A condition-based maintenance policy for stochastically deteriorating systems

We focus on the analytical modeling of a condition-based inspection/replacement policy for a stochastically and continuously deteriorating single-unit system. We consider both the replacement threshold and the inspection schedule as decision variables for this maintenance problem and we propose to implement the maintenance policy using a multi-level control-limit rule.In order to assess the performance of the proposed maintenance policy and to minimize the long run expected maintenance cost per unit time, a mathematical model for the maintained system cost is derived, supported by the existence of a stationary law for the maintained system state.Numerical experiments illustrate the performance of the proposed policy and confirm that the maintenance cost rate on an infinite horizon can be minimized by a joint optimization of the maintenance structure thresholds, or equivalently by a joint optimization of a system replacement threshold and the aperiodic inspection schedule.     

Online maintenance policy for a deteriorating system with random change of mode

Most of maintenance policies proposed in the literature for gradually deteriorating systems, consider a stationary deterioration process. This paper is an attempt to take into account stochastically deteriorating systems which are subject to a sudden change in their degradation process. A technical device subject to gradual degradation is considered. It is assumed that the level of degradation can be resumed by a single scalar variable. An online maintenance decision rule is proposed, which makes it possible to take into account in real time the online information available on the operating mode of the system as well as its actual deterioration level. We show the efficiency of considering online decision rules for maintenance with respect to traditional maintenance policies based on a static alarm threshold. Numerical simulations are given, to assess and optimize the performance of the maintained system from its asymptotic unavailability point of view. It is compared to the results obtained with classical control-limit maintenance policies.     

An extended extreme shock maintenance model for a deteriorating system

In this paper, we study a deteriorating system which is suffering random shocks from its environment. Assume that in the system's operating stage, whenever a shock arrives, it will do some damage to the system, but shocks with a “small” level of damage are harmless for the system, while shocks with a “large” level of damage may result in the system's failure. The system's deterioration is caused by both the external shocks and the internal load. In the external, the magnitude of the shock damage the system can bear is decreasing with respect to the number of repairs taken. In the internal, the consecutive repair time is increasing in the number of repairs taken. A replacement policy N, by which the system is replaced at the time of the Nth failure, is adopted. An explicit expression of the long run average cost per unit time is derived, and an optimal policy N^* for minimizing the long run average cost per unit time is determined analytically. A numerical example is also given.     

退化串联可修系统瞬态可靠性分析

可修串联系统是一类经典的可靠性模型,在实际工程中较为常见．为满足工程实际需求,所研究的系统由2个部件和1个维修工组成．假设工作时间、维修时间和部件更换时间均服从指数分布,在维修之后系统不能修复如新．系统采用部件故障N次之后将被更新的维修策略．在这些假设下利用几何过程和马尔科夫过程对系统进行建模,再利用半马尔科夫过程和数值积分方法给出系统瞬态可用度和（0,t］时间内故障次数的计算公式．最后给出算例并应用Monte Carlo方法对所得公式进行验证．为进一步研究复杂机械系统的可靠性提供了理论基础．     

Models for maintenance optimization: a study for repairable systems and finite time periods

The problem of selecting a suitable maintenance policy for repairable systems and for a finite time period is presented. Since the late seventies, examples of models assessing corrective and preventive maintenance policies over an equipment life cycle exist in the literature. However, there are not too many contributions regarding real implementation of these models in the industry, considering realistic timeframes and for repairable systems. Modeling this problem requires normally the representation of different corrective and/or preventive actions that could take place at different moments, driving the equipment to different states with different hazard rates.An approach to pattern the system under finite periods of time has been the utilization of semi-Markovian probabilistic models, allowing later a maintenance policy optimization using dynamic programming. These models are very flexible to represent a given system, but they are also complex and therefore very difficult to handle when the number of the system possible states increases.This paper explores the trade-off between flexibility and complexity of these models, and presents a comparison in terms of model data requirements versus potential benefits obtained with the model.     

A study on inspection schemes in optimal design of control charts for deteriorating processes

The non-uniform inspection scheme obtained by the constant integrated hazard procedure overcomes the uniform scheme economically in optimal design of control charts. The comperative study is generalized in this paper to an optimization problem which looks for the optimal sampling points among all possible sampling schemes. The objective function is simplified here by modelling sequential time intervals as a family of functions of the first sampling interval, which also has been induced by the constant integrated hazard approach. The study demonstrates the model implementation through the economic design of $\overline{X}$ and T²-Hotelling control charts, both under the two widely used process failure mechanisms, that is, Weibull and Chen distributions. A comprehensive numerical investigation illustrates the possibility of existence of sampling schemes which outperform the constant integrated hazard approach and emphasizes the necessity of further investigation into the solution procedure.     

Optimizing the performance of a repairable system under a maintenance and repair contract

In this article a number of maintenance models for finite horizons are reviewed. These methods have not been applied as frequently as their infinite horizon counterparts, and yet are very much applicable to systems under maintenance and repair contracts. The emphasis in this paper is on repairable systems under maintenance and repair contracts, where the decision has to be made whether and when to repair or replace the system. Based on a case study, a new finite horizon model will be constructed and new approaches to analyze and improve repair/replacement decisions under a finite horizon introduced. Finally, the meaning of ‘risk’ and ‘criticality’ in the context of maintenance contracts will be discussed and quantified. Copyright © 2007 John Wiley & Sons, Ltd.     

A bivariate optimal replacement policy for a multistate repairable system

In this paper, a deteriorating simple repairable system with k+1 states, including k failure states and one working state, is studied. It is assumed that the system after repair is not “as good as new” and the deterioration of the system is stochastic. We consider a bivariate replacement policy, denoted by (T,N), in which the system is replaced when its working age has reached T or the number of failures it has experienced has reached N, whichever occurs first. The objective is to determine the optimal replacement policy (T,N)^* such that the long-run expected profit per unit time is maximized. The explicit expression of the long-run expected profit per unit time is derived and the corresponding optimal replacement policy can be determined analytically or numerically. We prove that the optimal policy (T,N)^* is better than the optimal policy N^* for a multistate simple repairable system. We also show that a general monotone process model for a multistate simple repairable system is equivalent to a geometric process model for a two-state simple repairable system in the sense that they have the same structure for the long-run expected profit (or cost) per unit time and the same optimal policy. Finally, a numerical example is given to illustrate the theoretical results.     

Designing a Bayesian network for preventive maintenance from expert opinions in a rapid and reliable way

In this study, a Bayesian Network (BN) is considered to represent a nuclear plant mechanical system degradation. It describes a causal representation of the phenomena involved in the degradation process. Inference from such a BN needs to specify a great number of marginal and conditional probabilities. As, in the present context, information is based essentially on expert knowledge, this task becomes very complex and rapidly impossible. We present a solution, which consists of considering the BN as a log-linear model on which simplification constraints are assumed. This approach results in a considerable decrease in the number of probabilities to be given by experts. In addition, we give some simple rules to choose the most reliable probabilities. We show that making use of those rules allows to check the consistency of the derived probabilities. Moreover, we propose a feedback procedure to eliminate inconsistent probabilities. Finally, the derived probabilities that we propose to solve the equations involved in a realistic Bayesian network are expected to be reliable. The resulting methodology to design a significant and powerful BN is applied to a reactor coolant sub-component in EDF Nuclear plants in an illustrative purpose.     

An optimal geometric process model for a cold standby repairable system

In this paper a cold standby repairable system consisting of two identical components and one repairman is studied. Assume that each component after repair is not ‘as good as new'. Under this assumption, by using a geometric process, we consider a replacement policy N based on the number of repairs of component 1. Our problem is to determine an optimal replacement policy N* such that the long-run expected reward per unit time is maximized. The explicit expression of the long-run expected reward per unit time is derived and the corresponding optimal repair replacement policy can be determined analytically or numerically. Finally, a numerical example is given.     

On a dynamic preventive maintenance policy for a system under inspection

The purpose of this article is to propose both state and time-dependent preventive maintenance policy for a multi-state deteriorating system, which is equipped with inspection equipment(s) connected to a computer center. After the system being identified as state x at nd through computation by the computer center after inspection (or measurement) via equipment(s), one maintenance action with the minimum expected total cost since nd till Nd (where N=n+K for a fixed integer 0<K<∞) will be chosen from the set A_x of alternatives also with the help of the computer center. In real case, the expected total costs since nd till Nd will be time-dependent and so is the maintenance action chosen at nd. A numerical example is given to illustrate such a maintenance policy for a Markovian deteriorating system to describe its state dependent aspect only for simplicity reason. Due to the fact that both equipment measurement and computer computation take time, the preventive maintenance policy for a sufficiently small d may be used in fact as the one under continuous inspection.     

Predictive maintenance policy for a gradually deteriorating system subject to stress

This paper deals with a predictive maintenance policy for a continuously deteriorating system subject to stress. We consider a system with two failure mechanisms which are, respectively, due to an excessive deterioration level and a shock. To optimize the maintenance policy of the system, an approach combining statistical process control (SPC) and condition-based maintenance (CBM) is proposed. CBM policy is used to inspect and replace the system according to the observed deterioration level. SPC is used to monitor the stress covariate. In order to assess the performance of the proposed maintenance policy and to minimize the long-run expected maintenance cost per unit of time, a mathematical model for the maintained system cost is derived. Analysis based on numerical results are conducted to highlight the properties of the proposed maintenance policy in respect to the different maintenance parameters.     

Dependability and performance stochastic modelling of a two-unit repairable production system with preventive maintenance

In this paper, a two-unit multistate repairable production system is considered in which preventive maintenance (PM) is implemented in order to improve its dependability and performance. A general model is provided for the production system using a semi-Markov process, for examining system’s limiting behaviour. Apart from combining redundancy with PM, we introduce scenarios like imperfect and failed maintenance which are usually met in real life production systems. For the proposed model, we calculate the availability, the mean time to failure and the total operational cost and we formulate optimisation problems settled with respect to the system’s inspection times. The main aim of our work is to determine the optimal inspection times and consequently the optimal PM policies to be adopted in order to optimise system’s dependability and performance.     

Optimum policies for a system with general imperfect maintenance

This study considers periodic preventive maintenance policies, which maximizes the availability of a repairable system with major repair at failure. Three types of preventive maintenance are performed, namely: imperfect preventive maintenance (IPM), perfect preventive maintenance (PPM) and failed preventive maintenance (FPM). The probability that preventive maintenance is perfect depends on the number of imperfect maintenances conducted since the previous renewal cycle, and the probability that preventive maintenance remains imperfect is not increasing. The optimum preventive maintenance time that maximizes availability is derived. Various special cases are considered. A numerical example is given.     

On the optimal scheduling of periodic tests and maintenance for reliable redundant components

Periodically, some m of the n redundant components of a dependable system may have to be taken out of service for inspection, testing or preventive maintenance. The system is then constrained to operate with lower (n−m) redundancy and thus with less reliability during these periods. However, more frequent periodic inspections decrease the probability that a component fail undetected in the time interval between successive inspections. An optimal time schedule of periodic preventive operations arises from these two conflicting factors, balancing the loss of redundancy during inspections against the reliability benefits of more frequent inspections.Considering no other factor than this decreased redundancy at inspection time, this paper demonstrates the existence of an optimal interval between inspections, which maximizes the mean time between system failures. By suitable transformations and variable identifications, an analytic closed form expression of the optimum is obtained for the general (m, n) case. The optimum is shown to be unique within the ranges of parameter values valid in practice; its expression is easy to evaluate and shown to be useful to analyze and understand the influence of these parameters.Inspections are assumed to be perfect, i.e. they cause no component failure by themselves and leave no failure undetected. In this sense, the optimum determines a lowest bound for the system failure rate that can be achieved by a system of n-redundant components, m of which require for inspection or maintenance recurrent periods of unavailability of length t.The model and its general closed form solution are believed to be new [2] and [5]. Previous work [1], [4] and [10] had computed optimal values for an estimation of a time average of system unavailability, but by numerical procedures only and with different numerical approximations, other objectives and model assumptions (one component only inspected at a time), and taking into account failures caused by testing itself, repair and demands (see in particular [6], [7] and [9]).System properties and practical implications are derived from the closed form analytical expression. Possible extensions of the model are discussed. The model has been applied to the scheduling of the periodic tests of nuclear reactor protection systems.     

Integrated production quality and condition-based maintenance optimisation for a stochastically deteriorating manufacturing system

This paper investigates the problem of optimally integrating production quality and condition-based maintenance in a stochastically deteriorating single- product, single-machine production system. Inspections are periodically performed on the system to assess its actual degradation status. The system is considered to be in ‘fail mode’ whenever its degradation level exceeds a predetermined threshold. The proportion of non-conforming items, those that are produced during the time interval where the degradation is beyond the specification threshold, are replaced either via overtime production or spot market purchases. To optimise preventive maintenance costs and at the same time reduce production of non-conforming items, the degradation of the system must be optimally monitored so that preventive maintenance is carried out at appropriate time intervals. In this paper, an integrated optimisation model is developed to determine the optimal inspection cycle and the degradation threshold level, beyond which preventive maintenance should be carried out, while minimising the sum of inspection and maintenance costs, in addition to the production of non-conforming items and inventory costs. An expression for the total expected cost rate over an infinite time horizon is developed and solution method for the resulting model is discussed. Numerical experiments are provided to illustrate the proposed approach.     

A quantification algorithm for a repairable system in the GO methodology

The GO methodology is an effective method of system reliability analysis. It has been applied to non-repairable systems. This paper discusses the application of the GO method to a repairable system which is described by a Markov model and presents the quantification algorithm of the steady characteristics of the repairable system. The calculation formulas of the ordinary operators and the logical gates are derived and the steady reliability parameters of the system such as average operation probability and average failure frequency can be directly computed by the GO method. The result of an example shows that the algorithm is correct. The algorithm will be useful for the safety analysis of most engineering repairable systems.     

An optimal replacement policy for a repairable system based on its repairman having vacations

This paper studies a cold standby repairable system with two different components and one repairman who can take multiple vacations. If there is a component which fails and the repairman is on vacation, the failed component will wait for repair until the repairman is available. In the system, assume that component 1 has priority in use. After repair, component 1 follows a geometric process repair, while component 2 can be repaired as good as new after failures. Under these assumptions, a replacement policy N based on the failed times of component 1 is studied. The system will be replaced if the failure times of component 1 reach N. The explicit expression of the expected cost rate is given, so that the optimal replacement time N^? is determined. Finally, a numerical example is given to illustrate the theoretical results of the model.     

An optimal production and shipment policy for a single-vendor single-buyer integrated system with both learning effect and deteriorating items

The collaboration of vendor and buyer is one of the key factors for successful supply chain management. The most common strategy for a collaborative system is to propose an integrated replenishment plan aimed at maintaining a win-win partnership for both vendor and buyer. The objective of this study is to develop a production and shipment model for a system that incorporates learning effect and deteriorating items and to derive an optimal joint total cost from the integrated perspective of both vendor and buyer. A simple solution procedure is presented to determine the optimal production time and number of deliveries. A numerical example is provided to illustrate the proposed model. A sensitivity analysis is conducted to study the effect of changes in the related parameters on the optimal solution. This paper shows that the proposed integrated model can result in a significant cost reduction as compared with the independent decisions made by either vendor or buyer.     

A model for optimal armature maintenance in electric haul truck wheel motors: a case study

The objective of the work presented in this paper is the determination of an optimal age-based maintenance strategy for wheel motor armatures of a fleet of Komatsu haul trucks in a mining application in Chile. For such purpose, four years of maintenance data of these components were analyzed to estimate their failure distribution and a model was created to simulate the maintenance process and its restrictions. The model incorporates the impact of successive corrective (on-failure) and preventive maintenance on necessary new component investments. The analysis of the failure data showed a significant difference in failure distribution of new armatures versus armatures that had already undergone one or several preventive maintenance actions. Finally, the model was applied to calculate estimated costs per unit time for different preventive maintenance intervals. From the resulting relationship an optimal preventive maintenance interval was determined and the operational and economical consequences and effects with respect to the actual strategy were quantified. The application of the model resulted in the optimal preventive maintenance interval of 14,500 operational hours. Considering the failure distribution of the armatures, this optimal strategy is very close to a run-to-failure scenario.