An inspection model for a multi‐component system subject to 2 types of failures

Group maintenance is common and of significant importance for complex systems in industrial applications. This paper proposes a novel inspection and replacement model for a multi‐component system whose components are all subject to 2 typical failure modes, ie, catastrophic failure and minor failure. A catastrophic failure stops the system immediately, whereas a minor failure is not fatal and could only be identified by periodic inspection. At either a catastrophic or a minor failure, replacement is immediate. The maintenance cost model could be constructed through calculating the distribution of the “forward time”, which denotes the time elapse to a catastrophic failure since the previous inspection. The objective of this paper is to minimize the expected cost per unit time of the system via the optimization of the inspection interval. A case study on offshore wind turbine blades is presented to illustrate the maintenance model.     

Probabilistic optimization of welded joints maintenance versus fatigue and fracture

This paper presents a probabilistic maintenance optimization procedure for welded joints damaged by fatigue. The linear elastic fracture mechanics stands as a basis for fatigue crack growth while the crack depth at failure is determined according to brittle or ductile fracture. The first order reliability method being applied, the assessment is then based on reliability indices. At an inspection instant, different events can occur: no crack detection, crack detection, and repair. All these events are uncertain and are expressed in terms of probabilities. As they are cost-dependent, the total expected cost of maintenance could be obtained. The inspection instant is therefore searched by minimizing that total expected cost. Such an approach appears as a good compromise between reliability and costs. The paper provides some sensitivity studies and an application on a real case.     

A joint spare part and maintenance inspection optimisation model using the Delay-Time concept

Spare parts and maintenance are closely related logistics activities where maintenance generates the need for spare parts. When preventive maintenance is present, it may need more spare parts at one time because of the planned preventive maintenance activities. This paper considers the joint optimisation of three decision variables, e.g., the ordering quantity, ordering interval and inspection interval. The model is constructed using the well-known Delay-Time concept where the failure process is divided into a two-stage process. The objective function is the long run expected cost per unit time in terms of the three decision variables to be optimised. Here we use a block-based inspection policy where all components are inspected at the same time regardless of the ages of the components. This creates a situation that the time to failure since the immediate previous inspection is random and has to be modelled by a distribution. This time is called the forward time and a limiting but closed form of such distribution is obtained. We develop an algorithm for the optimal solution of the decision process using a combination of analytical and enumeration approaches. The model is demonstrated by a numerical example.     

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 Functional Inspection Model for the Immeasurable Potential Failure State

Functional inspection is a type of preventive maintenance of Reliability Centered Maintenance(RCM). We, in this paper, establish a functional inspection model(FIM)——the cost model and the availability model for the immeasurable potential failure state based on the delay time concept. This model can be used to determine the appropriate Functional Inspection Interval(FII) to achieve the goal of specific cost and availability and to assist in maintenance decision making.     

Condition-based inspection scheme for condition-based maintenance

In condition-based maintenance (CBM) with periodic inspection, the item 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 minimisation of long-run average maintenance costs per unit time due to preventive and failure replacements. It is assumed that inspections are performed at equal time intervals and that the corresponding cost is negligible. However, in many practical situations where CBM is implemented, e.g. manufacturing processes, inspections require labours, specific test devices, and sometimes suspension of operations. Thus, when inspection cost is considerable, it is reasonable to inspect less frequently during the time the item is in healthier states, and, more frequently as time passes and/or the item degrades, namely, a condition-based inspection scheme. This paper proposes a novel two-phase approach for determination of replacement threshold and a condition-based inspection scheme for CBM. 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, then, relaxed and its consequences on total average cost are evaluated using a proposed iterative procedure to obtain a cost-effective condition-based inspection scheme. The proposed approach can be utilised in many CBM applications. For the sake of simplicity of presentation, the approach is illustrated through a simplified case study already reported by some researchers referenced in the paper.     

Risk-informed optimisation of railway tracks inspection and maintenance procedures

Nowadays, efforts are being made by the railway industry for the application of reliability-based and risk-informed approaches to maintenance optimisation of railway infrastructures, with the aim of reducing the operation and maintenance expenditures while still assuring high safety standards.In particular, in this paper, we address the use of ultrasonic inspection cars and develop a methodology for the determination of an optimal strategy for their use. A model is developed to calculate the risks and costs associated with an inspection strategy, giving credit to the realistic issues of the rail failure process and including the actual inspection and maintenance procedures followed by the railway company.A multi-objective optimisation viewpoint is adopted in an effort to optimise inspection and maintenance procedures with respect to both economical and safety-related aspects. More precisely, the objective functions here considered are such to drive the search towards solutions characterized by low expenditures and low derailment probability. The optimisation is performed by means of a genetic algorithm. The work has been carried out within a study of the Norwegian National Rail Administration (Jernbaneverket).     

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.     

Optimal inspection and preventive maintenance of units with revealed and unrevealed failures

The maintenance of a single unit system that alternates operating and idle periods is studied. In the former case the failures are detected as soon as they occur and only by special testing or inspection in the latter. This paper aims at minimizing the cost per unit of time for an infinite time span by selection of a unique interval, for both inspection and maintenance. A special feature of this model is the possibility of a less than perfect testing as the inspections may fail and give a wrong result. It is further assumed that both preventive and corrective maintenance make the unit as good as new with the durations of inspections and maintenances being negligible. The existence of an optimum interval and how it depends on both the cost parameters and the reliability characteristics of the unit is discussed.     

Optimal inspection policies with predictive and preventive maintenance

A model is proposed to study the inspection and maintenance policy of systems whose failures can be detected only by periodic tests or inspections. Using predictive techniques, the time of the system failure can be predicted for some failure modes. If the system is found failed in an inspection, a corrective maintenance action is carried out. If the system is in a good condition but the predictive test diagnoses a failure in the period until the next inspection, then the system is replaced. The cost rate function is obtained for general distribution function of the signal time of a future failure and for one specific distribution function recently proposed. An algorithm is presented to find the optimal time between inspections and predictive tests and the optimal system replacement times for an age replacement policy. Numerical experiments illustrate the model.     

M out of n inspected systems subject to shocks in random environment

Consider a parallel redundant system, consisting n components, that is subject to shocks. The shocks cause the components to fail with certain probabilities. Shocks arrival rate and components’ failure probabilities may depend on an external Markovian environment. We consider warm and cold stand-by systems. Systems’ failures are silent. The system is maintained through inspection and repair/replacement. We propose several state-dependent maintenance policies and derive system availability and cost function.     

A modelling procedure to optimize component safety inspection over a finite time horizon

In this paper a model of a safety inspection process is proposed for the expected consequence of inspections over a finite time horizon. A single dominant failure mode is modelled, which has considerable safety or risk consequences assumed measurable either in cost terms or in terms of the probability of failure over the time horizon. The model established extends earlier work assuming an infinite time horizon, and uses the concept of delay time and asymptotic results from the theory of renewal and renewal reward processes. The paper establishes a pragmatic procedure for formulating objective functions which may be optimized to determine the optimal inspection intervals. Merits of both the exact and asymptotic formulations of these objective functions for possible use in the inspection optimization process are considered. Although the procedure for developing an objective function over a finite time zone inspection process assumes perfect inspection, it can be generalized to the imperfect inspection case. Because of the intractability of the mathematics, it is suggested that when optimizing an inspection process over a finite time zone, an asymptotic formulation of the objective function should be optimized, and this solution then checked and if necessary refined, using simulation calculation. A numerical example illustrates the performance of the basic periodic inspection policy over different time horizons using the asymptotic solution. The results are compared with simulations performed to estimate the exact expected cost measure. It is shown that the simpler asymptotic solution is satisfactory in the case considered, especially when the time horizon is relatively long. © 1997 John Wiley & Sons, Ltd.     

A data-driven maintenance policy for railway wheelset based on survival analysis and Markov decision process

Wheelsets absorb a significant part of the maintenance budget of any train operating company. Although wheel wear has been an extensively discussed topic in the literature, wear rates are very rarely characterized by using degradation data in a real-world case study aimed at identifying optimal maintenance policies including both degradation and recovery modeling. Furthermore, wheel defects, which impose an additional challenge to the modeling of the lifecycle of the wheels, are usually considered separately in the literature. In this study, conducted at a Portuguese train operating company, 17 years of inspection data are used to estimate wheel wear rates and survival curves, which are further incorporated into a Markov decision process (MDP) model. A bidimensional framework considering discrete intervals of wheel diameter along with a quantitative variable (kilometers since last turning/renewal) is used to represent the possible wheel states, while the probability of a defect interfering with the wheel maintenance schedule is modeled by contemplating survival curves derived from a Cox proportional-hazards model. Optimal results in terms of minimal cost policy are discussed in the context of the MDP, but a more realistic and easy-to-implement policy fixing one of the parameters is compared with the optimal policy. Results showed that in practice train operating companies might benefit from using the easy-to-implement policy, which has an associated long-run average cost only about 1% higher than the one suggested by the optimal decision map.     

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.     

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.     

Maintenance scheduling of a manufacturing system subject to deterioration

This paper presents an integrated model for the joint determination of both optimal inspection strategy and optimal repair policy for a manufacturing system whose resulting output is subject to system state. An appropriate maintenance strategy is essential to optimize revenue from a manufacturing system which is in continuous operation and subject to deterioration. The optimum policy balances the amount of maintenance required to increase availability against the loss of revenue arising from the down time: insufficient maintenance leads to an increase in the number of defective items, low profit and low maintenance cost; excessive maintenance results in a reduction in the proportion of defective items, high profit and high maintenance cost. In this paper, an intensity control model adapted to partial information provides an optimal inspection intensity and repair degree of the system as an optimal control process to yield maximum revenue. The solution is obtained through formulating an equivalent deterministic Hamilton-Jacobi equation. A numerical example is provided to illustrate the behavior of the optimal control process. The optimal control process determines a solution to both optimum inspection frequency and optimal replacement policy which results in an optimal production run length of the system.     

Integration of SPC and performance maintenance for supply chain system

In this paper, a supply chain system is viewed as a maintainable system, and the economic-statistical design of a likelihood ratio control chart with a maintenance application is considered for this system. The supply chain system is described by a three-state: normal state, warning state and failure state. A likelihood ratio control chart is used to monitor the system given that only categorical observations can be obtained. When the chart signals, a full inspection is performed to determine the actual system state (normal or warning), and preventive maintenance is immediately performed in the warning state. In addition, the supply chain system must be corrected upon failure (i.e. corrective maintenance), and should be maintained in a scheduled time (i.e. planned maintenance). A mathematical model is developed for the joint optimisation of the control chart parameters and planned maintenance time based on renewal theory. An example is presented to illustrate how to determine the optimal design parameters. We also investigate the effect of coefficients and statistical constraints on the decision variables and the expected cost.     

Failure modeling and optimizing preventive maintenance strategy during two-dimensional extended warranty contracts

Offering extended warranty (EW) contracts for products such as automobiles is a good source of revenue for manufactures, insurers and third party companies. However, difficulties in the modeling of product’s failure process and assessing corrective and preventive maintenance actions’ effects on the reliability of product enforce the service providers to propose limited EW contracts with simple “minimal repair at failures” servicing strategy. In this paper for a product sold with a two-dimensional warranty, we model the failure process of product, the effect of imperfect preventive maintenance (PM) and corresponding servicing cost in terms of product’s age and usage. Then, we propose a mathematical optimization model to derive optimal number and degrees of preventive repairs to minimize the EW provider’s servicing cost. We also provide some guidelines to help the EW provider to design flexible EW contracts and determine their corresponding optimal maintenance strategies. To reproduce an illustrative numerical example, we use the failure history of a commercial vehicle produced in a plant in Iran. The provided results reveal that considering proper preventive maintenance strategy during the EW period may effectively reduces the cost of EW servicing.     

A condition-based maintenance policy with non-periodic inspections for a two-unit series system

This paper considers a condition-based maintenance policy for a two-unit deteriorating system. Each unit is subject to gradual deterioration and is monitored by sequential non-periodic inspections. It can be maintained by good as new preventive or corrective replacements. Every inspection or replacement entails a set-up cost and a component-specific unit cost but if actions on the two components are combined, the set-up cost is charged only once. A parametric maintenance decision framework is proposed to coordinate inspection/replacement of the two components and minimize the long-run maintenance cost of the system. A stochastic model is developed on the basis of the semi-regenerative properties of the maintained system state and the associated cost model is used to assess and optimize the performance of the maintenance model. Numerical experiments emphasize the interest of a control of the operation groupings.     

On risk-based operation and maintenance of offshore wind turbine components

Operation and maintenance are significant contributors to the cost of energy for offshore wind turbines. Optimal planning could rationally be based on Bayesian pre-posterior decision theory, and all costs through the lifetime of the structures should be included. This paper contains a study of a generic case where the costs are evaluated for a single wind turbine with a single component. Costs due to inspections, repairs, and lost production are included in the model. The costs are compared for two distinct maintenance strategies, namely with and without inclusion of periodic imperfect inspections. Finally the influence of different important parameters, e.g. failure rate, reliability of inspections, inspection interval, and decision rule for repairs, is evaluated.