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.     

Optimal age replacement scheduling for a random work system with random lead time

System maintenance and spare parts are two closely related logistics activities since maintenance generates the demand for spare parts. Most studies on integrated models of preventive replacement and inventory of spare parts have focused on age replacement scheduling, while random replacement policy, which is sensible and necessary in practice, is rarely discussed and applied. The purpose of this paper is to present a generalised age replacement policy for a system which works at random time and considers random lead time for replacement delivery. To model an imperfect maintenance action, we consider that the system undergoes minimal repairs at minor failures and corrective replacements at catastrophic failures. Before catastrophic failures, the system is replaced preventively at age T or at the completion of a working time, whichever occurs first. The main objective is to determine an optimal schedule of age replacement that minimises the mean cost rate function of the system in a finite time horizon. The existence and uniqueness of optimal replacement policy are derived analytically and computed numerically. It can be seen that the proposed model is a generalisation of the previous works in maintenance theory.     

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.     

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.     

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.     

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.     

Time-based replacement policies for a fault tolerant system subject to degradation and two types of shocks

A single component nonrepairable system suffering from both an internal stochastic degradation process and external random shocks is investigated in this paper. More specifically, the Wiener process with a positive drift coefficient is introduced to describe the gradual deterioration and the arrival number of external shocks is counted with a nonhomogeneous Poisson process (NHPP). Meanwhile, fault tolerant design is incorporated into the stochastically deterioration system so as to protect it from shock failures to some extent and is consummately addressed via a generalized m − δ shock model. From the actual engineering point of view, external shocks are typically classified into two distinct categories in this current research, that is, a minor shock (Type I shock) increasing the damage load on current degradation level and a traumatic shock (Type II shock) resulting in system catastrophic failure immediately. The closed-form expression of system survival function is derived analytically and is viewed as the generalization of existing reliability function for systems subject to dependent and competing failure processes. Based on which, two time-based maintenance (TBM) policies including an age replacement model and a block replacement model are scheduled, where the expected long-run cost rate (ELRCR) in each model is, respectively, optimized to seek the optimal replacement interval. In the illustrative example part, a subsea blowout preventer (BOP) control system is arranged to validate the theoretical results numerically. To compare which policy is more profitable under different conditions, the relative gain on optimal maintenance cost rate of the two TBM policies is presented.     

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.     

An adaptive degradation‐based maintenance model taking into account both imperfect adjustments and AGAN replacements

This paper presents an adaptive maintenance model for equipment that can be adjusted (minor preventive maintenance, imperfect state) or replaced (major preventive maintenance, as good as new) at specific scheduled times based on degradation measurements. An initial reliability law that uses a degradation‐based model is built from the collection of hitting times of a failure threshold. Inspections are performed to update the reliability, the remaining useful life, and the optimum time for preventive maintenance. The case of both as good as new replacements and imperfect adjustments is considered. The proposed maintenance model is based on the optimization of the long‐term expected cost per unit of time. The model is then tested on a numerical case study to assess its effectiveness. This results in an improvement for the occurrences of maintenance tasks that minimizes the mean cost per unit of time as well as an optimized number of adjustments that can be considered before replacing an item. The practical application is a decision aid support to answer the 2 following questions: Should we intervene now or wait for the next inspection? For each intervention, should we adjust or replace the item of equipment? The originality is the presence of 2 criteria that help the maintainer to decide to postpone or not the preventive replacement time depending on the measured degradation and to decide whether the item should be adjusted or replaced.     

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.     

Long-term predictive opportunistic replacement optimisation for a small multi-component system using partial condition monitoring data to date

The advanced condition monitoring tools and sensors have changed the decision making on maintenance in modern manufacturing. To face the change, an integrated ‘prognostics-replacement’ framework is proposed to optimise the replacement decision from component-level layer into production system-level layer by using condition monitoring data in this paper. Some special situations such as no failure or suspension histories of many of same or similar components for prognosis, etc., are considered. A novel degradation prediction model is introduced and the failure risk of a component is estimated based on its degradation level and service time. A total current-term cost rate function is defined to determine the replacement clusters and time for performing replacement from an integrated and economic view. A conservative window is used to adjust the replacement time and overcome the prognostic results varying at different inspection time in a long task. To optimise the replacement clusters effectively, a random-keys genetic algorithm (GA) based on convex set theory is developed. The proposed framework is validated by different small systems. Two commonly adopted replacement policies are compared. Sensitive analysis is conducted and the results show the outperformance of our proposed framework.     

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.     

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.     

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.     

Determining the optimal maintenance action for a deteriorating repairable system

This paper develops a decision model for risk management of the deterioration of a repairable system. When a failure occurs in a deteriorating system, an optimal maintenance decision that includes the possibility of system replacement, as compared to mere deterioration reduction, should be made. There are many uncertainties associated with deterioration, however, so the decision may require a probabilistic analysis. Here, a well-known nonhomogeneous Poisson process with a power law intensity function is used to model the uncertain behavior of the deteriorating system. A Bayesian statistical approach is adopted to allow for the uncertainty of the parameters of the power law intensity function, which imposes a conjugate prior distribution of the parameters. A power law maintenance cost function and the failure cost are analyzed to determine the magnitude of failure risk reduction by minimizing the expected cost incurred from the maintenance action and future failures. A numerical example is given.     

Optimal Bayesian maintenance policy for a gearbox subject to two dependent failure modes

Most maintenance optimization models of gear systems have considered single failure mode. There have been very few papers dealing with multiple failure modes, considering mostly independent failure modes. In this paper, we present an optimal Bayesian control scheme for early fault detection of the gear system with dependent competing risks. The system failures include degradation failure and catastrophic failure. A three‐state continuous‐time–homogeneous hidden Markov model (HMM), namely the model with unobservable healthy and unhealthy states, and an observable failure state, describes the deterioration process of the gear system. The condition monitoring information as well as the age of the system are considered in the proposed optimal Bayesian maintenance policy. The objective is to maximize the long‐run expected average system availability per unit time. The maintenance optimization model is formulated and solved in a semi‐Markov decision process (SMDP) framework. The posterior probability that the system is in the warning state is used for the residual life estimation and Bayesian control chart development. The prediction results show that the mean residual lives obtained in this paper are much closer to the actual values than previously published results. A comparison with the Bayesian control chart based on the previously published HMM and the age‐based replacement policy is given to illustrate the superiority of the proposed approach. The results demonstrate that the Bayesian control scheme with two dependent failure modes can detect the gear fault earlier and improve the availability of the system.     

Preventive maintenance and replacement policies for deteriorating production systems subject to imperfect repairs

This paper presents a special case of integration of the preventive maintenance into the repair/replacement policy of a failure-prone system. The machine of the considered system exhibits increasing failure intensity and increasing repair times. To reduce the failure rate and subsequent repair times following a failure, there is an incentive to perform preventive maintenance on the machine before failure. When a failure occurs, the machine can be repaired or replaced by a new one. Thus the machine's mode at any time can be classified as either operating, in repair, in replacement or in preventive maintenance. The decision variables of the system are the repair/replacement switching age or number of failures at the time of the machine's failure and the preventive maintenance rate. The problem of determining the repair/replacement and preventive maintenance policies is formulated as a semi-Markov decision process and numerical methods are given in order to compute optimal policies which minimise the average cost incurred by preventive maintenance, repair and replacement over an infinite planning horizon. As expected, the decisions to repair or to replace the machine upon a failure are modified by performing preventive maintenance. A numerical example is given and a sensitivity analysis is performed to illustrate the proposed approach and to show the impact of various parameters on the control policies thus obtained.     

基于遗传算法和状态信息的多设备混联系统维护调度优化

针对多设备混联系统维护优化的建模复杂性,系统分析了设备间的相互依赖性,建立了混联系统的维护调度模型。首先利用威布尔分布模拟设备的衰退过程;定义小修、大修和更换3种维护方式,以及3种维护方式对设备故障率的影响;考虑故障成本、维护成本、资源成本和停机成本,建立了系统一次维护活动的费用模型。其次,基于每次维护活动的费用模型,建立了系统维护多阶段的总费用率模型。最后,通过算例证明了提出的多设备混联系统维护调度优化模型的有效性     

Reliability evaluation and opportunistic maintenance policy based on a novel delay time model

The delay time concept is widely adopted in literature to model the two‐stage failure process of most industrial systems which can be divided into normal stage (from new to an initial point of a defect) and defective stage (from defect arrival point to failure). Most existing delay time models assume that the normal and defective stages are independent. A generalized delay time model is proposed in this paper by considering the dependence between the normal and defective stages which is reflected in the fact that they share the same external shock process. According to the definition of shot‐noise process, external shocks will incur random hazard rate increments in the two stages. The failure state is self‐announcing, whereas the defective state can only be detected by block‐based inspection or opportunistic inspection offered by unexpected shutdown due to unavoidable external factors. The system is correctively replaced upon the occurrence of a system failure or preventively replaced at the detection of a defective state. Based on the stochastic failure model and maintenance policy, this paper evaluates system reliability performance and average long‐run cost rate via a Markov‐chain based approach. Finally, a case study on a steel convertor plant is given to demonstrate the applicability of the proposed model.     

A Cost-Minimization Model for Multicharacteristic Component Inspection

In this paper a mathematical model is developed for determining the optimal number of inspections for multicharacteristic components where failure can be catastrophic. The model optimizes the expected total cost per accepted component resulting from (1) type I errors, (2) type II errors, (3) cost of added inspection, and (4) ordering of quality characteristics for inspection. The model considers components with several characteristics to be inspected. Failure to meet the quality requirements of any one characteristic results in the rejection of the component. Taking into consideration all three costs referred to above, a mathematical expression for expected total cost per accepted component is obtained. Also, an expression is developed for finding the optimal sequence of characteristic inspection. Finally, a computational procedure is outlined to determine the optimal sequence of characteristic inspection and the optimal number of inspections using the two expressions stated above.