Value of condition monitoring for optimal replacement in the proportional hazards model with continuous degradation

This article investigates the value of perfect monitoring information for optimal replacement of deteriorating systems in the Proportional Hazards Model (PHM). A continuous-time Markov chain describes the condition of the system. Although the form of an optimal replacement policy for system under periodic monitoring in the PHM was developed previously, an approximation of the Markov process as constant within inspection intervals led to a counter intuitive result that less frequent monitoring could yield a replacement policy with lower average cost. This article explicitly accounts for possible state transitions between inspection epochs to remove the approximation and eliminate the cost anomaly. However, the mathematical evaluation becomes significantly more complicated. To overcome this difficulty, a new recursive procedure to obtain the parameters of the optimal replacement policy and the optimal average cost is presented. A numerical example is provided to illustrate the computational procedure and the value of condition monitoring. By taking the monitoring cost into consideration, the relationships between the unit cost of periodic monitoring and the upfront cost of continuous monitoring under which the continuous, periodic, or no monitoring scheme is optimal are obtained

Multi-State System Reliability: A New and Systematic Review

AbstractReliability analysis considering multiple possible states is known as multi-state (MS) reliability analysis. Multi-state system reliability models allow both the system and its components to assume more than two levels of performance. Through multi-state reliability models provide more realistic and more precise representations of engineering systems, they are much more complex and present major difficulties in system definition and performance evaluation. MSS reliability has received a substantial amount of attention in the past four decades. This article presents a new and systematic review about multi-state system reliability. A timely review is an effective work related to improving the development of MSS theory. The review about the latest studies and advances about multi-state system reliability evaluation, multi-state systems optimization and multi-state systems maintenance is summarized in this paper

Semi-Markov and delay time models of maintenance

This thesis is concerned with modelling inspection policies of facilities which Qraduallv deteriorate in time. The context of inspection policies lends itself readily to probabilistic modelling. Indeed, many of the published theoretical models to be found in the literature adopt a Markov approach, where states are usually 'operating', 'operating but fault present', and 'failed'. However, most of these models fail to discuss the 'fit' of the model to data,a nd virtually no exampleso f actual applications or case-studiesa re to be found. hi a series of recent papers dating from 1984, a robust approach to solve these problems has been introduced and developed as the Delay Time Model (DTM). The central concept for this model is the delay time, h, of a fault which is the time lapse from when a fault could first be noticed until the time when its repair can be delayed no longer because of unacceptable consequences. The bottle neck in delay time modelling is how to estimate the delay time distribution parameters. Two methods for estimating these parameters have been developed. namely the subjective method and the objective method. Markov models have the advantage of an extensive body of theory. 'fliere are, however. difficulties of definition, measurement, and calculation when applying Markov models to real-world situations within a maintenance context. Indeed. this problem has motivated the current research which ainis to explore the two modelling methodologies in cases where comparison is valid, and also to gain an insight as to how robust Markov inspection models can be as decision-aids where Markovian properties are not strictly satisfied. It Nvill be seen that a class of inspection problems could be solved by a serni- Markov model using the delay time concept. In this thesis, a typical senii-i%Ia, rkov inspection model based upon the delay time concept is presented for a complex repairable systein that may fail during the course of its service lifetime and the results are compared. Finally, a case study of the senii-Markov inspection model and the delay time model is discussed

A unified methodology of maintenance management for repairable systems based on optimal stopping theory

This dissertation focuses on the study of maintenance management for repairable systems based on optimal stopping theory. From reliability engineering’s point of view, all systems are subject to deterioration with age and usage. System deterioration can take various forms, including wear, fatigue, fracture, cracking, breaking, corrosion, erosion and instability, any of which may ultimately cause the system to fail to perform its required function. Consequently, controlling system deterioration through maintenance and thus controlling the risk of system failure becomes beneficial or even necessary. Decision makers constantly face two fundamental problems with respect to system maintenance. One is whether or when preventive maintenance should be performed in order to avoid costly failures. The other problem is how to make the choice among different maintenance actions in response to a system failure. The whole purpose of maintenance management is to keep the system in good working condition at a reasonably low cost, thus the tradeoff between cost and condition plays a central role in the study of maintenance management, which demands rigorous optimization. The agenda of this research is to develop a unified methodology for modeling and optimization of maintenance systems. A general modeling framework with six classifying criteria is to be developed to formulate and analyze a wide range of maintenance systems which include many existing models in the literature. A unified optimization procedure is developed based on optimal stopping, semi-martingale, and lambda-maximization techniques to solve these models contained in the framework. A comprehensive model is proposed and solved in this general framework using the developed procedure which incorporates many other models as special cases. Policy comparison and policy optimality are studied to offer further insights. Along the theoretical development, numerical examples are provided to illustrate the applicability of the methodology. The main contribution of this research is that the unified modeling framework and systematic optimization procedure structurize the pool of models and policies, weed out non-optimal policies, and establish a theoretical foundation for further development

Optimal replacement in the proportional hazards model and its applications in a product-service system

Condition-based maintenance is rapidly gaining favor as a way to prevent the failures of capital-intensive assets and to maintain them in good operating condition with minimum cost. A valuable and increasingly prevalent way to incorporate condition information into risk estimation is by the proportional hazards model (PHM), which explicitly includes both the age and the condition information in the calculation of the hazard function. This dissertation consists of three papers, in which the optimal replacement policies for systems whose deterioration process follows the PHM are developed under different settings; and a joint optimization of the asset and inventory management problem in the context of a product-service system is considered. In the first paper, a continuous time Markov covariate process is assumed to describe the condition of a system that is under periodic monitoring. Although the form of an optimal replacement policy for such a system in the PHM was developed previously, an approximation of the Markov process as constant within inspection intervals led to a counter-intuitive result that less frequent monitoring could yield a replacement policy with lower average cost. Accounting for possible state transitions between inspection epochs removes the approximation and eliminates the cost anomaly. A new recursive procedure to obtain the parameters of the optimal replacement policy is presented. By comparing the replacement and monitoring costs of different monitoring scheme, the value of condition information is evaluated. In the second paper, the optimal replacement policy for systems in the PHM with semi-Markovian covariate process and continuous monitoring is developed. Numerical examples and sensitivity analysis provide some insights about the suitability of a Markov approximation and the impact of the variations in the input parameters on the cost. In applying the optimal replacement policies to a product-service system, where the producers provide the use of the products to customers while retaining ownership, the coupling between the decision making for preventive replacement and the decision making for inventory management is evident. In the third paper, an integrated model is proposed for the preventive maintenance of a fleet of products and the inventory management of a hybrid manufacturing-remanufacturing system in the context of a product-service system. A joint optimization technique is developed to obtain the optimal parameters for the operational policy of the integrated model to minimize the long run average cost per unit time. In addition, the effect of the assumption that the replaced products are not sorted is evaluated

Last time buy and repair decisions for spare parts

Original Equipment Manufacturers (OEM’s) of advanced capital goods often offer service contracts for system support to their customers, for which spare parts are needed. Due to technological changes, suppliers of spare parts may stop production at some point in time. As a reaction to that decision, an OEM may place a so-called Last Time Buy (LTB) order to cover demand for spare parts during the remaining service period, which may last for many years. The fact that there might be other alternative sources of supply in the next periods\ud complicates the decision on the LTB. In this paper, we develop a heuristic method to find the near- optimal LTB quantity in presence of an imperfect repair option of the failed parts that can be returned from the field. Comparison of our method to simulation shows high approximation accuracy. Numerical experiments reveal that repair is an excellent option as\ud alternative sourcing, even if it is more expensive than buying a new part, because of postponement of the repair decisions. In addition, we show the impact of other key parameters on costs and LTB quantity

Spare parts planning and control for maintenance operations

This paper presents a framework for planning and control of the spare parts supply chain inorganizations that use and maintain high-value capital assets. Decisions in the framework aredecomposed hierarchically and interfaces are described. We provide relevant literature to aiddecision making and identify open research topics. The framework can be used to increasethe e¿ciency, consistency and sustainability of decisions on how to plan and control a spareparts supply chain. This point is illustrated by applying it in a case-study. Applicability of theframework in di¿erent environments is also investigated

Optimal Overhaul-Replacement Policies for Repairable Machine Sold with Warranty

This research deals with an overhaul-replacement policy for a repairable machine sold with Free Replacement Warranty (FRW). The machine will be used for a finite horizon, T (T <ï‚¥), and evaluated at a fixed interval, s (s< T). At each evaluation point, the buyer considers three alternative decisions i.e. Keep the machine, Overhaul it, or Replace it with a new identical one. An overhaul can reduce the machine age virtually, but not to a point that the machine is as good as new. If the machine fails during the warranty period, it is rectified at no cost to the buyer. Any failure occurring before and after the expiry of the warranty is restored by minimal repair. An overhaul-replacement policy is formulated for such machines by using dynamic programming approach to obtain the buyer's optimal policy. The results show that a significant rejuvenation effect due to overhaul may extend the length of machine life cycle and delay the replacement decision. In contrast, the warranty stimulates early machine replacement and by then increases the replacement frequencies for a certain range of replacement cost. This demonstrates that to minimize the total ownership cost over T the buyer needs to consider the minimal repair cost reduction due to rejuvenation effect of overhaul as well as the warranty benefit due to replacement. Numerical examples are presented for both illustrating the optimal policy and describing the behavior of the optimal solution

Practical Methods for Optimizing Equipment Maintenance Strategies Using an Analytic Hierarchy Process and Prognostic Algorithms

Many large organizations report limited success using Condition Based Maintenance (CbM). This work explains some of the causes for limited success, and recommends practical methods that enable the benefits of CbM. The backbone of CbM is a Prognostics and Health Management (PHM) system. Use of PHM alone does not ensure success; it needs to be integrated into enterprise level processes and culture, and aligned with customer expectations. To integrate PHM, this work recommends a novel life cycle framework, expanding the concept of maintenance into several levels beginning with an overarching maintenance strategy and subordinate policies, tactics, and PHM analytical methods. During the design and in-service phases of the equipment’s life, an organization must prove that a maintenance policy satisfies specific safety and technical requirements, business practices, and is supported by the logistic and resourcing plan to satisfy end-user needs and expectations. These factors often compete with each other because they are designed and considered separately, and serve disparate customers. This work recommends using the Analytic Hierarchy Process (AHP) as a practical method for consolidating input from stakeholders and quantifying the most preferred maintenance policy. AHP forces simultaneous consideration of all factors, resolving conflicts in the trade-space of the decision process. When used within the recommended life cycle framework, it is a vehicle for justifying the decision to transition from generalized high-level concepts down to specific lower-level actions. This work demonstrates AHP using degradation data, prognostic algorithms, cost data, and stakeholder input to select the most preferred maintenance policy for a paint coating system. It concludes the following for this particular system: A proactive maintenance policy is most preferred, and a predictive (CbM) policy is more preferred than predeterminative (time-directed) and corrective policies. A General Path prognostic Model with Bayesian updating (GPM) provides the most accurate prediction of the Remaining Useful Life (RUL). Long periods between inspections and use of categorical variables in inspection reports severely limit the accuracy in predicting the RUL. In summary, this work recommends using the proposed life cycle model, AHP, PHM, a GPM model, and embedded sensors to improve the success of a CbM policy

Preventive maintenance and replacement scheduling : models and algorithms.

Preventive maintenance is a broad term that encompasses a set of activities aimed at improving the overall reliability and availability of a system. Preventive maintenance involves a basic trade-off between the costs of conducting maintenance/replacement activities and the cost savings achieved by reducing the overall rate of occurrence of system failures. Designers of preventive maintenance schedules must weigh these individual costs in an attempt to minimize the overall cost of system operation. They may also be interested in maximizing the system reliability, subject to some sort of budget constraint. In this dissertation, we present a complete discussion about the problem definition and review the literature. We develop new nonlinear mixed-integer optimization models, solve them by standard nonlinear optimization algorithms, and analyze their computational results. In addition, we extend the optimization models by considering engineering economy features and reformulate them as a multi-objective optimization model. We optimize this model by generational and steady state genetic algorithms as well as by a simulated annealing algorithm and demonstrate the computational results obtained by implementation of these algorithms. We perform a sensitivity analysis on the parameters of the optimization models and present a comparison between exact and metaheuristic algorithms in terms of computational efficiency and accuracy. Finally, we present a new mathematical function to model age reduction and improvement factor parameter used in optimization models. In addition, we develop a practical procedure to estimate the effect of maintenance activity on failure rate and effective age of multi component systems