Optimal maintenance service contract negotiation with aging equipment

In recent years, there has been a growing trend to out-source service operations in which the equipment maintenance is carried out by an external agent rather than in-house. Often, the agent (service provider) offers more than one option and the owners of equipment (customers) are faced to the problem of selecting the optimal option, under the terms of a contract. In the current work, we develop a model and report results to determine the agent’s optimal strategy for a given type of contract. The model derives in a non-cooperative game formulation in which the decisions are taken by maximizing expected profits. This work extends previous models by considering the realistic case of equipments having an increasing failure intensity due to imperfect maintenance, instead of the standard assumption that considers failure times are exponentially distributed (constant failure intensity). We develop a model using a linear function of time to characterize the failure intensity. The main goal, for the agent, is to determine the pricing structure in the contract and the number of customers to service. On the other hand, for the clients, the main goal is to define the period between planned actions for preventive maintenance and the time to replace equipments. In order to give a complete characterization of the results, we also carry out a sensitivity analysis over some of the factors that would influence over the failure intensity.     

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.     

Three-level warranty service contract among manufacturer,agent and customer: A game-theoretical approach

A warranty is a service contract between a manufacturer and a customer which plays a vital role in many businesses and legal transactions. In this paper, various three-level service contracts will be presented among the following three participants; a manufacturer, an agent, and a customer. In order to obtain a better result, the interaction between the aforementioned participants will be modeled using the game theory approach. Under non-cooperative and semi-cooperative games, the optimal sale price, warranty period and warranty price for the manufacturer and the optimal maintenance cost or repair cost for the agent are obtained by maximizing their profits. The satisfaction of the customer is also maximized by being able to choose one of the suggested options from the manufacturer and the agent, based on the risk parameter. Several numerical examples and managerial insights are presented and used to illustrate the models presented in this paper.     

The signal model: A model for competing risks of opportunistic maintenance

This paper presents a competing risks reliability model for a system that releases signals each time its condition deteriorates. The released signals are used to inform opportunistic maintenance. The model provides a framework for the determination of the underlying system lifetime from right-censored data, without requiring explicit assumptions about the type of censoring to be made. The parameters of the model are estimated from observational data by using maximum likelihood estimation. We illustrate the estimation process through a simulation study. The proposed signal model can be used to support decision-making in optimising preventive maintenance: at a component level, estimates of the underlying failure distribution can be used to identify the critical signal that would trigger maintenance of the individual component; at a multi-component system level, accurate estimates of the component underlying lifetimes are important when making general maintenance decisions. The benefit of good estimation from censored data, when adequate knowledge about the dependence structure is not available, may justify the additional data collection cost in cases where full signal data is not available.     

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.     

A batch arrival retrial queue with general retrial times under Bernoulli vacation schedule for unreliable server and delaying repair

This paper deals with the steady state behaviour of an M^x/G/1 queue with general retrial time and Bernoulli vacation schedule for an unreliable server, which consists of a breakdown period and delay period. Here we assume that customers arrive according to compound Poisson processes. While the server is working with primary customers, it may breakdown at any instant and server will be down for short interval of time. Further concept of the delay time is also introduced. The primary customer finding the server busy, down or vacation are queued in the orbit in accordance with FCFS (first come first served) retrial policy. After the completion of a service, the server either goes for a vacation of random length with probability p or may continue to serve for the next customer, if any with probability (1 − p). We carry out an extensive analysis of this model. Finally, we obtain some important performance measures and reliability indices of this model.     

A maintenance model with failures and inspection following Markovian arrival processes and two repair modes

We consider a deteriorating system submitted to external and internal failures, whose deterioration level is known by means of inspections. There are two types of repairs: minimal and perfect, depending on the deterioration level, each one following a different phase-type distribution. The failures and the inspections follow different Markovian arrival processes (MAP). Under these assumptions, the system is governed by a generalized Markov process, whose state space and generator are constructed. This general model includes the phase-type renewal process as a special case. The distribution of the number of minimal and perfect repairs between two inspections are determined. A numerical application optimizing costs is performed, and different particular cases of the model are compared.     

Machine reliability and preventive maintenance planning for cellular manufacturing systems

The paper proposes a preventive maintenance (PM) planning model for the performance improvement of cellular manufacturing systems (CMS) in terms of machine reliability, and resource utilization. In a CMS, parts are processed by a group of interdependent machines, where machine reliability plays an important role in the performance improvement of the cell. Assuming that machine failure times follow a Weibull distribution, the proposed model determines a PM interval and a schedule for performing PM actions on each machine in the cell by minimizing the total maintenance cost and the overall probability of machine failures. The model uses a combined cost and reliability based approach, and optimizes maintenance costs by administering a group maintenance policy subject to a desirable machine reliability threshold. The study also proposes a CMS design model that integrates the above PM concepts into the design process. Illustrative examples are presented to demonstrate the applicability of the proposed approach.     

A note on replacement policy for a system subject to non-homogeneous pure birth shocks

A system is subject to shocks that arrive according to a non-homogeneous pure birth process. As shocks occur, the system has two types of failures. Type-I failure (minor failure) is removed by a general repair, whereas type-II failure (catastrophic failure) is removed by an unplanned replacement. The occurrence of the failure type is based on some random mechanism which depends on the number of shocks occurred since the last replacement. Under an age replacement policy, a planned (or scheduled) replacement happens whenever an operating system reaches age T. The aim of this note is to derive the expected cost functions and characterize the structure of the optimal replacement policy for such a general setting. We show that many previous models are special cases of our general model. A numerical example is presented to show the application of the algorithm and several useful insights.     

A number-dependent replacement policy for a system with continuous preventive maintenance and random lead times

This paper considers a number-dependent replacement policy for a system with two failure types that is replaced at the nth type I (minor) failure or the first type II (catastrophic) failure, whichever occurs first. Repair or replacement times are instantaneous but spare/replacement unit delivery lead times are random. Type I failures are repaired at zero cost since preventive maintenance is performed continuously. Type II failures, however, require costly system replacement. A model is developed for the average cost per unit time based on the stochastic behavior of the system and replacement, storage, and downtime costs. The cost-minimizing policy is derived and discussed. We show that the optimal number of type I failures triggering replacement is unique under certain conditions. A numerical example is presented and a sensitivity analysis is performed.     

The availability model and parameters estimation method for the delay time model with imperfect maintenance at inspection

The delay time model (DTM) is widely used to model the two-stage failure process and is helpful for developing cost-effective inspection/maintenance plans. Imperfect maintenance is common in practice, but seldom considered in DTM. An improved DTM with imperfect maintenance at inspection has been developed based on the assumption of imperfect inspection maintenance and perfect failure maintenance. The model of the long-run availability for the improved DTM is established. Parameters estimation method and the test for goodness of fit method are given. Numerical simulations are performed to study the influence of imperfect maintenance on the long-run availability and to validate the credibility of the parameters estimation method. The results show that imperfect maintenance will decrease the long-run availability. The existence of the optimal inspection interval regarding the maximum long-run availability is tightly related to the improvement factor, which denotes the maintenance effect. The parameters estimation method proves credible. The maximum likelihood estimations of the reliability parameters can be easily achieved by the Genetic Algorithms (GAs) searching tool.     

A mathematical model for a capacity reservation contract

It is common practice in many industries to use a replenishment contract with a mechanism of capacity reservation. In this paper, we focus on a multi-period capacity reservation contract practiced between a buyer, who buys a single type of product and sells it to end-customers, and two or more heterogeneous suppliers, who produce and replenish the product as agreed upon contractually.In this paper, a mathematical model including several key features of a real contract is developed for a single supplier situation from the buyer’s perspective. It is then extended to a multiple supplier model for a system in which there are several heterogeneous suppliers with different capacities and prices. A rolling-horizon implementation strategy is suggested for the efficient application of the models. Extensive computational experiments demonstrate that the model and strategy can produce cost effective contractual terms for the buyer within a few seconds.     

A two-period supply contract model for a decentralized assembly system

Supply contract helps in coordinating the supply of quantities from different suppliers in order to meet the demand for a product. In this paper, supply contract models are developed by considering an assembly system operated under a centralized and a decentralized control modes. The centralized control mode considers a single decision maker and offers a global optimal solution. However, the decentralized control mode considers each player in the contract as a decision maker and offers local optimal solutions based on the production and cost characteristics of each player. Such local optimal solutions are adjusted through coordinating parameters to obtain global optimal solutions. If a contract developed for a decentralized control mode achieves the global optimal solution, then the supply chain (or channel) is said to be coordinated.     

A facility location and installation of resources model for level of repair analysis

The Level of Repair Analysis – LORA – is an analytic methodology aimed at determining: (i) the optimal location of facilities that compose a maintenance structure; (ii) the quantity of required resources in each facility; and (iii) the best repair policies, i.e., rules that determine if a given component should be discarded or repaired, and where those actions should take place. This work presents a mixed-integer programming model for LORA that is more comprehensive than others in the literature, being suitable to many practical situations. The model was applied to 15 substantial real world problems, and considering distinct maintenance policies to some of them, resulted in 22 different solutions, all of which could be achieved by a commercial Mixed-Integer Programming (MIP) solver in reasonable times.     

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.     

Time and inventory dependent optimal maintenance policies for single machine workstations: An MDP approach

In this work the problem of obtaining an optimal maintenance policy for a single-machine, single-product workstation that deteriorates over time is addressed, using Markov Decision Process (MDP) models. Two models are proposed. The decision criteria for the first model is based on the cost of performing maintenance, the cost of repairing a failed machine and the cost of holding inventory while the machine is not available for production. For the second model the cost of holding inventory is replaced by the cost of not satisfying the demand. The processing time of jobs, inter-arrival times of jobs or units of demand, and the failure times are assumed to be random. The results show that in order to make better maintenance decisions the interaction between the inventory (whether in process or final), and the number of shifts that the machine has been working without restoration, has to be taken into account. If this interaction is considered, the long-run operational costs are reduced significantly. Moreover, structural properties of the optimal policies of the models are obtained after imposing conditions on the parameters of the models and on the distribution of the lifetime of a recently restored machine.     

An algorithmic approach for maintenance management based on advanced state space systems and harmonic regressions

Point mechanisms are special track elements which failures results in delays and increased operating costs. In some cases such failures cause fatalities. A new robust algorithm for fault detection of point mechanisms is developed. It detects faults by comparing what can be considered the ‘normal’ or ‘expected’ shape of some signal with respect to the actual shape observed as new data become available. The expected shape is computed as a forecast of a combination of models. The proposed system deals with complicated features of the data in the case study, the main ones being the irregular sampling interval of the data and the time varying nature of the periodic behaviour. The system models are set up in a continuous-time framework and the system has been tested on a large dataset taken from a point mechanism operating on a commercial line.     

A compact optimization model for the tail assignment problem

This paper investigates a new model for the so-called Tail Assignment Problem, which consists in assigning a well-identified airplane to each flight leg of a given flight schedule, in order to minimize total cost (cost of operating the flights and possible maintenance costs) while complying with a number of operational constraints. The mathematical programming formulation proposed is compact (i.e., involves a number of $0?1$ decision variables and constraints polynomial in the problem size parameters) and is shown to be of significantly reduced dimension as compared with previously known compact models. Computational experiments on series of realistic problem instances (obtained by random sampling from real-world data set) are reported. It is shown that with the proposed model, current state-of-the art MIP solvers can efficiently solve to exact optimality large instances representing 30-day flight schedules with typically up to 40 airplanes and 1500 flight legs connecting as many as 21 airports. The model also includes the main existing types of maintenance constraints, and extensive computational experiments are reported on problem instances of size typical of practical applications.     

A phase-type geometric process repair model with spare device procurement and repairman’s multiple vacations

This paper analyzes a phase-type geometric process repair model with spare device procurement lead time and repairman’s multiple vacations. The repairman may mean here the human beings who are used to repair the failed device. When the device functions smoothly, the repairman leaves the system for a vacation, the duration of which is an exponentially distributed random variable. In vacation period, the repairman can perform other secondary jobs to make some extra profits for the system. The lifetimes and the repair times of the device are governed by phase-type distributions (PH distributions), and the condition of device following repair is not “as good as new”. After a prefixed number of repairs, the device is replaced by a new and identical one. The spare device for replacement is available only by an order and the procurement lead time for delivering the spare device also follows a PH distribution. Under these assumptions, the vector-valued Markov process governing the system is constructed, and several important performance measures are studied in transient and stationary regimes. Furthermore, employing the standard results in renewal reward process, the explicit expression of the long-run average profit rate for the system is derived. Meanwhile, the optimal maintenance policy is also numerically determined.     

Joint optimization of spare parts ordering and maintenance policies for multiple identical items subject to silent failures

In this paper the joint maintenance and spare parts ordering problem for more than one identical operating items is studied. The operating items may suffer two types of silent failures: a minor failure, which results in item malfunctioning, and a major failure, which renders the item completely out-of-function. Inspections are periodically held to detect any failures and the inspected items are preventively maintained, repaired or replaced according to their condition. Two ordering policies are investigated to supply the necessary spare parts: a periodic review and a continuous review policy. The expected total maintenance and inventory cost per time unit is derived and the proposed models are optimized for real case data. In addition, the sensitivity of the proposed models is studied through numerical examples and the effect of some key problem characteristics on the optimal decisions is discussed.