Optimal adaptive replacement in a renewal process

In this paper we present an exact method for computing the Weibull renewal function and its derivative for application in maintenance optimization. The computational method provides a solid extension to previous work by which an approximation to the renewal function was used in a Bayesian approach to determine optimal replacement times. In the maintenance scenario, under the assumption an item is replaced by a new one upon failure, the underlying process between planned replacement times is a renewal process. The Bayesian approach takes into account failure and survival information at each planned replacement stage to update the optimal time until the next planned replacement. To provide a simple approach to carry out in practice, we limit the decision process to a one‐step optimization problem in the sequential decision problem. We make the Weibull assumption for the lifetime distribution of an item and calculate accurately the renewal function and its derivative. A method for finding zeros of a function is adapted to the maintenance optimization problem, making use of the availability of the derivative of the renewal function. Furthermore, we develop the maximum likelihood estimate version of the Bayesian approach and illustrate it with simulated examples. The maintenance algorithm retains the adaptive concept of the Bayesian methodology but reduces the computational need. Copyright © 2014 John Wiley & Sons, Ltd.     

Consensus in Byzantine asynchronous systems

This paper presents a consensus protocol resilient to Byzantine failures. It uses signed and certified messages and is based on two underlying failure detection modules. The first is a muteness failure detection module of the class . The second is a reliable Byzantine behaviour detection module. More precisely, the first module detects processes that stop sending messages, while processes experiencing other non-correct behaviours (i.e., Byzantine) are detected by the second module. The protocol is resilient to F faulty processes, Fmin((n−1)/2,C) (where C is the maximum number of faulty processes that can be tolerated by the underlying certification service).The approach used to design the protocol is new. While usual Byzantine consensus protocols are based on failure detectors to detect processes that stop communicating, none of them use a module to detect their Byzantine behaviour (this detection is not isolated from the protocol and makes it difficult to understand and prove correct). In addition to this modular approach and to a consensus protocol for Byzantine systems, the paper presents a finite state automaton-based implementation of the Byzantine behaviour detection module. Finally, the modular approach followed in this paper can be used to solve other problems in asynchronous systems experiencing Byzantine failures.     

Assigning priorities for maintenance,repair and refurbishment in managing a municipal housing stock

The municipality of Lisbon owns a large housing stock that requires maintenance, repair and refurbishment. Taken together, these activities imply a financial effort each year that clearly exceeds the available budget, and therefore it is critical that the decisions on which sub-set of potential activities should be carried out in each coming year are based on sound analysis and evaluation. The design and construction process of a model to assist the Lisbon Municipality to assign priorities to these activities is described. The macbeth approach was extensively used, in an interactive and constructive process, to derive the value functions associated with each criterion and their respective weights, reflecting municipal policies and their officials preferences and attitudes. The paper also presents the procedure used to determine multidimensional reference-profiles that define urgency categories, enabling to assign each potential action to one of these categories. Finally, a specific model was defined to aggregate elemental building jobs in “packages”, when there are arguments (in terms of cost reduction, action coherence, urban environment impact synergies, etc.) that favour their joint execution under a single contract.     

Bayesian semiparametric analysis for a single item maintenance optimization

We address the problem of a finite horizon single item maintenance optimization structured as a combination of preventive and corrective maintenance in a nuclear power plant environment. We present Bayesian semiparametric models to estimate the failure time distribution and costs involved. The objective function for the optimization is the expected total cost of maintenance over the pre-defined finite time horizon. Typically, the mathematical modeling of failure times are based on parametric models. These models fail to capture the true underlying relationships in the data; indeed, under a parametric assumption, the hazard rates are treated as unimodal, which, as shown in this paper, is incorrect. Importantly, assuming an increasing failure rate, as is typically done, we show, is way off the mark in the present context. Since hazard and cost estimates feed into the optimization phase, from a risk management perspective, potentially gross errors, resulting from purely parametric models, can be obviated. We show the effectiveness of our approach using real data from the South Texas Project Nuclear Operating Company (STPNOC) located in Bay City, Texas.     

Profust reliability of a gracefully degradable system

Research in traditional reliability theory is based mainly on probist reliability, which uses a binary state assumption and classical reliability distributions. In the present paper the binary state assumption has been replaced by a fuzzy state assumption, thereby leading to profust reliability estimates of a powerloom plant, which is modelled as a two unit gracefully degradable system. Results of Bowles and Palaez [Application of fuzzy logic to reliability engineering, Proc. IEEE 83(3) (1995) 435–449] have been deduced as a particular case of results presented here. It is also recognized that estimation of system parameters such as failure rates, is vital in reliability estimation. Available methods for such estimation do not cover the underlying uncertainty in the failure data collection involving human judgment, evaluation and decision. In this paper we introduce a new approach based on fuzzy set theory to estimate such system parameters.     

Indirect assessment of the bivariate survival function

Estimating the bivariate survival function has been a major goal of many researchers. For that purpose many methods and techniques have been published. However, most of these techniques and methods rely heavily on bivariate failure data. There are situations in which failure time data are difficult to obtain and thus there is a growing need to assess the bivariate survival function for such cases. In this paper we propose two techniques for generating families of bivariate processes for describing several variables that can be used to indirectly assess the bivariate survival function. An estimation procedure is provided and a simulation study is conducted to evaluate the performance of our proposed estimator.     

Measuring the efficiency of highway maintenance contracting strategies: A bootstrapped non-parametric meta-frontier approach

Highly deteriorated US road infrastructure, major budgetary restrictions and the significant growth in traffic have led to an emerging need for improving performance of highway maintenance practices. Privatizing some portions of road maintenance operations by state Departments of Transportation (DOTs) under the auspices of performance-based contracts has been one of the innovative initiatives in response to such a need. This paper adapts the non-parametric meta-frontier framework to the two-stage bootstrapping technique to develop an analytical approach for evaluating the relative efficiency of two highway maintenance contracting strategies. The first strategy pertains to the 180 miles of Virginia’s Interstate highways maintained by Virginia DOT using traditional maintenance practices. The second strategy pertains to the 250 miles of Virginia’s Interstate highways maintained via a Public Private Partnership using a performance-based maintenance approach. The meta-frontier approach accounts for the heterogeneity that exists among different types of highway maintenance contracts due to different limitations and regulations. The two-stage bootstrapping technique accounts for the large set of uncontrollable factors that affect the highway deterioration processes. The preliminary findings, based on the historical data for the state of Virginia, suggest that road authorities (counties) that have used traditional contracting for transforming the maintenance expenditures into the improvement of the road conditions seem to be more efficient than road authorities that have used the performance-based contracting. This paper recommends that road authorities use hybrid contracting approaches that include best practices of both traditional and performance-based highway maintenance contracting.     

A novel heuristic approach to determine compromise management for end-of-life electronic products

The European Union directive of Waste Electrical and Electronic Equipment for recycling end-of-life (EOL) products has had a significant impact on global enterprises. Recent studies have shed light on optimization of the EOL process. In addition to identifying the most economical EOL process, identifying the EOL process with the smallest environmental load is equally important, and this is thus a bi-criteria optimization problem. This study attempts to optimize EOL processes for electronic products based on a three-stage heuristic approach, which simultaneously minimizes cost and environmental impact. The proposed heuristic approach then assesses the most common disassembly and recycling processes by using the characteristics of electronic product recycling. Next, the best process for this bi-criteria optimization problem is identified by using the compromise programming method. The empirical analysis is based on data for notebook, and the potential impact on best EOL processes when notebook adopt new product designs is also discussed.     

Decision dependent stochastic processes

Managers, typically, are unaware of the significant impact their decisions could have on the random mechanism driving a data generating process. Here, a new parametric Bayesian technique is introduced that would allow managers to obtain an estimate of the impact of their decisions on the stochastic process driving the data; this, in turn, should enhance a company’s overall decision-making capabilities. This general approach to modeling decision-dependency is carried out via an efficient Markov chain Monte Carlo method. A simulated example, and a real-life example, using historical maintenance and failure time data from a system at the South Texas Project Nuclear Operating Company, exemplifies the paper’s theoretical contributions. Conclusive evidence of decision dependence in the failure time distribution is reported, which in turn points to an optimal maintenance policy that results in potentially large financial savings to the Texas-based company.     

Optimal maintenance strategy under renewable warranty with repair time threshold

In this paper, we consider a periodic preventive maintenance model, from the manufacturer's perspective, which can be implemented to reduce the maintenance cost of a repairable product during a given warranty period. The product is assumed to deteriorate with age and the warranty policy we adopt in this paper takes into account the two factors of failure time and repair time of the product when the product failure occurs. Under the proposed two-factor warranty, a repair time threshold is pre-determined and if the repair takes more time than that of the threshold, the failed product is replaced with a renewed warranty policy. Otherwise, the product is only minimally repaired to return to the operating state. During such a renewable warranty period, preventive maintenance is conducted to reduce the rate of degradation periodically while the product is in operation. By assuming certain cost structures, we formulate the expected warranty cost during the warranty period from the manufacturer's perspective when a periodic preventive maintenance strategy is adapted. Although more frequent preventive maintenance increases the warranty cost, the chance of product failures would be reduced. The main aim of this paper is to accomplish the optimal trade-off between the warranty cost and the preventive maintenance period by determining the optimal preventive maintenance period that minimizes the total expected warranty cost during the warranty period. Assuming the power law process for the product failures, we illustrate our proposed maintenance model numerically and study the impact of relevant parameters on the optimal preventive maintenance policy.     

Discrete time modeling of mean-reverting stochastic processes for real option valuation

In this paper the recombining binomial lattice approach for modeling real options and valuing managerial flexibility is generalized to address a common issue in many practical applications, underlying stochastic processes that are mean-reverting. Binomial lattices were first introduced to approximate stochastic processes for valuation of financial options, and they provide a convenient framework for numerical analysis. Unfortunately, the standard approach to constructing binomial lattices can result in invalid probabilities of up and down moves in the lattice when a mean-reverting stochastic process is to be approximated. There have been several alternative methods introduced for modeling mean-reverting processes, including simulation-based approaches and trinomial trees, however they unfortunately complicate the numerical analysis of valuation problems. The approach developed in this paper utilizes a more general binomial approximation methodology from the existing literature to model simple homoskedastic mean-reverting stochastic processes as recombining lattices. This approach is then extended to model dual correlated one-factor mean-reverting processes. These models facilitate the evaluation of options with early-exercise characteristics, as well as multiple concurrent options.     

Optimal inspection and replacement policies for multi-state deteriorating systems

In this paper, a phase-type approach is proposed to derive optimal inspection and replacement policies for semi-Markovian deteriorating systems. In this approach, the general sojourn time distributions of a semi-Markovian maintenance model are approximated by acyclic phase-type distributions. Using the approximation, a semi-Markovian maintenance model can be transformed into a Markovian maintenance model such that the analytical tractability of Markov processes can be preserved. Based on the Markovian model, algorithms are provided to derive the optimal state-dependent and state-age-dependent inspection and replacement policies such that the expected long-run cost rate is minimized. Furthermore, procedures are developed to implement the optimal policies on semi-Markovian deteriorating systems. The implementation of the optimal policies are illustrated by numerical examples.     

Simultaneous production and maintenance planning for a single capacitated resource facing both a dynamic demand and intensive wear and tear

This paper presents a generic modeling framework to simultaneously decide about production quantities and maintenance operations for a capacitated resource facing a dynamic demand for different types of products. As the resource needs to be setup for each specific type of product, a lot-sizing problem occurs. In addition it is assumed that production causes intensive wear and tear. For this reason frequent maintenance activities need to be coordinated with the production operations in order to efficiently use the capacitated resource. A single generic model is presented to capture alternative forms of maintenance and different modes of interaction between maintenance and setups. As the model is numerically intractable for standard branch and bound algorithms, we solve it heuristically via a decomposition using a Fix-and-Optimize approach. Numerical results show that the proposed solution method produces high-quality results quickly. We further study the impact of simultaneous vs. sequential decisions about production and maintenance in the case of intensive wear and tear.     

A new approach to stochastic evolution equations with adapted drift

In this paper we develop a new approach to stochastic evolution equations with an unbounded drift A which is dependent on time and the underlying probability space in an adapted way. It is well-known that the semigroup approach to equations with random drift leads to adaptedness problems for the stochastic convolution term. In this paper we give a new representation formula for the stochastic convolution which avoids integration of non-adapted processes. Here we mainly consider the parabolic setting. We establish connections with other solution concepts such as weak solutions. The usual parabolic regularity properties are derived and we show that the new approach can be applied in the study of semilinear problems with random drift. At the end of the paper the results are illustrated with two examples of stochastic heat equations with random drift.     

On a New Shot Noise Process and the Induced Survival Model

Traditionally, in applications, the shot noise processes have been studied under the assumption that the underlying arrival point process (shock process) is the homogeneous (or nonhomogeneous) Poisson process. However, most of the real life shock processes do not possess the independent increments property and the Poisson assumption is made just for simplicity. Recently, in the literature, a new point process, the generalized Polya process (GPP), has been proposed and characterized. The GPP is defined via the stochastic intensity that depends on the number of events in the previous interval and, therefore, does not possess the independent increments property. In this paper, we consider the GPP as an underlying shock process for the shot noise process. The corresponding survival model is considered and the survival probability and its failure rate are derived and thoroughly analyzed. Furthermore, a new concept, the history-dependent residual life time, is defined and discussed.     

Evaluation of the expected makespan of a set of non-resumable jobs on parallel machines with stochastic failures

In this paper we consider a production process at operative level on m$m$ identical parallel machines, which are subject to stochastic machine failures. To avoid long downtime of the machines, caused by unexpected failures, preventive maintenance activities are planned and conducted, but if a failure could not be averted a corrective maintenance has to be performed. Both maintenance activities are assumed to restore the machine to be “as good as new”. The maintenance activities, the number of jobs and their allocation to machines as well as their sequence have a large impact on the performance of the production process and the delivery dates.     

Justification for the next generation of maintenance modelling techniques

Variant forms of reliability centred maintenance (RCM) have been the maintenance improving tools of choice for the last 20 years. In this case study paper, justification is made for implementing, and a path is laid out to implement, Operations Research in the form of statistical modelling as the next step forward after RCM. The lack of failure data issue has been addressed by using elicitation protocols to provide component lifetime distributions. Graphical analysis and Crowe/AMSAA (Army Materials Systems Analysis Activity) methodologies are developed as a basis for justifying expenditures on maintenance improvement initiatives. A review of historical empirical—inferential techniques dating back to WWII is presented as well as discussions of the current applicability of the same. The deregulation of the Electrical Generation Industry has produced severe restraints on the publishing of failure data. Owing to a fortuitous set of circumstances, a limited amount of data became releasable, which allowed the promise of the method to be demonstrated.     

Optimal component replacement decisions using vibration monitoring and the proportional-hazards model

This paper describes a case study in which the Weibull proportional-hazards model is used to determine the optimal replacement policy for a critical item which is subject to vibration monitoring. Such an approach has been used to date in the context of monitoring through oil debris analysis, and this approach is extended in this paper to the vibration monitoring context. The Weibull proportional-hazards model is reviewed along with the software EXAKT used for optimization. In particular the case considers condition-based maintenance for circulating pumps in a coal wash plant that is part of the SASOL petrochemical company. The condition-based maintenance policy recommended in this study is based on histories collected over a period of 2 years, and is compared with current practice. The policy is validated using data that arose from subsequent operation of the plant.     

Application of multi-dimensional procurement auction in single-period inventory models

Procurement is one of the major activities in the Manufacturing Resource Planning (MRP II), which is closely coupled with inventory management. Any improvement in this area will have a direct impact on the performance of the entire supply chain. Auction mechanism can be a successful procurement method when there are several potential suppliers available. In this paper, we consider a single-period inventory model when the selection of the supplier is done through a reverse auction with bids consisting of several attributes, namely price, shortage quantity, and lead time. The multi-dimensionality of the bid increases the complexity of the underlying problem creating a need for an approach to determine an approximate optimal target level. This is needed for the initiation of the auction and the procurement process. Monte-Carlo simulation method was used to investigate the performance of the approximation. Simulation results show that the analytical method provides an acceptable approximation for the optimal target inventory level.     

Concurrent optimization in designing for logistics support

Concurrent Engineering has always been an important field within military industry and is gaining recognition within commercial industry as well. Studies have suggested that long-range research efforts need to be directed to the area of integrated logistics. In order to satisfy the overall logistics objectives, product designs must incorporate consideration of the impact that design decisions have on operations, maintenance, transportation and supply. This paper presents a model that carries out a concurrent optimization of a product design and its associated manufacturing and logistics support systems. We offer this model as a framework for decision support of concurrent engineering activities.