Optimal Inspection Interval Research Articles

Opportunistic maintenance for a novel load-sharing system with dependent degradation rate and volatility

For traditional degrading load-sharing systems, a typical assumption lies in the only effect of unit load on its degradation rate. However, motivated by a laser system example with positive correlation between degradation rate and volatility, we present a novel load-sharing system with general degradation rate-volatility-load correlation. Furthermore, to take account for unit economic dependence caused by sharable maintenance set-up cost, and the window period generated by the maintenance on some unit, opportunistic maintenance (OM) strategy is introduced to offer the opportunity of simultaneously maintaining another working unit under control-limit criteria. Based on the semi-regenerative process, the long-run average cost rate is minimized to obtain the optimal inspection interval, preventive maintenance and OM thresholds. Compared to the traditional condition-based maintenance strategy separately for each unit, the effectiveness of OM strategy is validated through numerical examples and case studies, offering broad managerial insights for engineers to reduce maintenance expenses.

Bayesian-informed fatigue life prediction in shallow shell structures with the dual boundary element method

This study introduces an innovative approach for statistically inferring the Equivalent Initial Flaw Size Distribution (EIFSD) in shallow shell structures with the aim of predicting fatigue life. The proposed approach integrates Bayesian inference and surrogate modelling techniques, and utilizes a long crack growth model. The EIFSD is crucial for estimating fatigue life and ensuring structural durability. To showcase the proposed methodology, a numerical example featuring a fuselage window structure under multi-axial loading, employing the Dual Boundary Element Method (DBEM) for crack growth modelling, is presented. Efficiency gains in the inference of the EIFSD are achieved through the development of surrogate models, notably a Co-Kriging model that significantly reduces computational time and outperforms a Kriging model in error reduction. The study explores two assumptions for inspection data sourcing, leading to enhanced methodological effectiveness across varying uncertainty levels. It considers the separate effects of Paris Law constants and loading conditions under increased uncertainty, presenting cases that demonstrate the Co-Kriging model’s high accuracy and computational efficiency. The proposed methodology’s robustness is further validated by assessing the impact of prior distribution quality on Bayesian inference, showing the method’s adaptability to high uncertainty while maintaining a good level of accuracy. This study also demonstrates an approach for fatigue life estimation of structures using the inferred EIFSD. By evaluating the structure up to a critical crack length, the methodology allows for the accurate estimation of fatigue life, which, in turn, facilitates the determination of optimal inspection intervals. Notably, under conditions of high uncertainty, the method showcased a maximum difference of 1.51% in the estimated fatigue life when compared to the true EIFSD, underscoring the technique’s high accuracy and reliability.

Joint optimization of preventive maintenance and triggering mechanism for k-out-of-n: F systems with protective devices based on periodic inspection

Systems with protective devices (PDs) have attracted increasing research interests due to their extensive engineering applications. In practice, the PDs are triggered to function under certain conditions. However, existing studies focus on the reliability modelling and analysis for such systems, and the joint optimization of maintenance and PD's triggering mechanism has not been investigated. Consequently, this paper explores the joint optimization of maintenance and triggering mechanism for k-out-of-n: F systems with PDs. A new triggering mechanism of the PD is proposed based on the number of failed or unhealthy components. The working PD can reduce the impacts of shocks on components. Based on the detected system status through periodic inspections, corresponding actions including corrective maintenance for components or the PD, preventive maintenance for components or shutting down the PD can be decided to improve the system reliability. The operation process of the established system is modelled by Markov decision process, and optimal actions under diverse system states are obtained via value iteration algorithm. The optimal inspection interval and triggering mechanism are derived by solving the optimization model aiming to minimize the expected total cost. Finally, the applicability of the proposed model is validated by abundant numerical examples.

Novel condition-based opportunistic maintenance policy for series systems with dependent competing failure processes

This paper investigates a novel condition-based opportunistic maintenance model for a two-component series system. The system comprises two non-identical components, that is, Component 1 and Component 2, suffering from shocks with different intensities. The two components are subject to dependent competing failure processes, that is, soft and hard failures. The component fails whichever type of failure process occurs. At each inspection, the replacement decision for components is made according to the condition of both components. In addition, when Component 1 is preventively replaced and Component 2 reaches the opportunistic maintenance threshold, opportunistic maintenance (OM) is implemented on Component 2. The optimal inspection interval, preventive replacement (PR) threshold, and OM threshold are derived by minimizing the long-run expected maintenance cost rate. Finally, the superiority of the proposed maintenance model is verified by an illustrative example.

Optimal Preventive Maintenance Scheduling of Multi State System. A Comparative Study of Different Meta-heuristic Algorithms

This work presents a comparative study of different meta-heuristic algorithms which are commonly used in the literature, such as Genetic Algorithms, Particle Swarm Optimization, Artificial Bee Colony and Grey Wolf Optimizer. These algorithms are applied to solve a multi-state system maintenance optimization problem considering time and system availability constraints. The objective is to find the optimal inspection and maintenance intervals for each component of the system in order to minimize the preventive maintenance cost of overall the system. The performances of the algorithms are compared using different metrics, regarding the quality and stability of the results and the speed of convergence, in order to determine the most efficient algorithms.

Dynamic probability modeling-based inspection intervals optimization for civil aircraft composite structures using Bayesian updating

The evaluation of damage tolerance in composite materials is essential for ensuring the safety of aircraft structures. One of the most challenging aspects of applying probability modeling-based methods to evaluate damage tolerance is determining the actual damage size distributions for in-service aircraft structures. Although existing nondeterministic approaches have been used to optimize inspection intervals of composite structures, few studies have investigated the effects of updates on the actual damage size distribution and its impact on both the probability of structural failure and inspection intervals. This paper proposes a dynamic optimization method for inspection intervals of composite structures based on Bayesian updating. The damage size distribution of the composite structure is characterized by a general stochastic distribution. A Bayesian updating methodology is presented to iteratively update the actual damage size distribution whenever new data becomes available. Based on the constructed probability model, the inspection intervals of composite structures are determined under the objectives of optimal safety and economy for civil aircraft using a Monte Carlo approach. Compared to prior distribution models, the proposed method achieves higher safety for structures during a single inspection, reduces the failure probability of structures throughout their entire service life, and incurs lower maintenance costs. It also enables maintenance personnel to flexibly adjust inspection intervals while facilitating quantitative evaluation of both failure probabilities and maintenance costs associated with these intervals. These findings suggest that the proposed method holds great potential in enabling maintenance personnel to make informed decisions regarding inspection intervals for improved safety and economic performance.

Joint optimization of maintenance and spares inventory policy for a series-parallel system considering dependent failure processes

This paper investigates the joint optimization of condition-based opportunistic maintenance and spare inventory policies for a series-parallel system consisting of software and components. Software failure follows a homogeneous Poisson process. Components are subject to mutually dependent competing failure processes. When the software failure occurs, an opportunistic inspection will be implemented for the components. Besides the maintenance policy, the (s, S) inventory policy is applied for components. The maintenance and order decisions will be made according to the conditions of the components and inventory level at each inspection. The state transition probabilities and expected sojourn times can be obtained by the formulated semi-Markov decision process. The optimal inspection interval, the preventive replacement threshold of the component, and the order point can be derived by minimizing the expected average cost rate. Finally, the effectiveness and superiority of the proposed joint optimization model are verified by an illustrative example.

Robust estimation of dependent competing risk model under interval monitoring and determining optimal inspection intervals

AbstractRecently, a growing interest is evident in modelling dependent competing risks in lifetime prognosis problems. In this work, we propose to model the dependent competing risks by Marshal‐Olkin bivariate exponential distribution. The observable data consists of a number of failures due to different causes across different time intervals. The failure count data is common in instances like one‐shot devices where the state of the subjects is inspected at different inspection times rather than the exact failure times. The point estimation of the lifetime distribution in the presence of competing risk has been studied through a divergence‐based robust estimation method called minimum density power divergence estimation (MDPDE) with and without constraint. The optimal value of the tuning parameter has been obtained. The testing of the hypothesis is performed based on a Wald‐type test statistic. The influence function is derived for the point estimator and the test statistic, reflecting the degree of robustness. Another key contribution of this work is determining the optimal inspection times based on predefined objectives. This article presents the determination of multi‐criteria‐based optimal design. Population‐based heuristic algorithm nondominated sorting‐based multiobjective Genetic algorithm is exploited to solve this optimization problem.

Condition-based maintenance considering imperfect inspection for a multi-state system subject to competing and hidden failures

Unexpected failures may cause huge economic losses and bring about uncontrolled risks and damage to humans and the environment. Condition-based maintenance is considered one of the most effective maintenance methods, which can reduce and eliminate possible failures and consequently ensure the safety and operating process effectiveness of systems. Inspection quality is an important factor affecting the effect of condition-based maintenance since imperfect inspection may result in inappropriate maintenance decisions. However, the factor of imperfect inspection is rarely considered when maintaining multi-state systems subjected to competing and hidden failures. In this paper, a periodical inspection policy is utilized to identify all states of a system subject to a three-state degradation process and random shocks. Inspections for all system states are considered imperfect. Upon the inspection outcome, the system may be replaced by a failure-based corrective replacement once it is detected as failed, or is renewed by a defect-based preventive replacement if a defect is identified. Moreover, an age-based preventive replacement is also required if the system is still normal up to the preset number of inspections. Subsequently, a condition-based maintenance model is constructed based on the probabilities of different renewal scenarios. Eventually, the applicability and effectiveness of the proposed model are verified by a numerical example. The results indicate that minimizing the constructed maintenance model can achieve the optimal inspection interval, which is greatly influenced by the factor of imperfect inspection. This research can provide references for decision-makers to optimize inspection and maintenance strategies.

Optimal Maintenance of a System With Multiple Deteriorating Components Served by Dedicated Teams

To maintain a multi-component system, different dedicated service teams with different skill sets and tools are often involved. Such a relationship constitutes maintenance team coalition. In most cases, it may not be the best to plan each team's maintenance activities independently as such independent decisions may not achieve the required system-level reliability performance (RP). To balance the reliability and costs of components in achieving a high level of system RP, an efficient method is to assign a failure penalty cost to each maintenance team and then develop their optimal maintenance policy. In this article, the Shapley value is utilized for fair penalty costs allocation to avoid any interest for teams to secede the coalition, whose actual role is to evaluate the criticality level of each component in the context of coalition. Moreover, imperfect inspection and imperfect repair are quite common in practice because of limited resources, technologies and time. To address these practical concerns, a new reliability-centered hybrid preventive maintenance policy is proposed. The optimal inspection interval and age-based replacement interval are determined for each team to minimize the cost rate over an infinite time horizon. Several numerical examples illustrate that the proposed decision-making method is effective in handling such complex maintenance problems involving a coalition of dedicated maintenance teams.

Сравнение методик расчета инспекционного интервала при реализации риск- ориентированного подхода к инспекции технологического оборудования

The article deals with the problems of conducting periodic inspections of equipment. This is due to the high frequency of equipment shutdown for its technical diagnostics and examination in accordance with the requirements of regulatory and technical documentation, in particular the Federal norms and rules «Rules for the safe operation of process pipelines». It is noted that the inspection is an important tool for ensuring the integrity of the equipment and, as a result, the industrial safety of the facility. At the same time, it is indicated that the inspection can be implemented on the basis of one of two approaches: regulated and risk-oriented. A general description of the inspection methodology, taking into account risk factors, is presented. It is pointed out that a risk-based approach to inspections is widespread in a number of countries. Various methods of implementing this approach are given, taking into account a large number of standards. The basics of API 581 3rd Edition and S-RBI techniques used for inspections are described. The technological process of the gas condensate stabilization system of a plant for the production of liquefied natural gas is described. A process pipeline is considered as an object of the study, for which an inspection interval is determined using the API 581 3rd Edition methodology. At the first stage of determining the inspection interval according to the S-RBI methodology, the process of assessing the criticality of the failure is described. The second step describes the process of determining the confidence factor, where the focus is on the estimation of the uncertainty in predicting the corrosion rate. At the third stage, the coefficient of the inspection interval is determined based on the data on the criticality of the failure and the reliability factor. Then an example of calculating the inspection interval for the object under study is given. Based on the results obtained, a conclusion was made about the comparability of API 581 3rd Edition and S-RBI methods. Both methods have their advantages and disadvantages, but at the same time they provide optimization of the scope of inspection work while maintaining a high level of industrial safety of the facility. In order to improve production efficiency, reliability and safety of pressure equipment, and optimize inspection intervals (which will allow to reduce the financial costs of enterprises), it is advisable to apply the above practices in the Russian Federation, providing the required legal and regulatory framework.

Inspection interval optimization of a weighted-K-out-of-N system with identical multi-state load-sharing components

This paper aims to optimize the inspection interval of a weighted-K-out-of-N system consisting of identical components. The components are multi-state and load-sharing, meaning they have different discrete working states, and moving to a degraded working state will increase their failure rates. Depending on the condition of the components at the end of each inspection interval and a pre-defined working state threshold, the components may continue working at the beginning of the next inspection interval or be sent for repair, where the repair time is fixed. The model aims to find the optimal inspection interval as well as the pre-defined working state threshold for sending the components for repair. We first define a new method for determining the system states. Then the general formulas are provided to calculate the transition probabilities between the system states. Finally, a Knowledge-Based Modified Exact (K-BME) technique is adapted to optimize the model for different-sized problems. The results show that the adapted K-BME can find the optimal solutions in significantly less computational time.

Multi-objective optimal maintenance strategy considering imperfect preventive maintenance: A case study on railway VOBC

Preventive maintenance procedures for systems are designed to improve long-term operating performance and reduce maintenance costs. This paper attempts to seek a trade-off between system reliability and maintenance costs and explores the optimal multi-objective maintenance strategy applicable to different field situations. We first provide an overview of the problem and analyze the impacts of varying different maintenance activities on reliability. Then, a mathematical model of reliability losses and maintenance costs is defined and derived, which will be used to construct a multi-objective maintenance strategy. In this research, the PSO-SA stochastic optimization algorithm is proposed to discover the Pareto frontier to find the optimal preventive maintenance threshold and inspection interval that minimizes reliability loss and maintenance costs. Finally, a case study is performed with railway VOBC as an illustration. The analysis results illustrate that the proposed multi-objective maintenance strategy can satisfy the preferences of various decision-makers. It is suitable for different maintenance needs and can support the development of on-site maintenance strategies.

Optimal condition‐based maintenance policy for systems with mutually dependent competing failure

AbstractIn this paper, a novel condition‐based maintenance (CBM) policy for systems with mutually dependent competing failure processes (DCFPs) is studied. The cumulative random shocks contribute to the increased rate of degradation, meanwhile, the hard failure threshold is reduced when the amount of degradation reaches a threshold. The degradation process is simulated by a non‐stationary Gamma process and random shocks are modeled as a homogeneous Poisson process. Preventive replacement (PR) and corrective replacement (CR) are accounted for in the developed maintenance strategy. The optimal periodic inspection interval, PR threshold, and the number of cumulative random shocks can be derived by minimizing the average long‐term maintenance cost rate. In the end, a numerical case is applied to demonstrate the availability of the developed models.

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.

점검-정비 모형에서 열화부품의 발견확률을 고려한 시스템의 최적 점검주기

Purpose: The determination of the optimal inspection interval of a system is a critical factor that can influence its maintenance. Frequent inspections yield shorter inspection intervals and higher inspection costs compared with infrequent inspections, which lead to an increase in the total maintenance cost due to the frequent occurrence of failures. The objective of this study is to determine the optimal inspection interval, which minimizes the total expected cost until the system is overhauled.BRMethods: We developed an inspection - maintenance cost model by considering the unit inspection cost, the cost for preventive maintenance, and the cost for corrective maintenance as well as the cost and quantity of a component, the distribution of the lifetime of components, and the probability of finding fault or failure during inspections.BRResults: We propose a novel method for determining the optimal inspection interval, which minimizes the total expected cost. The proposed method can be applied to systems consisting of one or more types of components. The data, which is derived from the case study that is documented in the previous research [13], are utilized to illustrate that the proposed method is effective for determining the optimal inspection interval and for conducting sensitivity analysis. Finally, we apply the proposed method to determine the optimal inspection interval pertaining to a component of auxiliary power that is built into railway trains. Consequently, we observed that a relationship exists between the reduction in the cost of operating the system and the current inspection interval.BRConclusions: The proposed method can be effective for other repairable systems, which undergo inspection, preventive maintenance, and corrective maintenance.

Joint optimization of inspection-based and age-based preventive maintenance and spare ordering policies for single-unit systems

This paper presents a joint optimization policy of preventive maintenance (PM) and spare ordering for single-unit systems, which deteriorate subject to the delay-time concept with three deterioration stages. PM activities that combine a nonperiodic inspection scheme with age-replacement are implemented. When the system is detected to be in the minor defective stage by an inspection for the first time, place an order and shorten the inspection interval. If the system has deteriorated to a severe defective stage, it is either repaired imperfectly or replaced by a new spare. However, an immediate replacement is required once the system fails, the maximal number of imperfect maintenance (IPM) is satisfied or its age reaches to a pre-specified threshold. In consideration of the spare's availability as needed, there are three types of decisions, i.e., an immediate or a delayed replacement by a regular ordered spare, an immediate replacement by an expedited ordered spare with a relative higher cost. Then, some mutually independent and exclusive renewal events at the end of a renewal cycle are discussed, and the optimization model of such a joint policy is further developed by minimizing the long-run expected cost rate to find the optimal inspection and age-replacement intervals, and the maximum number of IPM. A Monte-Carlo based integration method is also designed to solve the proposed model. Finally, a numerical example is given to illustrate the proposed joint optimization policy and the performance of the Monte-Carlo based integration method.

Modeling dynamic environment effects on dependent failure processes with varying failure thresholds

Devices usually fail due to multiple dependent competing failure processes resulting from internal degradation and random shocks, whose behavior may vary in different environments. This paper focuses on systems suffering from randomly occurring shocks described by Poisson processes and internal degradation characterized by linear path models simultaneously, where the wear rate, shock arrival rate, shock load size, and shock damage amount are modulated by Markovian environments, especially the hard failure threshold differs in distinct environments. Reliability analysis is performed where analytical formulas and simulation algorithms for computing reliability indexes of systems are provided, such as the reliability function. Two maintenance models are developed for systems, including a real-time maintenance policy where the computation formula for the availability function is derived, and a periodic inspection policy in which an optimization model is proposed to find the optimal inspection interval that minimizes the average long-run cost rate. Finally, an illustrative example of floating offshore wind turbine systems is given to demonstrate possible applications of the developed models and proposed methods.

Reliability optimization problem with the mixed strategy, degrading components, and a periodic inspection and maintenance policy

Redundant components stored in the standby mode degrade over time due to harsh environmental conditions. A proper inspection and maintenance plan is, therefore, required to combat performance degradation while maintaining system reliability. The present study presents a new reliability model for a system composed of simultaneously active and standby components with the standby ones prone to degradation. In this model, a periodic inspection and preventive maintenance policy is adopted for the standby components that needs to be duly scheduled. Thus, not only should the optimal component types be identified but the number of active and standby components in each subsystem needs to be determined as well. The objective function is to find optimal inspection intervals that ensure maximum system reliability with system constraints duly considered. For this purpose, a model is proposed for the problem at hand and a genetic algorithm is developed for its solution. Finally, a numerical example and an industrial case study are presented to verify the efficiency of the proposed model through sensitivity analysis in the presence and absence of the inspection policy.

Reliability-Centered Maintenance Strategy for Redundant Power Networks Using the Cut Set Method

In this study, we present an efficient maintenance strategy for securing stable power supplies in power facilities. In general, industrial customers that may face large outage costs from power supply interruptions prepare highly reliable systems with redundant network topologies. When establishing a maintenance schedule for an industrial power system, the condition of the equipment should be inspected first. However, frequent inspections may result in excessive inspection costs, and infrequent inspections may reduce the reliability of the system. Therefore, it is necessary to determine an optimal maintenance and inspection interval that balances the demand for reliable electricity and the need to limit maintenance and inspection costs. Accordingly, considering the topology of the equipment in terms of the system as a whole, a reliability-centered maintenance algorithm was derived to determine the specific combinations of equipment conditions that cause power outages. Generally, the more redundant the elements in the system were, the less the load experienced power outages. We also examined the unavailability, which is an indicator that predicts the probability of the load becoming unpowered. Finally, we obtained an optimal inspection interval and maintenance decision table for events that occur in practice.