为目标函数的数学模型,以检测间隔和刀具更换间隔为策略,确定最优的策略使得目标函数达到最小,并求出了经长期运行单位时间内期望费用的明显表达式.最后还对结果进行了讨论.     

Optimal solutions for the machining economics problem with stochastically distributed tool lives

This paper proposes analytical models and numerical procedures for simultaneously determining the optimal cutting speed and tool replacement policy in machining economics problems with stochastic tool lives when the objective is the minimization of the machining cost per part. It is shown that the objective function is separable for certain phase type tool life distributions, including Gamma, which leads to an efficient solution procedure.     

Optimal fleet replacement: A case study on a Spanish urban transport fleet

Optimizing the average annual cost of a bus fleet has become an increasing concern in transport companies management around the world. Nowadays, there are many tools available to assist managerial decisions, and one of the most used is the cost analysis of the life cycle of an asset, known as “life cycle cost”. Characterized by performing deterministic analysis of the situation, it allows the administration to evaluate the process of fleet replacement but is limited by not contemplating certain intrinsic variations related to vehicles and for disregarding variables related to exigencies of fleet use. The main purpose of this study is to develop a combined model of support to asset management based in the association of the life cycle cost tool and the mathematical model of Monte Carlo simulation, by performing a stochastic analysis considering both age and average annual mileage for optimum vehicle replacement. The utilized method was applied in a Spanish urban transport fleet, and the results indicate that the use of the stochastic model was more effective than the use of the deterministic model.     

Optimal policies for a delay time model with postponed replacement

We develop a delay time model (DTM) to determine the optimal maintenance policy under a novel assumption: postponed replacement. Delay time is defined as the time lapse from the occurrence of a defect up until failure. Inspections can be performed to monitor the system state at non-negligible cost. Most works in the literature assume that instantaneous replacement is enforced as soon as a defect is detected at an inspection. In contrast, we relax this assumption and allow replacement to be postponed for an additional time period. The key motivation is to achieve better utilization of the system’s useful life, and reduce replacement costs by providing a sufficient time window to prepare maintenance resources. We model the preventive replacement cost as a non-increasing function of the postponement interval. We then derive the optimal policy under the modified assumption for a system with exponentially distributed defect arrival time, both for a deterministic delay time and for a more general random delay time. For the settings with a deterministic delay time, we also establish an upper bound on the cost savings that can be attained. A numerical case study is presented to benchmark the benefits of our modified assumption against conventional instantaneous replacement discussed in the literature.     

Determining the optimal procurement policy and maximum allowable lifespan for machining tools with stochastically distributed toollife

For high-value added products, machining tools’ lifespan significantly influences the quantity of procurement in machining process. Preemption of tools from the workpiece while processing is continuing is sometime beneficial to safeguard the product from the damage due to tool failure or its malfunction. Also an early discard of a tool is costly for the manufacturing operation. Therefore an optimal strategy for the tool life is sought here to determine the maximum allowable tool lifespan to preempt from the workpiece and to have an appropriate amount of tool stock in the crib to ascertain the proper running of the production schedule and tool inventory. Therefore, an impact of the machining tool lifespan on the production-inventory policy of the system is investigated in this paper. An integrated lifespan related inventory model for machining tools is developed to meet the responding accurate requirement of procurement and inventory. Two numerical examples are presented to illustrate the integrated model. The results show that the practical lifespan adoption of machining tools has significant impact on the whole quantity of procurement, and eventually influences the coordinating economic decision making.     

Optimal age-replacement model with age-dependent type of failure and random lead time based on a cumulative repair-cost limit policy

In this paper, we consider an age-replacement model with minimal repair based on a cumulative repair cost limit and random lead time for replacement delivery. A cumulative repair cost limit policy uses information about a system’s entire repair cost history to decide whether the system is repaired or replaced; a random lead time models delay in delivery of a replacement once it is ordered. A general cost model is developed for the average cost per unit time based on the stochastic behavior of the assumed system, reflecting the costs of both storing a spare and of system downtime. The optimal age for preventive replacement minimizing that cost rate is derived, its existence and uniqueness is shown, and structural properties are presented. Various special cases are included, and a numerical example is given for illustration. Because the framework and analysis are general, the proposed model extends several existing results.     

Opportunity-based age replacement with a one-cycle criterion

In this paper age replacement (AR) and opportunity-based age replacement (OAR) for a unit are considered, based on a one-cycle criterion, both for a known and unknown lifetime distribution. In the literature, AR and OAR strategies are mostly based on a renewal criterion, but in particular when the lifetime distribution is not known and data of the process are used to update the lifetime distribution, the renewal criterion is less appropriate and the one-cycle criterion becomes an attractive alternative. Conditions are determined for the existence of an optimal replacement age T^* in an AR model and optimal threshold age T_opp^* in an OAR model, using a one-cycle criterion and a known lifetime distribution. In the optimal threshold age T_opp^*, the corresponding minimal expected costs per unit time are equal to the expected costs per unit time in an AR model. It is also shown that for a lifetime distribution with increasing hazard rate, the optimal threshold age is smaller than the optimal replacement age. For unknown lifetime distribution, AR and OAR strategies are considered within a nonparametric predictive inferential (NPI) framework. The relationship between the NPI-based expected costs per unit time in an OAR model and those in an AR model is investigated. A small simulation study is presented to illustrate this NPI approach.     

An Equipment Replacement Problem

This paper describes a study undertaken to develop a model for the replacement of a particular type of machine. The dominant operating costs are identified, and existing replacement models reviewed. One of the most important factors is the cost of production stoppages which can sometimes result from the breakdown of these machines. In order to predict the effects of this in terms of the machines' age, a simulation model is developed.The results from the replacement model are investigated in terms of their sensitivity to the variability in the estimates of the parameters required by the model. In particular some interesting results relating the method used for calculating the resale values and the optimal replacement interval are presented.     

Equipment Replacement in an Unsteady Economy

The decision problem concerning the replacement of members of a fleet of fork lift trucks during a period of inflation and economic uncertainty is considered. Based upon the analysis of data collected over a 2 year period of considerable inflation, a model of the expected operating costs for a truck is developed. The usual replacement criteria are not applicable here and an alternative criterion function based upon relatively short term estimates of costs and discount rate is presented. Using this function, the replacement decision is determined for both constant and variable discount rate situations.     

Efficiency consideration of generalized age replacement policy

Under the generalized age replacement policy, the system is replaced either at the predetermined age or upon failure if its corresponding repair time exceeds the threshold, whichever comes first. In this paper, we investigate the optimal choice of the pre‐determined preventive replacement age for a nonwarranted system, which minimizes the expected cost rate during the life cycle of the system from the customer's perspective under certain cost structures. Furthermore, we discuss several properties of such a generalized age replacement policy in comparison with the traditional age replacement policy. An efficiency, which represents the fractional time that the system is on, is defined under the proposed generalized age replacement policy and its monotonicity properties are investigated as well. The main objective of this study is to investigate the advantageous features of the generalized age replacement policy over the traditional age replacement policy with regard to the availability of the repairable system. Assuming that the system deteriorates with age, we illustrate our proposed optimal policies numerically and observe the impact of relevant parameters on the optimal preventive replacement age.     

Novel hybrid heuristics for an extension of the dynamic relay deployment problem over disaster areas

In this paper, we propose a novel autonomous intelligent tool for the optimum design of a wireless relayed communication network deployed over disaster areas. The so-called dynamic relay deployment problem consists of finding the optimum number of deployed relays and their location aimed at simultaneously maximizing the overall number of mobile nodes covered and minimizing the cost of the deployment. In this paper, we extend the problem by considering diverse relay models characterized by different coverage radii and associated costs. To efficiently tackle this problem we derive a novel hybrid scheme comprising: (1) a Harmony Search (HS)-based global search procedure and (2) a modified version of the well-known K-means clustering algorithm as a local search technique. Single- and bi-objective formulations of the algorithm are proposed for emergency and strategic operational planning, respectively. Monte Carlo simulations are run over a emulated scenario based on real statistical data from the Castilla La Mancha region (center of Spain) to show that, in comparison with a standard implementation of the K-means algorithm followed by a exhaustive search procedure over all relay-model combinations, the proposed scheme renders on average better coverage levels and reduced costs providing, at the same time, an intelligent tool capable of simultaneously determining the number and models of the relays to be deployed.