Optimal Inspection Schedule Research Articles

Machine learning-assisted optimal schedule of underground water pipe inspection

There are over 2.2 million miles of underground water pipes serving the cities in the United States. Many are in poor conditions and deteriorate rapidly. Failures of these pipes could cause enormous financial losses to the customers and communities. Inspection provides crucial information for pipe condition assessment and maintenance plan; it, however, is very expensive for underground pipes due to accessibility issues. Therefore, water agencies commonly face the challenge to 1) decide whether it is worthwhile to schedule expensive water pipe inspections under financial constraints, and 2) if so, how to optimize the inspection schedule to maximize its value. This study leverages the physical model and data-based ML (ML) models for underground water pipe failure prediction to shed light on these two important questions for decision making. Analyses are firstly conducted to assess the value of water pipe inspection. Results by use of a physical-based failure model and Monte Carlo simulations indicate that by inspecting pipe’s condition, i.e., assessment of pipe’s erosion depth, the uncertainty of water pipe failure prediction can be narrowed down by 51%. For optimal inspection schedule, an artificial neural network (ANN) model, trained with historical inspection data, is evaluated for its performance in forecasting the future pipe failure probability. The results showed that a biased pipe failure prediction can occur under limited rounds of inspection. However, incorporating more rounds of inspection allows to predict the pipe failure conditions over its life cycle. From this, an optimal inspection plan can be proposed to achieve the maximum benefits of inspection in uncertainty reduction. A few salient results from the analyses include 1) the optimal schedule for inspection is not necessarily equal in the time interval, 2) by setting the goal of uncertainty reduction, an optimal inspection schedule can be obtained, where ML (ML) model augmented by continuously training with inspection data allows to reliably predict water pipe failure conditions over its life cycle. While this study focuses on underground pipe inspection, the general observations and methodology are applicable to optimize the inspection of other types of infrastructure as well.

Entropy-based framework for optimal life-cycle management of multiple fatigue cracks in ship structures

Cyclic loading of ship structures can result in multiple cracks at fatigue-prone details. While these cracks are generally considered a nuisance, they can result in catastrophic failure if left unrepaired. On the other hand, periodic inspection and repair of these cracks can result in a large financial burden. Accordingly, careful scheduling of inspection and repair of the cracks is needed to avoid catastrophic failures while ensuring low cost. Life-cycle analysis offers a reasonable means to establish cost-effective scheduling of maintenance and repair strategies for civil and marine infrastructure. Studies exist on life-cycle cost frameworks for the assessment and repair of multiple fatigue cracks utilizing non-linear optimization strategies. In this study, we establish a new probabilistic life-cycle cost framework that improves on existing approaches by utilizing the concept of entropy to determine optimal inspection and repair scheduling for ship structures with multiple cracks. The parameters influencing the propagation rate of the cracks are considered random variables with predefined statistical distributions. A parametric study is conducted to assess the impact of some parameters, such as design life and loading cycles on the obtained life-cycle cost. The results show stark improvement in achieving optimal scheduling of inspection and repair with low cost over traditional optimizations.

The Optimization Of Failure Risk Estimation On The Uniform Corrosion Rate With A Non-Linear Function

Failures in the oil and gas pipeline system are conditions that must be avoided and anticipated because the losses due to the failures can occur at a very high level. Internal corrosion is one of the significant causes of the failures in pipeline systems. In addition, this type of corrosion is due to the high content of carbon dioxide and other corrosive substances in crude oil and natural gas. Therefore, an optimal inspection scheduling system is required to prevent the possibility of pipeline failures due to corrosion and to avoid any overspending on the budget due to excessive inspection scheduling. Risk-based testing (RBI) is one of the best methods to define a test planning system by using an optimal risk assessment. In this article, a Monte Carlo random number generator is applied by using a huge number of random iterations to approximate the actual risk value of a pipeline system with a limited sample at the scene. The nonlinear corrosion rate function is used for comparison with the commonly used linear corrosion rate function based on ASTM G-16 95. Once a risk value is estimated, the value is monitored based on an assessment of the risk matrix for each corrosion rate function by using the RBI method. The results show that the nonlinear corrosion rate function provides a more accurate approach to estimating the actual risk value and ultimately leads to an optimal inspection planning system.

Efficient Structural Reconnaissance Surveying for Regional Postseismic Damage Inference with Optimal Inspection Scheduling

Efficient Structural Reconnaissance Surveying for Regional Postseismic Damage Inference with Optimal Inspection Scheduling

Optimal Inspection Scheduling Model for Monitoring Railway Track Grids

The optimization of railway track inspection schedules is of great significance for the monitoring of railway track conditions and reasonable organization of track maintenance tasks. Here, an optimal inspection scheduling model for monitoring railway tracks is proposed. Railway track inspection activities are divided into equal‐length units in the time and spatial location dimensions. The various constraints and objectives on the time and location of different track inspection activities are defined in detail regarding subdivisions of individual management units. The objectives of the model development are to achieve a more optimized equilibrium and robustness of the track inspection schedule. Based on the maximum entropy criterion, entropy is used to measure the distribution equilibrium of the inspection schedule in the time dimension. The proposed model is verified using actual data from the Lanxin railway.

Predictive information and maintenance optimization based on decision theory: a case study considering a welded joint in an offshore wind turbine support structure

Predictive information and maintenance optimization for deteriorating structures is concerned with scheduling (a) the collection of information by inspection and monitoring and (b) maintenance actions such as repair, replacement, and retrofitting based on updated predictions of the future condition of the structural system. In this article, we consider the problem of jointly identifying—at the beginning of the service life—the optimal inspection time and repair strategy for a generic welded joint in a generic offshore wind turbine structure subject to fatigue. The optimization is performed based on different types of decision analyses including value of information analyses to quantify the expected service life cost encompassing inspection, repair, and fatigue damage for all relevant combinations of inspection time, repair method, and repair time. Based on the analysis of the expected service life cost, the optimal inspection time, repair method, and repair time are identified. Possible repair methods for a welded joint in an offshore environment include welding and grinding, for which detailed models are formulated and utilized to update the joint’s fatigue performance. The decision analyses reveal that an inspection should be scheduled approximately at mid-service life of the welded joint. A repair should be performed in the same year after an indication and measurement of a fatigue crack given an optimal inspection scheduling. This article concludes with a discussion on the results obtained from the decision and value of information analyses.

Reinforcement learning for optimal policy learning in condition‐based maintenance

Condition-based maintenance (CBM) involves taking decisions on maintenance or repair based on the actual deterioration conditions of the components. The long-run average cost is minimised by choosing the right maintenance action at the right time. In this study, the CBM decision-making problem is modelled as a continuous semi-Markov decision process (CSMDP). It consists of a chain of states representing various stages of deterioration, a set of maintenance actions, their costs and scheduled inspection policy. The application of a reinforcement learning (RL) algorithm based on the average reward for CSMDPs in CBM is described. The RL algorithm is used to learn the optimal maintenance decisions and inspection schedule based on the current health state of the component.

Optimal Inspection and Preventive Maintenance Scheduling of Mining Equipment

A typical mining company has three important assets: the human labor-force, the orebody, and the equipment. Trucks, excavators, drilling machines, crushers, grinders, classifiers, and concentrators represent the equipment. Mining operations that want to take advantage of economies of scale have huge equipment fleet, and the worth of the equipment could be more than a hundred million dollars. The reliability and availability of this equipment play critical roles in increasing the efficiency and productivity of a mining operation. This paper proposes an effective maintenance management approach to be used in the mining industry such that equipment availability and reliability are improved while potential failures are prevented. Using failure data of a mining truck fleet in an open-pit Canadian mining operation, a case study is conducted in two steps. The first step focuses on determining optimal inspection intervals based on the desired reliability level in such a way as to detect potential catastrophic failures that represent considerable maintenance and downtime costs. The second step develops a preventive maintenance scheduling plan that differentiates between physical and virtual age considering the degradation of systems and their rejuvenation after each repair. The research outcomes show that the proposed approach has the potential to increase the benefit obtained from the mining equipment and can be used in mining operations.

Optimal inspection and maintenance for a repairable k-out-of-n: G warm standby system

In many cases, the safety and the reliability of a warm standby system heavily rely on the successful activation and the subsequent operation of its standby components. Optimal inspection and maintenance schedule is one of the most common but essential activities in the real world applications to manage standbys effectively and efficiently. In this paper, we propose a novel state-based method by incorporating inspection activities into multiphase Markov process to model the dynamic behaviors of a general repairable k-out-of-n: G warm standby system with common-cause failures. Here the effects of inspection errors are taken into consideration. Then the expected total cost and the average unavailability of the system are expressed as exact closed formulas regarding the inspection interval (or inspection frequency) in a cycle. Finally, the inspection and maintenance optimization problem is formulated as a nonlinear optimization program which aims to find the optimal periodic inspection interval on a finite time horizon by minimizing the expected total cost while taking into account the limitation of the average unavailability. The proposed modeling approach can be used in various industrial systems, where inspections and standbys are especially necessary, e.g., a feedwater subsystem of a nuclear power plant. A simplified numerical example illustrates the models and the calculations with sensitivity analysis and Monte Carlo simulation.

Optimal inspection and repair scheduling for mitre lock gates

Hydraulic steel structures, especially lock gates, play an important role in inland waterway transport infrastructure. Navigation lock gates are normally designed to last for 100 years. However, after a few decades of operation, many welded joints of steel mitre gates may suffer deterioration and unexpected failures, occurring primarily due to fatigue. As emergency repairs are costly, time-consuming and disruptive, optimising the operation and maintenance plans of mitre gates is necessary. Risk-based inspection planning has been used for marine structures but is seldom applied to inland navigation lock gates. In this paper, a procedure is proposed for inspecting welded joints using observed water levels. Optimal inspection plans are then evaluated by risk analysis, combining failure probabilities and associated expected costs for different events. A mitre gate is used to illustrate the procedure. It was found that the total expected cost of inspections performed at regular time intervals was generally higher than inspections performed when a certain annual failure probability threshold was reached.

Data-driven predictive maintenance scheduling policies for railways

Inspection and maintenance activities are essential to preserving safety and cost-effectiveness in railways. However, the stochastic nature of railway defect occurrence is usually ignored in literature; instead, defect stochasticity is considered independently of maintenance scheduling. This study presents a new approach to predict rail and geometry defects that relies on easy-to-obtain data and integrates prediction with inspection and maintenance scheduling activities. In the proposed approach, a novel use of risk-averse and hybrid prediction methodology controls the underestimation of defects. Then, a discounted Markov decision process model utilizes these predictions to determine optimal inspection and maintenance scheduling policies. Furthermore, in the presence of capacity constraints, Whittle indices via the multi-armed restless bandit formulation dynamically provide the optimal policies using the updated transition kernels. Results indicate a high accuracy rate in prediction and effective long-term scheduling policies that are adaptable to changing conditions.

Cost effective scheduling of imperfect inspections in systems with hidden failures and rescue possibility

• Inspected non-repairable systems subject to a delay-time failure are considered. • A hidden failure cannot stop system functioning while a fatal failure causes the entire system loss. • A probabilistic model for evaluating performance metrics of the system is suggested. • A problem of finding the inspection schedule minimizing the total expected loss is formulated and solved. • Examples demonstrating the effects of system parameters on the optimization solutions are provided. Motivated by real-world critical applications such as aircraft, medical devices, and military systems, this paper models non-repairable systems subject to a delay-time failure process involving hidden and fatal failures in two stages during their missions. A hidden failure cannot cause the system to stop functioning while a fatal failure causes the entire system loss. The system undergoes scheduled inspections for detecting the hidden failure. In the case of a positive inspection result, the system main mission is aborted and a rescue operation is started to mitigate the risk of the entire system loss. The inspections are imperfect and may produce false positive and negative failures. We propose probabilistic models for evaluating performance metrics of the system considered, including mission success probability, system survival probability, expected number of inspections during the mission, and total expected losses. Based on the evaluation models, we formulate and solve an optimization problem of finding the optimal inspection schedule on a fixed mission time horizon to minimize the total expected loss. Examples are provided to demonstrate the proposed methodology and effects of key system parameters on system performance and optimization solutions.

Evaluation of Optimization Method for Inspection Scheduling of Power Distribution Facilities Using Maintenance Data Accumulated by Power Utility

Power distribution companies must establish an optimal maintenance schedule that balances the reliability and efficiency of a number of widely scattered facilities. Accordingly, we have developed an optimization method for inspection scheduling by which optimal inspection schedules are planned using 1) a method to predict the inspection priority for each facility and 2) a method to establish an inspection schedule that minimizes the inspection cost. In this study, for step 1, a practical method using both inspection history and facility attributes is proposed. The method consists of two approaches: a relation analysis and a defect prediction. In the relation analysis, relations between facility defect and other maintenance data are analyzed using a multiple correlation analysis method on the basis of chi-square testing. And then, facility defect is predicted using the data items that correlated with the facility defect obtained from the relation analysis. A modified quantification method type II introducing biased posterior probability is proposed for the prediction. Furthermore, proposed method is demonstrated by utilizing maintenance data accumulated by a certain Japanese power utility company. Evaluation results show that inspection cost can be reduced by 36–58% compared with the conventional twice-every-two-years inspection while retaining reliability.

A myopic policy for optimal inspection scheduling for condition based maintenance

In this paper, we propose a decision policy for condition-based maintenance that schedules inspections according to the current health of the system, optimized myopically over the next inspection interval. In traditional condition-based maintenance practices, regular inspections are considered a given requirement. Most measurements, however, confirm that the machine in question is in good working order and that no maintenance is necessary. We consider the possibility that there are savings to be had in the number of inspections that are undertaken. As such, we use a proportional hazards model for risk of failure and a Markovian process to model the system covariates. The cost and time of inspections are incorporated into our model, and an optimal decision for one interval is made. This process can be repeated for each decision point, resulting in a decision policy that produces an inspect-or-replace result and an optimal time for the next inspection. Applied over the life of an asset, this policy can be used as a complete condition monitoring program supporting evidence based asset management.

Optimal inspection planning and repair under random crack propagation

Operation of damage-tolerant structures or components subject to random crack propagation requires constant monitoring by non-destructive inspections and systematic maintenance actions. Optimization of inspection schedules and repair strategies is a compromise between costs of inspections and repairs, and expected costs of failure. This paper advances the state of the art by: considering accurate polynomial chaos model of the random crack propagation process; considering number of inspections and crack repair size as design variables and; by performing sensitivity analysis of optimal inspection schedules and repair strategies with respect to the assumed costs of inspection and failure, as well as to the level of loading.

Optimal inspection and design of onshore pipelines under external corrosion process

Pipeline systems can be safely designed and operated by using conservative safety margins and approximations. However, when expected consequences of failure are accounted for, optimal designs or optimal inspection/maintenance plans cannot be found using overly conservative assumptions. Specifically, pipeline corrosion cannot be modeled using popular but overly conservative linear corrosion growth models. In this paper, a novel polynomial chaos corrosion growth model is constructed from extensive field data, and employed in the optimal design of an example buried pipeline. The optimal corrosion thickness, time to first inspection and time between successive inspections are considered as design variables. The design objective is to minimize total expected life-cycle costs, which include costs of construction, inspections and repair, and expected costs of failure. Expected numbers of failures, repairs and replacements are evaluated by a probabilistic analysis using Latin hypercube sampling, and a novel approach is presented in order to smoothen these expected numbers w.r.t. design variables. The resulting objective function is discontinuous, and presents many local minima; hence, global optimization algorithms are required. A multi-start simplex algorithm is employed, but results are also compared with a crude exhaustive search. Results are obtained for several cost configurations, reflecting different failure consequence scenarios. A discussion is presented with respect to the optimal inspection schedules and optimum corrosion thicknesses found herein.

Solving the Economic Lot and Inspection Scheduling Problem using the Extended Basic Period approach under Power-of-Two policy

The focus of this study is to solve the Economic Lot and Inspection Scheduling Problem (ELISP) using the Extended Basic Period (EBP) approach under Power-of-Two (PoT) policy. The objective of the ELISP is to determine an optimal cycle time and an optimal production and inspection schedule so as to minimize the total cost per unit time. Under PoT policy, we formulate a mathematical model by taking into account the constraints for both production and inspection capacities. Also, we propose a Hybrid Genetic Algorithm (HGA) which is equipped with a search algorithm that not only seeks to improve solution quality, but also assures a feasible solution for each chromosome obtained from the evolutionary processes. Our numerical experiments show that the proposed HGA effectively solves the ELISP using the EBP approach, and its solutions outperform the solutions from the ELISP using the Common Cycle approach.

A common cycle approach for solving the economic lot and inspection scheduling problem

In this study, we consider an imperfect production system in which the manager not only faces the Economic Lot Scheduling Problem, but also needs to conduct multiple inspections during a production lot of any product. Inspection plays an important role in an imperfect production system since it saves the cost from producing and restoring defective items though it also incurs extra inspection cost at the same time. In this study, we employ the common cycle approach in which all the products share the same replenishment cycle, and adopt a consensus inspection policy. The focus of this study is to determine the optimal cycle time and an optimal production and inspection schedule that minimize the total cost per unit time. We formulate a mathematical model in which we take into accounts both the production capacity and inspection capacity constraints. Also, we conduct full theoretical analysis and propose an effective search algorithm for solving an optimal solution. Our numerical experiments demonstrate the effectiveness of the proposed search algorithm.

The value of setup cost reduction and quality improvement on the optimal production run length and inspection schedules in a deteriorating production process

This paper presents an economic production quantity model taking into consideration of 1) investment in setup cost reduction; 2) investment in quality improvement; 3) investment in both setup cost reduction and quality improvement, to determine simultaneously optimal production run length and inspection schedules in a deteriorating production process. A simple and accurate algorithm is presented to locate the optimal production run length and then to find the optimal setup cost and optimal process quality simultaneously. A numerical experiment is carried out to compare the results of: 1) number of inspection schedules; 2) optimal production run length; 3) average cost per unit time of the proposed model to an existing model without considering the setup cost reduction and quality improvement. The results show that investment in setup cost reduction will result in reduction in primarily the optimal production run length means small lot size, while the investment in quality improvement results in number of inspections undertaken to be unity during each production run. The results show that investments in setup cost reduction and process quality improvements of a production process achieve some of the characteristics of JIT system such as small lot sizes and high quality.

The optimal production and quality policy for the vendor in a trade

Arranging an inspection schedule for the production process and taking inspection and burn-in tests to screen out defective items in a production lot before items are shipped to the buyer are widely used by the vendor, such that the defective percentage in an outgoing batch satisfies the quality requirement specified in the contract between them. For an inspection schedule, the number of inspections and the length of time intervals between two inspections are influential to both the precision of detecting the manufacturing process and the inspection cost. As to the inspection test, it is not perfect, so there are two types of errors (Types I and II). Nevertheless, compared with inspection test, burn-in is usually costly. Hence, how to make a suitable trade-off between these three treatments (i.e., inspection schedule, inspection test, and burn-in test) such that the outgoing batch satisfies the purchaser's quality requirement with low cost is an important issue. The main purpose of this paper is to deal with the problem of determining the optimal inspection schedule and the optimal mixed policy of inspection and burn-in, where the average outgoing quality is used as the measure of quality. More specifically, by using the criterion of maximizing the expected profit that the vendor makes in a trade, a nonlinear programming problem is built to determine (a) the number of inspections undertaken in the production process, (b) the times at which the production process is inspected, (c) the total number of items that the vendor should produce (or the production run time), (d) the number of items for inspection, the number of items for burn-in, and the number of items that need neither inspection or burn-in, and (e) the optimal burn-in time for those needing burn-in testing. An example is provided to illustrate the proposed method.