O.R. modelling of the deterioration and maintenance of concrete structures

This paper reports on a collaborative venture between operational researchers and civil engineers over 3 years. The main objectives were to collect and publish data on the observed rates of deterioration of particular defect types in a large number of concrete bridges, and to develop predictive mathematical models that relate inspection frequency to maintenance costs. The motivation was in part associated with the prototype modelling paper for inspection practices of major concrete structures, Christer (1988). The paper reports on the analysis of data collected and the estimation of deterioration using the concept of delay time. The two phase delay time model is extended to an extra phase in order to model the process of cracking and spalling in concrete. Maximum likelihood techniques are used to estimate modelling parameters and an appropriate test of fit is carried out. Cost based models are then formulated to predict the cost effects of maintenance and inspection decision options. The cost model is applied first to an element, and then to an aggregate number of component types to produce a cost model for maintenance of a bridge or set of bridges.     

A case study of modelling preventive maintenance of a production plant using subjective data

In this paper we describe a subjective data based case study carried out at a company manufacturing copper products, which parallels a previously published objective data based study at the same plant. The purpose of this study is twofold. The first is to model the implementation of Planned Preventive Maintenance (PM) to an Extrusion Press using the delay time concept. The second is to test a method for estimation of model parameters from subjective data in the context of delay time modelling. The parameter values of the underlying fault arrival process and the delay time distribution were, unlike in a parallel objective study, initially estimated from subjective data obtained through a questionnaire survey. Since bias was present in the initial subjective estimate, a method of removing it was developed to improve the model fit. On the basis of the data analysis and delay time modelling, improved PM policy and procedures were proposed to increase the effectiveness and efficiency of PM.     

Subjective estimation of the delay time distribution in maintenance modelling

In this paper, the problems in the current method for obtaining a subjective estimate of the delay time distribution used in maintenance modelling are discussed and a brief literature survey on assessing subjective probability and expert judgment in decision making is presented. Based upon the results of the survey and experience in conducting a subjective estimating procedure for the delay time distribution, a revised procedure and method for obtaining the subjective delay time estimate is proposed, and the models for combining experts' opinions and updating the delay time distribution are also discussed. Case examples are given in the paper to demonstrate the methodology.     

利用故障数据和估计的检查数据建立维修优化模型

利用时间延迟概念,根据故障记录数据和估计的检查数据建立了预防维修模型.通过对故障记录数据统计分析,提出了模型的假定条件.采用最大似然估计法,估计参数,包括缺陷发生率、不完全检查概率和时间延迟分布.建立了有关预防维修间隔期和总停机时间之间关系的检查模型,并根据估计参数和检查模型,计算最佳维修间隔期.     

An EM Algorithm for Batch Markovian Arrival Processes and its Comparison to a Simpler Estimation Procedure

Although the concept of Batch Markovian Arrival Processes (BMAPs) has gained widespread use in stochastic modelling of communication systems and other application areas, there are few statistical methods of parameter estimation proposed yet. However, in order to practically use BMAPs for modelling, statistical model fitting from empirical time series is an essential task. The present paper contains a specification of the classical EM algorithm for MAPs and BMAPs as well as a performance comparison to the computationally simpler estimation procedure recently proposed by Breuer and Gilbert. Furthermore, it is shown how to adapt the latter to become an estimator for hidden Markov models.     

Modelling in the absence of data: a case study of fleet maintenance in a developing country

Adequate and relevant objective data for modelling maintenance decision problems are often incomplete or not readily accessible. This is particularly true in developing countries. In this paper the experience gained between 1991–95 in conducting a maintenance study of an inter-city express bus fleet in a developing country is presented. The lack of available maintenance records and operating data rendered the study the most data-starved maintenance modelling exercise the authors have met before or since. The study required the use of subjective methods to both define the problem and to estimate parameters, and the application of recently developed concepts in maintenance modelling along with snapshot analysis and delay time modelling. This imposed a structured approach to problem recognition and problem solution. The study contributed both directly and indirectly to a change in work culture and to a reduction in bus breakdown rate. The company was re-visited 5?years later specifically to seek evidence of lasting impact. Some evidence existed and is reported in the paper.     

Modelling the probability assessment of system state prognosis using available condition monitoring information

^** Email: w.wang{at}salford.ac.uk This paper reports on a model to assess the current and futurestates of a monitored system based on measured condition monitoringinformation to date. The true state of the system is unobservable,but is assumed to be related to the measured condition monitoringinformation in a stochastic way. We further assume that thetransition of the system state follows a time-dependent Markovchain which has only three states, namely good, defective andfailed. This assumption effectively defines a two-stage failureprocess which is widely used in delay time modelling of maintainedsystems. Three modelling techniques are used to establish themodel. First, we use a hidden Markov model to describe the transitionsbetween system states. Second, the transition matrix is establishedbased on the well-known delay time concept. The last one isthe use of the filtering technique to construct the relationshipbetween measured condition information and the underlying truestate of the system. We also discuss the procedure for modelparameter estimation. A numerical example is presented to demonstratethe modelling ideas.     

Modelling condition monitoring intervals: A hybrid of simulation and analytical approaches

This paper reports on a study of modelling condition monitoring intervals. The model is formulated based upon two important concepts. One is the failure delay time concept, which is used to divide the failure process of the item into two periods, namely a normal working period followed by a failure delay time period from a defect being first identified to the actual failure. The other is the conditional residual time concept, which assumes that the residual time also depends on the history condition information obtained. Stochastic filtering theory is used to predict the residual time distribution given all monitored information obtained to date over the failure delay time period. The solution procedure is carried out in two stages. We first propose a static model that is used to determine a fixed condition monitoring interval over the item life. Once the monitored information indicates a possible abnormality of the item concerned, that is the start of the failure delay time, a dynamic approach is employed to determine the next monitoring time at the current monitoring point given that the item is not scheduled for a preventive replacement before that time. This implies that the dynamic model overrides the static model over the failure delay time since more frequent monitoring might be needed to keep the item in close attention before an appropriate replacement is made prior to failure. Two key problems are addressed in the paper. The first is which criterion function we should use in determining the monitoring check interval, and the second is the optimization process for both models, which can be solved neither analytically nor numerically since they depend on two unknown quantities, namely, the available condition information and a decision of the time to replace the item over the failure delay time. For the first problem, we propose five appealingly good criterion functions, and test them using simulations to see which one performs best. The second problem was solved using a hybrid of simulation and analytical solution procedures. We finally present a numerical example to demonstrate the modelling methodology.     

An approach via state estimation to differential games with information time lag

This paper deals with zero-sum two-person differential games in which one player has a deferred information on the state vector. This player mends this lack of information by using an adaptative deterministic extrapolation to estimate the plant state, and then, makes his decisions by means of the datas so obtained. An analysis of the phenomenon yields a criterion for optimizing the estimation which is based upon the Hamiltonian estimation of the perfect information game. A class of extrapolators is given by its dynamical equation. Then, the initial game is reduced to a new game containing pure time delay in the state and the controls.     

Sensitivity analysis of the newsvendor model

Quality of decisions in inventory management models depends on the accuracy of parameter estimates used for decision making. In many situations, error in decision making is unavoidable. In such cases, sensitivity analysis is necessary for better implementation of the model. Though the newsvendor model is one of the most researched inventory models, little is known about its robustness. In this paper, we perform sensitivity analysis of the classical newsvendor model. Conditions for symmetry/skewness of cost deviation (i.e., deviation of expected demand–supply mismatch cost from its minimum) have been identified. These conditions are closely linked with symmetry/skewness of the demand density function. A lower bound of cost deviation is established for symmetric unimodal demand distributions. Based on demonstrations of the lower bound, we found the newsvendor model to be sensitive to sub-optimal ordering decisions, more sensitive than the economic order quantity model. Order quantity deviation (i.e., deviation of order quantity from its optimum) is explored briefly. We found the magnitude of order quantity deviation to be comparable with that of parameter estimation error. Mean demand is identified as the most influential parameter in deciding order quantity deviation.     

Energy models for decision making

Since the 1973 oil crisis there has been an explosion in energy modelling activities throughout the world. A bewildering array of models have been or are being developed. The models differ in their geographical scope (local, national, regional or global), their technical scope (a process, an industry, an energy source or all energy industries), their timescale (one to one hundred years) and their systems boundaries (energy, economy, society). In addition there are crucial differences in the level of detail modelled, in the way time is structured and in the way in which decisions are included or perhaps excluded from the model.The natural questions to ask are what sort of models are now available; which models are suitable for which purposes; what has been learnt so far; which are the promising directions for future developments? This paper draws on modelling experience both within the National Coal Board and elsewhere to discuss these questions. The paper contains the following sections: energy models and decision making processes; choosing model boundaries; logic and facts, the basis of the model; choice of energy model; links to the economy; future directions. The subject will be of interest to specialist energy modellers and those interested more generally in strategic modelling for government and industry.     

Delay Time Models of Industrial Inspection Maintenance Problems

The technique of delay time analysis is here extended to problems of industrial plant maintenance. A basic model of inspection maintenance is presented, along with models of some of the variations which have been observed in practice. Numerical examples indicate both the nature and sensitivity of the output from the models.     

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.     

The robustness of the semi-Markov and delay time single-component inspection models to the Markov assumption

The context of planned preventive maintenance lends itself readilyto probabilistic modelling. Indeed, many of the published theoreticalmodels to be found in the literature adopt a Markov approach,where states are usually ‘operating’, ‘operatingat one of several levels of deterioration’, and ‘failed’.However, most of these models assume the required Markovianproperty and do not address the issue of testing the assumption,or the related task of estimating parameters. It is possiblethat data are inadequate to test the assumption, or that theMarkov property is believed to be not strictly valid, but acceptableas an approximation. In this paper we consider within a specificinspection–maintenance context the robustness of a Markov-basedmodel when the Markov assumption is not valid. This is achievedby comparing the output of an exact delay time model of an inspection–maintenanceproblem with that of a semi-Markov approximation. The importanceof establishing the vadility of the Markov property in the modellingapplication is highlighted. If the plant behaviour is seen tobe nearly Markov, in the case considered the semi-Markov modelgives a good approximation to the exact model. Conversley ifthe Markov assumption is not a good approximation, the semi-Markovmodel can lead to inappropriate advice.     

Online state of charge estimation of Li-ion battery based on an improved unscented Kalman filter approach

An improved unscented Kalman filter approach is proposed to enhance online state of charge estimation in terms of both accuracy and robustness. The goal is to address the drawback associated with the unscented Kalman filter in terms of its requirement for an accurate model and a priori noise statistics. Firstly, Li-ion battery modelling and offline parameter identification is performed. Secondly, a sensitivity analysis experiment is designed to verify which model parameter has the greatest influence on state of charge estimation accuracy, in order to provide an appropriate parameter for the model adaptive algorithm. Thirdly, an improved unscented Kalman filter approach, composed of a model adaptive algorithm and a noise adaptive algorithm, is introduced. Finally, the results are discussed, which reveal that the proposed approach’s estimation error is less than 1.79% with acceptable robustness and time complexity.     

Fuzzy logic based intersection delay estimation

A fuzzy logic based delay estimation system is proposed and modelled. Conventional method of delay study involves solving static engineering equations in which only technical factors (traffic demand, roadway geometry, and signal control, etc.) are considered and the affect of nontechnical factors (such as weather or visibility) cannot be analyzed since they do not follow a predefined process. The fuzzy logic based delay estimation combines the complex technical and nontechnical factors and is adaptive to the changing driving environment. The rule base of the delay estimation system is constructed either following a mathematical model or from real-time traffic operational data. Simulation and field test of the fuzzy system have shown that fuzzy logic based modelling is a promising approach to improving intersection delay estimation.     

A stochastic model for joint spare parts inventory and planned maintenance optimisation

Spare parts demands are usually generated by the need of maintenance either preventively or at failures. These demands are difficult to predict based on historical data of past spare parts usages, and therefore, the optimal inventory control policy may be also difficult to obtain. However, it is well known that maintenance costs are related to the availability of spare parts and the penalty cost of unavailable spare parts consists of usually the cost of, for example, extended downtime for waiting the spare parts and the emergency expedition cost for acquiring the spare parts. On the other hand, proper planned maintenance intervention can reduce the number of failures and associated costs but its performance also depends on the availability of spare parts. This paper presents the joint optimisation for both the inventory control of the spare parts and the Preventive Maintenance (PM) inspection interval. The decision variables are the order interval, PM interval and order quantity. Because of the random nature of plant failures, stochastic cost models for spare parts inventory and maintenance are derived and an enumeration algorithm with stochastic dynamic programming is employed for finding the joint optimal solutions over a finite time horizon. The delay-time concept developed for inspection modelling is used to construct the probabilities of the number of failures and the number of the defective items identified at a PM epoch, which has not been used in this type of problems before. The inventory model follows a periodic review policy but with the demand governed by the need for spare parts due to maintenance. We demonstrate the developed model using a numerical example.     

Chaos and reproduction in sea level

Prediction of sea-level is an important task for navigation, coastal engineering and geodetic applications, as well as recreational activities. This study presents a comparison of Chaos theory and Auto-Regressive Integrated Moving Average (ARIMA) techniques for sea level modelling for daily, weekly, 10-day and monthly time scale at the Cocos (Keeling) islands from 1992 to 2001. The state space reconstruction of the unknown underlying process is directly employed from time series data, through Takens delay embedding method: optimal embedding dimension and delay time are obtained from false nearest neighbours and average mutual information techniques, respectively. Optimal values are then used for the estimation of the correlation dimension and the largest Lyapunov exponent, for inspecting possible signatures of chaotic dynamics. We find a positive Lyapunov exponent an evident feature of chaos. Indeed, the nonlinear prediction of sea level, in the period ranging from January 2001 to December 2001, is in an excellent agreement with the data for the same period, evidencing the nonlinear nature of the process. ARIMA method is also used for sea level modelling, for the same time scales; the performances of the two models are compared using such statistical indices as the root mean square error (RMSE) and correlation coefficient (CC). The comparative analyses show that the chaos theory model has a slight edge over ARIMA while both models are in principal acceptable.     

Is It Better to Forget? Stimulus-Response, Prediction, and the Weight of Past Experience in a Fast-Paced Bargaining Task

Decision makers in dynamic environments such as air traffic control, firefighting, and call center operations adapt in real-time using outcome feedback. Understanding this adaptation is important for influencing and improving the decisions made. Recently, stimulus-response (S-R) learning models have been proposed as explanations for decision makers' adaptation. S-R models hypothesize that decision makers choose an action option based on their anticipation of its success. Decision makers learn by accumulating evidence over action options and combining that evidence with prior expectations. This study examines a standard S-R model and a simple variation of this model, in which past experience may receive an extremely low weight, as explanations for decision makers' adaptation in an evolving Internet-based bargaining environment. In Experiment 1, decision makers are taught to predict behavior in a bargaining task that follows rules that may be the opposite of, congruent to, or unrelated to a second task in which they must choose the deal terms they will offer. Both models provide a good account of the prediction task. However, only the second model, in which decision makers heavily discount all but the most recent past experience, provides a good account of subsequent behavior in the second task. To test whether Experiment 1 artificially related choice behavior and prediction, a second experiment examines both models' predictions concerning the effects of bargaining experience on subsequent prediction. In this study, decision models where long-term experience plays a dominating role do not appear to provide adequate explanations of decision makers' adaptation to their opponent's changing response behavior.