Imperfect Inspection Research Articles

Optimal Inspection Policy for a Three-Stage System With Imperfect Inspection and Repair

Optimal Inspection Policy for a Three-Stage System With Imperfect Inspection and Repair

Optimal maintenance over a finite time horizon for a system under imperfect inspection and dynamic working environment

Inspections play a crucial role in determining the state of a system and informing timely maintenance decisions. However, due to the limitations of adopted inspection technologies, inspection errors are often inevitable. More importantly, the likelihood of such errors is often influenced by the system's working environment that varies over time and space. Despite this, most studies on imperfect inspections largely overlook the effects of such dynamic working environments on inspection errors. To address this gap, this paper proposes a maintenance policy accounting for imperfect inspections for a degrading system with hidden failures under a dynamic working environment. We develop two models based on a recursive method. The first model examines a case where the working environment affects only inspection errors, whereas the second one accounts for its impact on both inspection errors and the system's degradation process. Our focus is to determine the optimal interval and number of inspections that minimize the expected maintenance cost over a finite time horizon. Numerical examples are provided to illustrate the proposed method to ensure the effectiveness of maintenance actions. The optimization outcomes not only offer a valuable tool for engineers seeking to reduce maintenance costs but also shed light on broader managerial implications.

A hybrid inspection-replacement policy for multi-stage degradation considering imperfect inspection with variable probabilities

A hybrid inspection-replacement policy for multi-stage degradation considering imperfect inspection with variable probabilities

Optimal inventory economic order quantity model for inventory system with imperfect inspection processes

Optimal inventory economic order quantity model for inventory system with imperfect inspection processes

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.

Mission Reliability Modeling of Multistation Manufacturing Systems Considering Cascading Functional Failure

The core function of the manufacturing system is to output high-quality products at a stable production rhythm. However, there are complex interactions between physical and functional failures of machines in the station. Functional failures can be propagated to other stations through material flow, resulting in the increasing risk of system performance degradation, which deserves further study. Therefore, in this article, a mission reliability modeling method considering the cascading functional failure of multistation manufacturing systems is presented. First, from the perspective of functional output, the cascading failure mechanism of a manufacturing system is discussed, and the connotation of functional failure and mission reliability is proposed. Second, the interaction model between machine performance and product quality is established to analyze the production rhythm considering the imperfect inspection. Third, the cascading functional failure model is constructed based on the mechanism of failure propagation. The integrated mission reliability modeling method of a multistation manufacturing system is proposed. Finally, a case study of a ferrite phase-shifting unit manufacturing system is conducted to illustrate the effectiveness and advancement of the proposed method.

Green consideration in a closed-loop supply chain model with imperfect inspection under learning impact

This study investigates a multi-echelon closed-loop supply chain model integrating learning impact with a single producer, single retailer, and single collector. Retail pricing, green innovation, and marketing efforts are assumed to have a linear relationship with end-user demand. The return of rejected goods occurs at random and is subject to an imperfect inspection procedure that is vulnerable to two different types of classification error. An S-shaped learning curve is considered to soothe the inspection process which is subject to inaccuracy. Numerical examples are used to illustrate the implications of the suggested model in order to achieve a goal that benefits both the consignor and the consignee. It is investigated whether the learning effect can outweigh the loss even when the inspection error has a detrimental effect on supply chain earnings. To identify the crucial parameters that can spark some truly exceptional managerial ideas, a sensitivity analysis is carried out.

Developing a framework for generating production-dependent failure rate through discrete-event simulation

Over the last decades, maintenance has experienced a transition from being a necessary evil to being a pivotal resource to create value for enterprises. Within the process of maintenance planning, distinct decisions could be responsible for different outcomes concerning profit and equipment reliability. Consequently, maintenance optimization has become pivotal to achieving relevant business goals. One of the most popular approaches to conduct maintenance optimization is simulation-based optimization, especially Discrete-Event Simulation (DES). Most works related to DES for maintenance optimization purposes focus on modeling imperfect maintenance or imperfect inspection and prognosis, while failures are often generated through a Weibull distribution. However, failure strongly depends on the production rate or the stress level, defining a Dynamic Non-Homogeneous Poisson Process (DNHPP). To this end, this paper proposes an algorithm for scheduling such DNHPP failure events in a DES framework model and, as a first implementation to apply it, an open-access library capable of generating stress level-dependent failures within the Rockwell ARENA© simulation environment. The developed package, that in the future will be ported to other relevant off-the-shelf simulation environments, provides a more realistic tool for maintenance engineers and researchers to optimize or compare maintenance strategies from an economic perspective.

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.

Classification of Systems and Maintenance Models

Maintenance is an essential part of long-term overall equipment effectiveness. Therefore, it is essential to evaluate maintenance policies’ effectiveness in addition to planning them. This study provides a classification of technical systems for selecting maintenance effectiveness indicators and a classification of maintenance models for calculating these indicators. We classified the systems according to signs, such as system maintainability, failure consequences, economic assessment of the failure consequences, and temporary mode of system use. The classification of systems makes it possible to identify 13 subgroups of systems with different indicators of maintenance effectiveness, such as achieved availability, inherent availability, and average maintenance costs per unit of time. When classifying maintenance models, we used signs such as the system structure in terms of reliability, type of inspection, degree of unit restoration, and external manifestations of failure. We identified one hundred and sixty-eight subgroups of maintenance models that differed in their values for specified signs. To illustrate the proposed classification of maintenance models, we derived mathematical equations to calculate all considered effectiveness indicators for one subgroup of models related to condition-based maintenance. Mathematical models have been developed for the case of arbitrary time-to-failure law and imperfect inspection. We show that the use of condition-based maintenance significantly increases availability and reduces the number of inspections by more than half compared with corrective maintenance.

A Bayesian framework for uncertainty quantification of perturbed gamma process based on simulated likelihood

The perturbed gamma process (PGP) has recently been widely used in modeling the noisy degradation data collected from engineering structures and components since it can simultaneously consider the temporal variability of degradation and measurement uncertainty. As a result of the sampling and inspection uncertainty in engineering practice, it is necessary to account for the resulting parameter uncertainty. Meanwhile, the flexibility of the form of measurement error motivates a potential demand for quantifying the model uncertainty and selecting the most fitting error model for the given inspection data. The Bayesian approach is well-suited to quantity the parameter uncertainty induced by imperfect inspection and limited inspection data, but its practical implementation is extremely challenging due to the intractable likelihood function of PGP. In the paper, a novel Bayesian framework for quantifying parameter and model uncertainty of PGP is presented, where the simulated likelihood that is an unbiased estimator generated by Sequential Monte Carlo (SMC) is introduced to overcome the intractable likelihood of PGP. More specifically, an Adaptive Particle Markov chain Monte Carlo (APMCMC) is proposed to perform the Bayesian sampling from the posterior distributions of parameters, achieving the requirement for the quantification of parameter uncertainty. By utilizing the posterior samples from APMCMC, a model selection method based on the Bayes factor is employed to determine the most fitting one from some alternative error models. Finally, two simulation examples are presented to illustrate the efficiency and accuracy of the proposed framework and its applicability is confirmed by a practical case involving the corrosion modeling of a group of pipelines.

Blockchain adoption or contingent sourcing? Advancing food supply chain resilience in the post-pandemic era

In the post-pandemic era, food supply chains and firms therein are facing unprecedented severe challenges, because once infection is detected, numerous products must be recalled or abandoned, and both suppliers and retailers in the supply chain suffer enormous loss. To survive under the pandemic, retailers have adopted different sourcing strategies, such as contingent sourcing, which, in turn, affect the upstream suppliers and hence the resilience of the whole supply chain. With the rapid development of digital technologies, retailers nowadays can utilize blockchain as a reliable and efficient way to reduce product risk and hence advance the resilience of food supply chains by improving product traceability and inspection accuracy, and making sourcing transparent. In this paper, we develop a game-theoretic model to investigate the interrelation between the retailer’s decisions on blockchain adoption and sourcing strategies. We consider that a retailer originally orders from a risky supplier while conducting an imperfect inspection to detect infected products before selling. The retailer may speculatively keep on ordering from the risky supplier or adopt contingent sourcing by ordering from an alternative safe supplier. The retailer also has an option to implement blockchain to improve the inspection accuracy and product traceability. We derive the optimal retail prices under different sourcing strategies with and without blockchain adoption and then analyze the incentives for sourcing strategy and blockchain adoption. Then, we identify the conditions of an all-win situation for food retailer, supplier, supply chain resilience, and consumers with/without government subsidy. Finally, we extend to consider the situation that some consumers have health-safety concerns and preferences for blockchain adoption.

Optimal Inventory Economic Order Quantity Model for Inventory System with Imperfect Inspection Processes

Optimal Inventory Economic Order Quantity Model for Inventory System with Imperfect Inspection Processes

Functional healthy state evaluation approach for manufacturing systems considering imperfect inspection based on extended stochastic flow network

The core function of a manufacturing system is to consistently and efficiently output a specified number of qualified products that can meet production demands. However, the imperfect inspection can sometimes bring disturbances to the work-in-process (WIP) quality and the processing machine degradation in the function realization process, and this aspect has not been paid due attention in existing research on manufacturing system health evaluation researches. Therefore, a functional healthy state evaluation approach for manufacturing systems considering imperfect inspection based on extended stochastic flow network (ESFN) is proposed in this paper. First, a function realization-oriented operational mechanism is expounded from the systematic perspective. On this basis, the connotation of the functional healthy state of the manufacturing system considering imperfect inspection is further defined. Second, an ESFN model is established to describe the relationship among processing machines, WIPs, and inspection machines in a running manufacturing system. Third, a functional healthy state evaluation approach for a manufacturing systems considering imperfect inspection is proposed. Finally, the effectiveness of the approach is verified by an illustrative example.

Optimal Preventive Maintenance Policy Considering Imperfect Inspection and Limiting the Number of Minimal Repairs for Degradation System

Optimal Preventive Maintenance Policy Considering Imperfect Inspection and Limiting the Number of Minimal Repairs for Degradation System

Economic Sustainability for Supply Chain with Multiple Instances Of Imperfect Machinery and Controllable Inspection Costs Under Paris Accord

Economic Sustainability for Supply Chain with Multiple Instances Of Imperfect Machinery and Controllable Inspection Costs Under Paris Accord

A condition-based maintenance policy considering failure dependence and imperfect inspection for a two-component system

In this paper, a condition-based maintenance of a two-component system under imperfect inspection is studied: component 1 is repairable and only two states (working and failed) are observable. Component 2 degrades with time. The degradation of component 2 is modelled by a Wiener process with different drift and volatility parameters depending on the working state of component 1. Component 2 fails if its degradation level exceeds a pre-defined threshold. A dual periodical inspection policy is proposed to monitor the system condition: component 1 is imperfectly inspected and the whole system is perfectly inspected with a longer period. Upon inspection, component 1 is replaced if a failure is detected. The whole system is renewed if the degradation of component 2 exceeds its preventive maintenance threshold. The problem is very complex due to the failure dependence between the two components and the partial revealed information within the system inspection period. Component 1 is impacted by the imperfect inspection. Component 2 may experience multiple changes of its degradation regime while only imperfect, partial change information is available. In this study, we intend to address these problems. The expression of the maintenance cost rate in the long-run is given to evaluate the maintenance policy. An algorithm is proposed to achieve the maintenance optimization. Numerical examples show the applicability of the model. It can provide reference to the decision-maker for optimizing the maintenance budget.

A closed-loop supply chain model with learning effect, random return and imperfect inspection under price- and quality-dependent demand

A closed-loop supply chain model with learning effect, random return and imperfect inspection under price- and quality-dependent demand

Optimization of inventory system with defects, rework failure and two types of errors under crisp and fuzzy approach

<p style='text-indent:20px;'>In this paper, a new approach was applied to a single-item single-source (<inline-formula><tex-math id="M1">\begin{document}$ SISS $\end{document}</tex-math></inline-formula>) system at the "<inline-formula><tex-math id="M2">\begin{document}$ EOQ-type $\end{document}</tex-math></inline-formula>" mode considering imperfect items and uncertainty environment. The mentioned method was intended to produce an optimum order/production quantity as well as taking care of imperfect processes. The imperfect proportion of the received lot size was described by an imperfect inspection process. That is, two-way inspection errors may be committed by the inspector as separate items. Thus, this survey was aimed to maximize the benefit in the traditional inventory systems. The incorporation of both defects and defective classifications (Type-<inline-formula><tex-math id="M3">\begin{document}$ I\&II $\end{document}</tex-math></inline-formula> errors) was illustrated, in a way that the defects were returned by the consumers. Moreover, this inventory model had an extra step in the scope of inspection; which occurred after the rework process with no inspection error. To get closer to the practical circumstances and to consider the uncertainty, the model was formulated in the fuzzy environment. The demand, rework, and inspection rates of the inventory system were considered as the triangular fuzzy numbers where the output factors of the inventory system were obtained via nonlinear parametric programming and Zadeh's extension principle. Finally, this scenario was illustrated through a mathematical model. The concavity of the objective function was also calculated and the total profit function was presented to clarify the solution procedure by numerical examples.</p>

Maintenance optimisation for systems with multi-dimensional degradation and imperfect inspections

In this paper, we develop a maintenance model for systems subjected to multiple correlated degradation processes, where a multivariate stochastic process is used to model the degradation processes, and the covariance matrix is employed to describe the interactions among the processes. The system is considered failed when any of its degradation features hits the pre-specified threshold. Due to the dormancy of degradation-based failures, inspection is implemented to detect the hidden failures. The failed systems are replaced upon inspection. We assume an imperfect inspection, in such a way that a failure can only be detected with a specific probability. Based on the degradation processes, system reliability is evaluated to serve as the foundation, followed by a maintenance model to reduce the economic losses. We provide theoretical boundaries of the cost-optimal inspection intervals, which are then integrated into the optimisation algorithm to relieve the computational burden. Finally, a fatigue crack propagation process is employed as an example to illustrate the effectiveness and robustness of the developed maintenance policy. Numerical results imply that the inspection inaccuracy contributes significantly to the operating cost and it is suggested that more effort should be paid to improve the inspection accuracy.