Long-run Maintenance Cost Research Articles

Hierarchical condition-based maintenance planning for corrosion process considering natural environmental impact

Condition-based maintenance (CBM) powered by corrosion inspection is vital to ensure the service safety and availability of equipment structure, especially in harsh natural environments. Preventive repair and coating are two effective measures widely adopted in corrosion-centered CBM implementation, whose collaborative planning, however, is rarely reported in corrosion control models. This paper proposes a hierarchical CBM policy oriented to gradual corrosion deterioration, which quantifies the comprehensive effect of corrosive environment and uncertain coating lifetime. The long-term corrosion is governed by a generalized stochastic process incorporating multiple environmental factors. Inspections are equally spaced to reveal corrosion severity, followed by a combination of recoating, imperfect repair and replacement to restore structure health. In particular, repair is executed if the accumulated corrosion exceeds a safe control limit, and replacement is immediate if (a) the repair number attains a pre-set threshold, and (b) the residual corrosion after repair remains above the limit. The impact of random coating lifetime on CBM performance is also analytically analyzed. The long-run maintenance cost is minimized through the joint optimization of inspection interval, corrosion control limit, and imperfect repair number. The model applicability is demonstrated through numerical experiments conducted on ship deck structures under marine environment.

Optimal Inspection Policy for a Single-Unit System Considering Two Failure Modes and Production Wait Time

In many real production systems, a system may be stopped due to a lack of demand or exhaustion of raw materials. This is known as production wait and provides a good opportunity for maintenance. Meanwhile, the increased complexity of the modern machines brings new challenges for modeling and analyzing their failure behaviors. To address these real-world problems, this article considers a single-unit system that may fail due to either hard failures or soft failures. The wait time of a system is utilized to conduct inspections and maintenance. The system is replaced when a defect is found during an inspection, a failure occurred or a prespecified age threshold is reached, whichever comes first. The cost model, which is the long-run maintenance cost per unit of time, is derived. The optimal periodical inspection interval and the threshold age to minimize the long run maintenance cost per unit of time is then obtained. A case study is conducted to demonstrate the proposed maintenance model. The study shows using the proposed maintenance model can reduce the cost. Sensitivity analysis illustrates how each cost parameter affects the optimal inspection interval and the optimal age threshold.

Reliability and hybrid maintenance modeling for competing failure systems with multistage periods

This paper deals with the reliability and hybrid maintenance models for systems which are subjected to competing and dependent failures due to degradation and external shocks. System studied here are with multistage periods, standby stage, working stage and the stop stage, which makes it different with previous literatures. The characters of degradation and external shocks vary with different periods and this also makes the proposed reliability model more challenging and more consistent with the engineering reality. Besides, a hybrid maintenance policy combined by age-based preventive maintenance and condition-based maintenance is studied by minimizing the average long-run maintenance cost. The optimal age-based preventive interval and the condition-based threshold are both calculated to manage the minimum maintenance cost. A numerical case demonstrates the availability and general applicability of proposed reliability and maintenance models at the end of this paper.

Reliability and condition-based maintenance modeling for systems operating under performance-based contracting

Performance-based contracting motivates service providers to implement effective maintenance policies so as to boost profits and improve system performance at a lower cost. This paper deals with reliability and condition-based maintenance modeling for single-unit systems operating under performance-based contracting. For a system subject to degradation and sudden shocks, there involves three states: normal, degraded and failed. Once entered into the degraded state, the system deteriorates faster and becomes more susceptible to shocks. The degradation conforms to a two-stage inverse Gaussian process with random effects characterizing unit-specific heterogeneity in the population. Furthermore, the arrival of sudden shocks follows a doubly stochastic Poisson process. A reliability model is developed based on degradation-based and shock-based failures modeling. Afterwards, the long-run maintenance cost rate and the average system availability are evaluated. Optimal inspection-based preventive replacement policy is obtained by maximizing the expected profit rate to the service provider. Finally, a numerical example along with sensitivity analysis of model parameters is presented to demonstrate the applicability and solution procedure of the proposed models.

A condition-based maintenance model with past-dependent imperfect preventive repairs for continuously deteriorating systems

Most condition-based imperfect maintenance models developed over the last few decades are memoryless in the sense that maintenance efficiency is completely [Formula: see text]-independent of previous interventions. However, many maintenance activities exhibit their past dependency in engineering practice, and this significant property should not be ignored in maintenance modeling. In this spirit, our aim is to develop a condition-based maintenance model for continuously deteriorating systems subject to a special kind of past-dependent imperfect repairs. Such a repair can put the system back to a deterioration level better than the one at just before the current repair, but worse than the one reached at the last repair. Besides, inspection and replacement are memoryless actions available for the system. They result in different effects on the system deterioration and incur different costs. To achieve high economic performances in the long term, these actions are coordinated into a control-limit deterioration-based maintenance policy. Its long-run maintenance cost rate is analytically evaluated using the semi-regenerative process theory. Numerous sensitivity studies to maintenance costs and to system characteristics give a thorough understanding about the policy behavior. Furthermore, comparisons with more classical policies justify the importance of incorporating the past dependency in maintenance modeling.

Modeling past-dependent partial repairs for condition-based maintenance of continuously deteriorating systems

We are interested in the stochastic modeling of a condition-based maintained system subject to continuous deterioration and maintenance actions such as inspection, partial repair and replacement. The partial repair is assumed dependent on the past in the sense that it cannot bring the system back into a deterioration state better than the one reached at the last repair. Such a past-dependency can affect (i) the selection of a type of maintenance actions, (ii) the maintenance duration, (iii) the deterioration level after a maintenance, and (iv) the restarting system deterioration behavior. In this paper, all these effects are jointly considered in an unifying condition-based maintenance model on the basis of restarting deterioration states randomly sampled from a probability distribution truncated by the deterioration levels just before a current repair and just after the last repair/replacement. Using results from the semi-regenerative theory, the long-run maintenance cost rate is analytically derived. Numerous sensitivity studies illustrate the impacts of past-dependent partial repairs on the economic performance of the considered condition-based maintained system.

Stochastic Filtering Approach for Condition-Based Maintenance Considering Sensor Degradation

This paper proposes a condition-based maintenance (CBM) policy for a deteriorating system whose state is monitored by a degraded sensor. In the literature of CBM, it is commonly assumed that inspection of system state is perfect or subject to measurement error. The health condition of the sensor, which is dedicated to inspect the system state, is completely ignored during system operation. However, due to the varying operation environment and aging effect, the sensor itself will suffer a degradation process and its performance deteriorates with time. In the presence of sensor degradation, the Kalman filter is employed in this paper to progressively estimate the system and the sensor state. Since the estimation of system state is subject to uncertainty, maintenance solely based on the estimated state will lead to a suboptimal solution. Instead, predictive reliability is used as a criterion for maintenance decision-making, which is able to incorporate the effect of estimation uncertainty. Preventive replacement is implemented when the estimated system reliability at inspection hits a specific threshold, which is obtained by minimizing the long-run maintenance cost rate. An example of wastewater treatment plant is used to illustrate the effectiveness of the proposed maintenance policy. It can be concluded through our research that: 1) disregarding the sensor degradation while it exists will significantly increase the maintenance cost and 2) the negative impact of sensor degradation can be diminished via proper inspection and filtering methods. Note to Practitioners —This paper was motivated by the observation of sensor degradation in wastewater treatment plants but the developed approach also applies to other systems such as manufacturing systems, chemical plants, and pharmaceutical factories, where sensors are dedicated to a long-time operation in a harsh environment. This paper investigates the impact of sensor degradation on CBM and suggests that the effect of sensor degradation should be carefully addressed while making maintenance decisions. Otherwise, it will lead to a suboptimal maintenance decision and increase the operating cost. An optimal maintenance decision, which contains the optimal inspection interval and reliability threshold, is achieved via minimizing the long-run cost rate. In the presence of measurement noise and intrinsic uncertainty from degradation, a stochastic filtering approach is employed to estimate the system and sensor state. Based on the estimated states and the calculated reliability, a dynamic maintenance decision is obtained at each inspection. This paper can be further extended considering non-Gaussian noise and alternative degradation processes.

Reliability and maintenance modeling for competing failures with intermission considered

There are many industrial systems experiencing multiple dependent competing failure processes, in detail degradation failure (soft failure) and catastrophic failure (hard failure). Earlier research studied failure behaviors and system reliability during operational period, but did not consider the intermission period. Some industrial systems are not always operating continuously while with intermissions or rest period. The degradation and random shock processes are different between operating period and intermissions, which caused it more challenging and complicated to establish reliability model. In this article, a new reliability model for multiple dependent competing failure processes is developed with intermission considered. The system reliability can be analyzed based on the proposed model more practically. Besides, a preventive replacement maintenance policy is studied by minimizing the average long-run maintenance cost with intermission periods considered. Finally, the availability and general applicability of presented model are demonstrated by a case in different parameter settings.

Optimal multi-level condition-based maintenance policy for multi-unit systems under economic dependence

The study aims to work on multi -level condition-based maintenance (CBM) policy for multi-unit systems under economic dependence. Failure modes of units are classified as hard failure or soft failure and taken into account in this paper. Unlike previous works which only considered setup cost dependence with a single failure mode, two types of economic dependence are considered, which are setup cost-saving, and additional cost and time that can be saved when identical maintenance tasks and expertise are needed. In this study, hard failure provides an opportunity for additional inspection and repair of soft-type units, and soft failure creates an opportunity for replacement of the hard-type unit as its age exceeds opportunistic threshold. They both undergo preventive maintenance (PM) when the level/age exceeds preventive threshold at inspection epochs. The objective of this study is to determine the optimal opportunistic control limit and preventive control limit for each unit such that the system’s average long-run maintenance cost per unit time is minimized. The optimization problem is formulated in a semi-Markov decision process (SMDP) framework. The explicit formula for the mean residual life is derived for the proposed model which enables the estimation of the remaining useful life and allows maintenance engineers to plan maintenance early based on the observed information. Finally, the method is illustrated by an industrial case study of a feed system of a machine tool. A comparison with other methods is given, which illustrates the effectiveness of our approach.

Condition-Based Maintenance for Repairable Deteriorating Systems Subject to a Generalized Mixed Shock Model

Based on reliability analysis for a system subject to $s$ -dependent competing risks of internal degradation and external shocks, we propose a condition-based maintenance policy considering imperfect repair for complex systems. The internal degradation (e.g., crack growth, erosion, or corrosion) can be modeled using a stochastic deterioration process. External shocks arriving at random times are divided into two classes based on their impacts on the system: 1) fatal shocks that can cause the system to fail immediately, if a shock belongs to any of three classic shock models (i.e., extreme shock model, run shock model, and $\delta $ -shock model), or the generalized mixed shock model; and 2) non-fatal shocks that can damage the system by randomly increasing the degradation level. Using the proposed condition-based maintenance policy, the system is inspected at fixed time intervals, and a decision for an appropriate maintenance action (i.e., no action, imperfect repair, preventive or corrective replacement) is made based on the actual health condition of the system detected through inspection. The imperfect repair restores the system by lowering the degradation amount to a certain level. The objective is to determine the optimal inspection interval that minimizes the expected long-run maintenance cost rate. A micro-electro-mechanical system example is used to evaluate the efficiency of the developed reliability and condition-based maintenance models.

A proactive group maintenance policy for continuously monitored deteriorating systems: Application to offshore wind turbines

This article presents an optimum proactive group maintenance policy for continuously monitored systems affected by stochastic deterioration (degradation). A system is composed of multiple nonidentical subsystems, each exposed to a gradual degradation phenomenon. When the length (or size) of degradation in a subsystem reaches a predetermined fault threshold, it fails and leads to failure of the whole system. In order to avoid system failures and to improve availability levels, a proactive group maintenance task is conducted once the degradation level of a subsystem exceeds an “alert” threshold (smaller than the fault threshold). In this maintenance task, the critical subsystem undergoes a state-dependent repair action, and a preventive maintenance is performed on the other subsystems. Furthermore, the whole system is preventively replaced because of safety requirements when its operational age attains a fixed value. We formulate a multivariate nonlinear maintenance optimization model to simultaneously determine the optimal alert thresholds for subsystems and the replacement time for system. The performance of the proposed maintenance policy, regarding the objective of minimum system’s average long-run maintenance cost per unit time, is compared to five conventional cases of maintenance policies: the reactive response, individual age-based, individual condition-based, bivariate age- and condition-based, and age-based group maintenance. A numerical example, using real-life data collected from an offshore wind dataset, is presented to illustrate the applicability of the proposed model to the maintenance of a group of wind turbine bearings.

A condition-based maintenance policy for multi-component systems with a high maintenance setup cost

Condition-based maintenance (CBM) is becoming increasingly important due to the development of advanced sensor and information technology, which facilitates the remote collection of condition data. We propose a new CBM policy for multi-component systems with continuous stochastic deteriorations. To reduce the high setup cost of maintenance, a joint maintenance interval is introduced. With this interval and the control limits of components as decision variables, we develop a model for the minimization of the average long-run maintenance cost rate of the systems. Moreover, a numerical study of a production system consisting of a large number of non-identical components is presented, including a sensitivity analysis. Finally, our policy is compared to a failure-based policy and an age-based policy, in order to evaluate the cost-saving potential.

An opportunistic condition-based maintenance policy for offshore wind turbine blades subjected to degradation and environmental shocks

Offshore wind turbine blades are subject to multiple types of internal and external damages. Internal damages (such as fatigue, wear and cracks) are generally caused by system degradation, whereas the external damages (such as icing, wind and wave shocks) result from harsh marine environments. In this paper, we investigate an optimal opportunistic condition-based maintenance (OCBM) policy for a multi-bladed offshore wind turbine system subjected to stress corrosion cracking (SCC) and environmental shocks. When the length of a crack in a blade reaches critical size D, the blade breaks and it has to be replaced by a new one. An environmental shock is minor with probability 1−p and catastrophic with probability p (0≤p≤1). A minor shock causes an instant drop in power output without resulting in any system failure, whereas a catastrophic shock stops the wind turbine and requires system replacement. When the length of a crack in one of the blades exceeds a threshold d (<D), it undergoes a major repair and a preventive maintenance (PM) action is performed on the other blade(s); otherwise, a planned PM task is conducted for the whole system when its operational age attains a value of T (>0). The problem is to simultaneously determine the optimal control parameters d⁎ and T⁎ such that the average long-run maintenance cost per blade per unit time is minimized. The explicit expression of the objective function is derived and under certain conditions, the existence and uniqueness of the optimal solution are shown for the infinite-horizon case. The proposed maintenance model is tested on a three-bladed wind turbine and its performance over the system life cycle is evaluated using a Monte-Carlo simulation technique.

Generalized reliability models and preventive maintenance policy for systems subject to competing dependent failure processes

We investigate in this paper systems reliability analysis using shock models. Two known modeling approaches are considered: the first one is a mixed shock model and the second one is based on mixed degradation and shocks. We generalize each of these two models considering a vulnerability level, L(t), which is a shock magnitude under which a shock has no effect on the system degradation process. A preventive maintenance policy is proposed for systems subject to mixed degradation and shocks. A mathematical model is developed in order to determine simultaneously the optimal age T* and the optimal number of shocks N* at which a preventive maintenance action should be undertaken (whichever comes first), minimizing the average long-run maintenance cost per time unit. Obtained numerical results are discussed.

An optimal age-based group maintenance policy for multi-unit degrading systems

In order to share maintenance set-up costs and reduce system breakdown, the group maintenance policies are widely used for complex multi-unit systems. In this paper, an optimal age-based group maintenance policy is proposed for a multi-unit series system whose components are subject to different gradual degradation phenomena. When the degradation level of a component reaches a given critical size, it is replaced by a new one and the other components undergo a preventive maintenance (PM) action; otherwise, a planned group PM is performed for the whole system at operational age T>0. The problem is to determine an optimal group maintenance time T⁎ such that the system’s average long-run maintenance cost per unit time is minimized. The explicit expression of the objective function is derived and sufficient conditions for existence and uniqueness of the optimal solution are obtained. Finally, the proposed maintenance policy is applied to a group of wind turbine bearings and the results are compared with the case without planned maintenance (i.e., reactive response) and with an individual age-based maintenance policy.

An optimal age–usage maintenance strategy containing a failure penalty for application to railway tracks

Railway track maintenance plays a key role in enhancing the reliability and safety of railway transportation, as it reduces the potential risks of defects and derailments. A railway track degrades over time, due to its cumulative usage (in terms of million gross tons) that results from traffic movements. When the cumulative usage reaches a failure threshold, the railway track breaks and has to be replaced with a new section. Moreover, the infrastructure owner charges the maintenance agent a specific penalty due to traffic disrruption and passenger dissatisfaction. To avoid such costly defects, the railway tracks must be preventively replaced at regular time intervals. In this paper, we propose an optimal bivariate (age–usage) maintenance strategy for railway tracks such that the average long-run maintenance cost per unit time is minimized. The proposed model is applied to 60E1 track on a small part of the Swedish heavy haul line ‘Malmbanan’, and the results are compared with two conventional age-based and usage-based maintenance policies. The results show that the proposed maintenance policy has a substantial potential to reduce the servicing costs of railway track maintenance.

A general approach to total repair cost limit replacement policies

A common replacement policy for technical systems consists in replacing a system by a new one after its economic lifetime, i.e. at that moment when its long-run maintenance cost rate is minimal. However, the strict application of the economic lifetime does not take into account the individual deviations of maintenance cost rates of single systems from the average cost development. Hence, Beichet proposed the total repair cost limit replacement policy: the system is replaced by a new one as soon as its total repair cost reaches or exceeds a given level. He modelled the repair cost development by functions of the Wiener process with drift. Here the same policy is considered under the assumption that the one-dimensional probability distribution of the process describing the repair cost development is given. In the examples analysed, applying the total repair cost limit replacement policy instead of the economic life-time leads to cost savings of between 4% and 30%. Finally, it is illustrated how to include the reliability aspect into the policy.

Optimal opportunistic maintenance model of multi-unit systems

An opportunistic maintenance model is presented for a continuously deteriorating series system with economical dependence. The system consists of two kinds of units, which are respectively subjected to the deterioration failure described by Gamma process and the random failure described by Poisson process. A two-level opportunistic policy defined by three decision parameters is proposed to coordinate the different maintenance actions and minimize the long-run maintenance cost rate of the system. A computable expression of the average cost rate is established by using the renewal property of the stochastic process of the maintained system state. The optimal values of three decision parameters are derived by an iteration approach based on the characteristic of Gamma process. The behavior of the proposed policy is illustrated through a numerical experiment. Comparative study with the widely used corrective maintenance policy demonstrates the advantage of the proposed opportunistic maintenance method in significantly reducing the maintenance cost. Simultaneously, the applicable area of this opportunistic model is discussed by the sensitivity analysis of the set-up cost and random failure rate.

A condition-based maintenance model for periodically inspected systems subjected to competing failure processes

A condition-based maintenance model for periodically inspected systems subject to degradation and random shocks is addressed in this paper. Upon inspection, one will need to determine whether to perform a preventive maintenance, corrective maintenance, or to do nothing. In this paper, we present an expected maintenance cost rate model for systems subject to a degradation process and cumulative shock damage. An optimal maintenance policy consisting of two decision variables such as the preventive maintenance threshold and periodical inspection time, is determined that minimizes the expected long-run maintenance cost per unit time. To improve the search and better ways to obtain the optimum solution, we also propose a heuristic algorithm procedure based on the mean time to first failure concept in order to find the best optimum solution. A numerical example is given to illustrate the ideas of modeling and algorithms.

Reliability and maintenance modeling for systems subject to multiple dependent competing failure processes

For complex systems that experience Multiple Dependent Competing Failure Processes (MDCFP), the dependency among the failure processes presents challenging issues in reliability modeling. This article, develops reliability models and preventive maintenance policies for systems subject to MDCFP. Specifically, two dependent/correlated failure processes are considered: soft failures caused jointly by continuous smooth degradation and additional abrupt degradation damage due to a shock process and catastrophic failures caused by an abrupt and sudden stress from the same shock process. A general reliability model is developed based on degradation and random shock modeling (i.e., extreme and cumulative shock models), which is then extended to a specific model for a linear degradation path and normally distributed shock load sizes and damage sizes. A preventive maintenance policy using periodic inspection is also developed by minimizing the average long-run maintenance cost rate. The developed reliability and maintenance models are demonstrated for a micro-electro-mechanical systems application example. These models can also be applied directly or customized for other complex systems that experience multiple dependent competing failure processes.