Optimal age-based inspection scheme for condition-based maintenance using A* search algorithm

In condition-based maintenance (CBM) with periodic inspection, the system is preventively replaced if failure risk, which is calculated based on the information obtained from inspection, exceeds a pre-determined threshold. The determination of optimal replacement threshold is often based on the minimisation of average maintenance costs per unit time due to preventive and failure replacements over a long time horizon. It is often assumed that inspections are performed at equal time intervals with no cost. However, in practice, inspections require labour, specific test devices, and sometimes suspension of operations and, thus, it is reasonable to inspect less frequently during the time the system is in its early age and/or in a healthier state and to perform inspections more frequently as time passes and/or as the system degrades. In other words, an age-based inspection scheme.

This paper proposes a novel two-phase approach for the determination of an optimal replacement threshold and an optimal age-based inspection scheme for CBM such that the total long-run average costs of replacements and inspections are minimised. First, it takes into account failure and preventive replacement costs to determine the optimal replacement threshold assuming that inspections are performed at equal time intervals with no cost. This assumption is, subsequently, relaxed and its consequences on total average cost are evaluated using a proposed iterative procedure based on A* search algorithm to obtain the optimal age-based inspection scheme. The proposed approach is illustrated through a numerical example.     

Contribution to optimization of preventive replacement

The paper presents a method for determining the optimal interval for preventive maintenance/replacement using either an age-based or diagnostic-based renewal strategy. For the case of a finite-time horizon, for which the computations are complicated, a simple formula is proposed for modifying the commonly used inifinite-time solution so that it gives a good approximation to the exact finite-time solution. Examples demonstrate that the method is sufficiently accurate and simple in practice for typical engineering components with Weibull life distributions and for a reasonable range of the cost factor (ratio of unit corrective to unit preventive maintenance costs). This paper investigates the problem of the accuracy of the results compared to the exact, finite-time solution for a selected matrix of time-to failure Weibull shape parameters and cost factors commonly occurring in technical practice. Applications offer substantial benefits to both manufacturer and user of technical equipment.     

An accurate approximate solution of optimal sequential age replacement policy for a finite-time horizon

It is difficult to find the optimal solution of the sequential age replacement policy for a finite-time horizon. This paper presents an accurate approximation to find an approximate optimal solution of the sequential replacement policy. The proposed approximation is computationally simple and suitable for any failure distribution. Their accuracy is illustrated by two examples. Based on the approximate solution, an approximate estimate for the total cost is derived.     

A graphical approach for confidence limits of optimal preventive maintenance cycles

Facilities management (FM) is the management of infrastructure resources and services to support and sustain the operational strategy of an organization over time. Maintenance is often the business process that has not been optimized and is considered as a liability of business operations. Therefore, extensive studies have been done to determine the optimal replacement interval for irreparable parts of repairable systems where typically the time between failures is characterized by lifetime distribution in which the parameters are estimated from failure data. As a result, the optimal preventive maintenance (PM) interval computed is exposed to sampling risk as the repair cost and failure data used for estimation are typically highly censored due to issues related to data collection and unobserved failures. In this paper, we present a graphical approach to obtain the confidence interval for the optimal PM interval that resulted from sampling variations parameter estimates. The proposed methodology is applied in the context of FM as a strategy for opportunistic replacement and for the purpose of validating the cost components in maintenance. Copyright © 2008 John Wiley & Sons, Ltd.     

Short communication optimal replacement scheduling in multi‐state series–parallel systems

The paper generalizes a replacement schedule optimization problem to multi‐state systems, where the system and its components have a range of performance levels—from perfect functioning to complete failure. The multi‐state system reliability is defined as the ability to satisfy a demand which is represented as a required system performance level. The reliability of system elements is characterized by their lifetime distributions with hazard rates increasing in time and is specified as expected number of failures during different time intervals. The optimal number of element replacements during the study period is defined as that which provides the desired level of the system reliability by minimum sum of maintenance cost and cost of unsupplied demand caused by failures. To evaluate multi‐state system reliability, a universal generating function technique is applied. A genetic algorithm (GA) is used as an optimization technique. Examples of the optimal replacement schedule determination are demonstrated. Copyright © 2000 John Wiley & Sons, Ltd.     

Optimum replacement of deteriorating and inadequate equipment

Determination of the optimum equipment replacement policy and time is of great economic importance. After a brief survey of the models which have been used for decision making, the paper looks at methods for detecting and quantifying growth of failure frequency (peril rate) in repairable equipment. It examines the trend detection methods of Laplace and Mann when the peril rate varies as a power of equipment age and also applies them to some actual field failure data. An economic model is developed, based on total discounted future cost and providing for ongoing future technological growth. The cost comprises not only the conventional cost of ownership, but also the shortfall between an equipment's achieved benefit and that which would be achieved by an ideal equipment in the same demand environment. The inclusion of this shortfall, called incapacity cost', enables the replacement decision to be based not only on the deterioration of equipment but also on its performance inadequacy and on the availability of technological improvement in present and future challengers. The formulation of the cost model is such that for both a single-replacement finite planning horizon and an infinite horizon the total discounted future cost is readily computed for a range of alternative replacement times and the optimum replacement programme thereby determined. The sensitivity of total cost to the replacement times and the sensitivity of the optimum times to the variability of assumed input data are easily examined. The application of the model to traffic signal equipment is described. In this application the total cost is shared between the nominal owner of the equipment and the community.     

Optimal replacement policy and inspection interval for condition-based maintenance

In condition-based maintenance (CBM), replacement policy is often defined as a rule for replacement or leaving an item (or a system) in operation until the next inspection, depending on monitoring results. The criterion for determining the optimal threshold for replacement, also known as optimal control limit, is to minimise the average maintenance costs per unit time due to preventive and failure replacements over a long time horizon. On the one hand, higher frequency of inspections provides more information about the condition of the system and, thus, maintenance actions are performed more effectively, namely, unnecessary preventive replacements are avoided and the number of replacements due to failure is reduced. Consequently, the cost associated to failure and preventive replacements are decreased. On the other hand, in many real cases, inspections require labour, specific test devices, and sometimes suspension of the operations and, thus, as the number of inspections increase, the inspection cost also increases. In this paper, preventive and failure replacement costs as well as inspection cost are taken into account to determine the optimal control limit and the optimal inspection interval simultaneously. The proposed approach is illustrated through a numerical example.     

A framework to practical predictive maintenance modeling for multi-state systems

A simple practical framework for predictive maintenance (PdM)-based scheduling of multi-state systems (MSS) is developed. The maintenance schedules are derived from a system-perspective using the failure times of the overall system as estimated from its performance degradation trends.

The system analyzed in this work is a flow transmission water pipe system. The various factors influencing PdM-based scheduling are identified and their impact on the system reliability and performance are quantitatively studied. The estimated times to replacement of the MSS may also be derived from the developed model.

The results of the model simulation demonstrate the significant impact of maintenance quality and the criteria for the call for maintenance (user demand) on the system reliability and mean performance characteristics. A slight improvement in maintenance quality is found to postpone the system replacement time by manifold. The consistency in the quality of maintenance work with minimal variance is also identified as a very important factor that enhances the system's future operational and downtime event predictability.

The studies also reveal that in order to reduce the frequency of maintenance actions, it is necessary to lower the minimum user demand from the system if possible, ensuring at the same time that the system still performs its intended function effectively.

The model proposed can be utilized to implement a PdM program in the industry with a few modifications to suit the individual industrial systems’ needs.     

Model-based Monte Carlo state estimation for condition-based component replacement

This paper presents a model-based Monte Carlo method, also called particle filtering, for estimating the failure probability of a component subject to degradation. The estimations are embedded within an optimal policy of condition-based component replacement, in which both replacement upon failure and preventive replacement are considered, and the decision variable is the expected cost per unit time. An application is reported with regards to a component subject to fatigue degradation, modeled by the well-known Paris-Erdogan law. The possibility of predicting accurately the component remaining life with the associated uncertainty and of updating the prediction on the basis of observations of the degradation process, opens the door for effective condition-based replacement planning and risk-informed life-extension for hazardous technologies, such as the nuclear, aerospace and chemical ones.     

Joint optimisation of production rate and preventive maintenance in machining systems

This paper studies an integrated control strategy of production and maintenance for a machining system which produces a single type of product to meet the constant demand. Different from previous research, we assume in this study that during the production, the production rate not only influences the life of cutting tool, but also the reliability of the machine. Both the replacement of cutting tool and the preventive maintenance (PM) of machine are considered in this paper. The machine is preventively maintained at the Nth tool replacement or correctively repaired at the machine failure, whichever occurs first. PM and corrective repair may cause shortage which can be reduced by controlling inventory. There are two decision variables p and N, where p denotes the production rate and N denotes the number of cutting tool replacement before the PM is performed. An integrated model is developed to simultaneously determine the optimal production rate and PM policy that minimise the total expected cost per unit item produced. Finally, an illustrative example and sensitivity analysis are given to demonstrate the proposed model.     

Age-based hybrid model for imperfect preventive maintenance

Several sequential Preventive Maintenance (PM) models for predetermined PM interval policies currently exist in the literature, however, much less effort has been devoted to age-based policies. The purpose of this paper is to develop a hybrid age-based model for imperfect PM involving maintainable and non-maintainable failure modes. The proposed hybrid model incorporates adjustment factors in both the hazard rate and effective age. PM is assumed to be imperfect. It reduces the age of the system and changes its hazard rate. The system undergoes a certain number of such PM actions before replacement. The problem is to determine the number of PM actions and the length of PM intervals that minimize the total long-term expected cost per unit time. Model analysis relating to the existence and uniqueness of optimal solutions is provided. Numerical examples are presented for illustrative purposes.     

Availability and cost functions for periodically inspected preventively maintained units

Unavailability and cost rate functions are developed for components whose failures can occur randomly but they are detected only by periodic testing or inspections. If a failure occurs between consecutive inspections, the unit remains failed until the next inspection. Components are renewed by preventive maintenance periodically, or by repair or replacement after a failure, whichever occurs first (age-replacement). The model takes into account finite repair and maintenance durations as well as costs due to testing, repair, maintenance and lost production or accidents. For normally operating units the time-related penalty is loss of production. For standby safety equipment it is the expected cost of an accident that can happen when the component is down due to a dormant failure, repair or maintenance. The objective of maintenance optimization is to minimize the total cost rate by proper selection of two intervals, one for inspections and one for replacements. General conditions and techniques are developed for solving optimal test and maintenance intervals, with and without constraints on the production loss or accident rate. Insights are gained into how the optimal intervals depend on various cost parameters and reliability characteristics.     

Optimal tool replacement with product quality deterioration and random tool failure

Operating the machine with a deteriorated cutting tool often leads to poor product quality performance and high risk of tool failure. Replacing the degraded tool is an effective measure to reduce product quality loss and chance of tool failure. Excessive tool replacements, however, may increase the production capacity loss and tool replacement cost. Taking these factors into consideration, this paper presents an approach for determining the optimal tool replacement time for cutting process. It assumes that the product quality deteriorates as cutting tool wears and tool failure occurs randomly during the cutting process. A product quality failure rate model is developed to characterise the deterioration of product quality during the cutting process, and the product quality loss is estimated based on this model. Weibull distribution is employed to describe the stochastic tool life. A tool replacement model is proposed based on balancing the product quality loss, penalty cost for possible tool failure, production capacity loss and tool replacement cost. Sensitivity analysis of the optimal tool replacement decision is presented.     

Sensor-driven prognostic models for equipment replacement and spare parts inventory

Accurate predictions of equipment failure times are necessary to improve replacement and spare parts inventory decisions. Most of the existing decision models focus on using population-specific reliability characteristics, such as failure time distributions, to develop decision-making strategies. Since these distributions are unaffected by the underlying physical degradation processes, they do not distinguish between the different degradation characteristics of individual components of the population. This results in less accurate failure predictability and hence less accurate replacement and inventory decisions. In this paper, we develop a sensor-driven decision model for component replacement and spare parts inventory. We integrate a degradation modeling framework for computing remaining life distributions using condition-based in situ sensor data with existing replacement and inventory decision models. This enables the dynamic updating of replacement and inventory decisions based on the physical condition of the equipment.     

Optimizing preventive maintenance for mechanical components using genetic algorithms

This paper presents periodic preventive maintenance (PM) of a system with deteriorated components. Two activities, simple preventive maintenance and preventive replacement, are simultaneously considered to arrange the PM schedule of a system. A simple PM is to recover the degraded component to some level of the original condition according to an improvement factor which is determined by a quantitative assessment process. A preventive replacement is to restore the aged component by a new one. The degraded behavior of components is modeled by a dynamic reliability equation, and the effect of PM activities to reliability and failure rate of components is formulated based on age reduction model. While scheduling the PM policy, the PM components within a system are first identified. The maintenance cost and the extended life of the system under any activities-combination, which represents what kind of activities taken for these chosen components, are analyzed for evaluating the unit-cost life of the system. The optimal activities-combination at each PM stage is decided by using genetic algorithm in maximizing the system unit-cost life. Repeatedly, the PM scheduling is progressed to the next stage until the system's unit-cost life is less than its discarded life. Appropriately a mechatronic system is used as an example to demonstrate the proposed algorithm.     

Optimisation of maintenance schedules and extents for composite power systems using multi-objective evolutionary algorithm

Reducing the overall cost and improving the reliability are the two primary but often conflicting objectives in power system. Preventive-maintenance schedules thus need to be optimised to trade-off among multiple objectives. An integrated methodology with three functional blocks is proposed in this study. The first block models the stochastic deterioration process of individual component with a continuous-time Markov model, of which transition rates are influenced by different maintenance extents and aging of components. The second block evaluates the reliability of a composite power system, taking into account the configuration and failure dependence of the system. Particularly, this block identifies the minimum cut sets with consideration of protection trip and operational switching. The third block employs the Pareto-based multi-objective evolutionary algorithm to find the optimal solutions in a large search space and provide a holistic view of relationships among conflicting multiple objectives. A novel representation of maintenance activities is introduced in this study specifying both the maintenance timings and extents, and is proven to outperform the authors' previous representation, specifying the maintenance frequencies only. Optimisation of the reliability, maintenance failure costs is carried out on the Roy Billinton Test System (RBTS) demonstrating the potential of this approach in handling complex systems.     

Age replacement policy: a multi-attribute value model

The classical optimal maintenance model associated with the age replacement policy is a cost model. The effectiveness of preventive maintenance should be evaluated from multiple aspects, which reflect the main maintenance objectives. The cost model just reflects one of the objectives. This paper provides a multiple attribute value model. Four attributes are considered. They are cost, availability, reliability and lifetime. The performance measures associated with reliability and lifetime objectives are first developed. The overall performance is represented by the overall value. The model is illustrated by a numerical example.     

Spreadsheet modeling of optimal maintenance schedule for components in wear-out phase

This paper addresses a method for determining the optimum maintenance schedule for components in the wear-out phase. The interval between maintenance for the components is optimized by minimizing the total cost. This consists of maintenance cost, operational cost, downtime cost and penalty cost. A decision to replace a component must also be taken when a component cannot attain the minimum reliability and availability index requirement. Premium solver platform, a spreadsheet-modeling tool, is utilized to model the optimization problem. Constraints, which are the considerations to be fulfilled, become the director of this process. A minimum and a maximum value are set on each constraint so as to give the working area of the optimization process. The optimization process investigates n-equally spaced maintenance at an interval of Tr. The increase in operational and maintenance costs due to the deterioration of the components is taken into account. This paper also performs a case study and sensitivity analysis on a liquid ring primer of a ship's bilge system.     

An economically designed, integrated quality and maintenance model using an adaptive Shewhart chart

This paper proposes a model for the economic design of a variable-parameter (Vp) Shewhart control chart used to monitor the mean in a process, where, apart from quality shifts, failures may also occur. Quality shifts result in poorer quality outcome, higher operational cost and higher failure rate. Thus, removal of such quality shifts, besides improving the quality of the outcome and reducing the quality cost, is also a preventive maintenance (PM) action since it reduces the probability of a failure and improves the equipment reliability. The proposed model allows the determination of the scheme parameters that minimize the total expected quality and maintenance cost of the procedure. The monitoring mechanism of the process employs an adaptive Vp-Shewhart control chart. To evaluate the effectiveness of the proposed model, its optimal expected cost is compared against the optimum cost of a fixed-parameter (Fp) chart.     

Block Replacement Policies with General Cost Structures

In this paper we investigate block replacement policies when the cosl structure associated with the operation of the system involves a cost c ₁ of replacement at failure, a cost c ₂ of preventive replacement, together with some discrete or continuous costs which are increasing with the age of the system.