Optimal Inspection Policy 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

Inspection policy optimization for hierarchical multistate systems under uncertain mission scenarios: A risk-averse perspective

Most engineered systems intend to perform missions with a pre-specified target success probability to reduce undesirable failure risks. Before executing the next mission, inspection activities are conducted across various physical levels for assessing the probability of mission success. However, due to the randomness of a system’s degradation behavior and the presence of measurement errors, inspection results inevitably contain uncertainty. Meanwhile, mission durations and acceptable system states may also be uncertain, due to uncontrollable factors, such as random operating environments and mission demands. In such a circumstance, it is of great significance to identify the optimal multilevel inspection policy to answer, as great confident as possible, the question that the system can complete the next mission with a target mission success probability. This paper develops a novel metric to gauge the effectiveness of a multilevel inspection policy to assess if the system can complete the next mission with a pre-specified target success probability from a risk-averse perspective, based on which an optimization method is proposed to seek an inspection policy under uncertain scenarios with the aim of minimizing the maximum regret of the proposed metric. A stochastic fractal search algorithm, along with two tailored local search rules, is designed to efficiently resolve the resulting optimization problem. Two cases, including a three-component system and a rocket fueling mechanism’s control system, are used to illustrate the efficacy of the proposed approach, which is capable of effectively identifying the risk of mission failures by inspection policies.

Operational Risk Management: Optimal Inspection Policy

Major banks around the world lost nearly $210 billion during the period of 2011–2016 due to operational risk events. To mitigate the severe consequences that can arise from such events, the Basel Regulatory Committee has mandated that financial institutions worldwide conduct inspections on operational risk. In light of the importance of operational risk and its current regulation in the industry, this paper proposes a continuous-time principal-agent model that explores the optimal inspection policy of a financial firm (principal) and the effort of its employees (agent) to reduce the occurrence of risk events. First, we characterize the optimal inspection strategy under two commonly used policies in practice, namely random and periodic policies. This characterization reveals the conditions for two different modes of inspection (effort inducement and error correction), as well as the nuanced interactions among the inspection frequency, the penalty charged for errors, and the wage paid to employees. Next, by comparing random and periodic policies, we find that the random policy outperforms the periodic policy if and only if the inspection cost is high. Furthermore, we propose a hybrid policy that strictly dominates the random policy and weakly dominates the periodic policy, suggesting that a proper reduction of the random element in the inspection policy, in the manner of our proposed hybrid policy, can always improve its performance. Finally, we examine the complete information benchmark (without moral hazard), supplemental mitigation strategies, and numerical studies to provide further insights and show the robustness of our main findings. This paper was accepted by Vishal Gaur, operations management. Supplemental Material: The e-companion is available at https://doi.org/10.1287/mnsc.2021.00322 .

Termination versus operation extension for degrading systems

Optimal cost-wise termination of operation for degrading engineering systems is considered that maximizes the expected profit for the infinite horizon. Termination reduces probability of the future failure that usually results in substantial loss. The cases of non-repairable and minimally repairable systems are discussed. The black-box scenario without additional information on stochastic process of degradation and that with additional information are considered. The novel sequential optimal inspection policy is described. It is proved that the termination time can be postponed in an optimal way if the degradation observed at inspection is smaller than the defined level. The developed approach allows for optimal usage of system’s “resource.” The detailed numerical examples illustrate the findings.

Optimal Inspection Policies to Minimize Expected Cost Rates

In this paper, we propose a computing algorithm to obtain optimal checking times which minimize the expected cost rate of sequential inspection models. This algorithm is applied to two modified inspection models with finite intervals such that the unit is checked at times [Formula: see text] ([Formula: see text]) for given [Formula: see text] and given [Formula: see text]. The modified algorithms are proposed and optimal checking times to minimize the expected cost rates are obtained. Numerical examples of each model are given to show how to use the algorithm. This method would be applied to other sequential inspection models by its suitable modifications.

Optimal inspection policy for a second-hand product with a two-dimensional warranty

Abstract This paper studies the situation in which a manufacturer acts as a dealer and buys a second-hand product from one customer and sells it with a two-dimensional warranty to another customer. The manufacturer plans to inspect the product during the warranty period to identify and remove hidden defects and hence prevent failure as well as their corresponding cost. We describe a two-dimensional delay time model in which the customer’s usage rate affects both the time to defect and delay time. This concept is then used to derive a new class of failure models, namely, the two-dimensional and two-stage failure model. The number and time of inspections are determined to minimize the service cost during the warranty period under periodic and sequential inspection policies. Our approach is illustrated using an example from the automobile industry. A sensitivity analysis evaluates the effect of changes in the parameters of the model. Results indicate that the proposed model can aid the decision-making of a manufacturer, particularly in relation to the effect of customers’ usage and the effect of inspection upon the service cost during the warranty period.

An inspection policy for shredder equipment used in steel production lines considering buffer level and operating time

On the basis of scrap metal recycling, the shredding process transforms a large variety of objects composed predominantly of steel in crunched scrap. The main equipment used in this process is called shredder: a device consisting of several hammers attached in a horizontal rotor. Due to high efforts involved in the transformation process, the maintenance is an essential aspect to ensure the continuity of the shredder operation. A non-efficient maintenance policy can have negative consequences for the shredder performance, whose failure can stop all downstream processes for which it provides the basic input (crunched scrap). In order to improve the performance of the steel production line, we are introducing an opportunistic inspection policy that makes use of the crushed scrap buffer level. The policy guides the execution of an inspection after a time T of continuous operation, when the system fails, when the buffer is full or empty, or when the opportunity criterion (operation time ≥ t AND buffer level ≥ h) is verified, whichever occurs first. At an inspection, the shredder is stopped, the hammers are inspected, and the failed and defective ones are replaced by new units. A discrete-event simulation model was developed and applied to the context of a real steel production line of a company. The optimal opportunistic inspection policy was obtained, and its performance was compared with that of the policy currently adopted by the company. The results showed the possibility of obtaining significant economic savings. A sensitivity analysis showed a cost reduction of around 95 %.

Optimal Periodic Inspection Policy for a Parallel System Subject to Continuous Bi-Levels Degradation

Each system goes through several intermediate states between its initial state and the failure state, which are called degradation states. In addition, knowing these intermediate states allows us the building of an effective maintenance plan for the system under consideration. In this paper, we have considered a two-component parallel system where each component is subjected to two levels of degradation. Our first objective is to identify the mathematical (probabilistic) model associated with this system and this when the hypothesis of periodic inspection of the system is retained. Then, the main idea is to build the economic model encompassing the different average costs (inspection costs, preventive maintenance costs and corrective maintenance costs) spent during a renewal cycle. The latter will allow us to determine the optimal “inspection interval” while minimizing the average global-cost spent. Finally, in order to illustrate and analyze the sensitivity of the optimal inspection policy to the various maintenance costs, numerical examples are presented.

Fixing Phantom Stockouts: Optimal Data‐Driven Shelf Inspection Policies

A “phantom stockout" is a retail stockout phenomenon caused by unobserved inventory shrinkage. Unlike conventional stockouts that can be corrected by inventory replenishment, a phantom stockout persists and requires human inspection. In this study, we formulate such a problem as an infinite‐horizon Bayesian dynamic program with joint inventory inspection and replenishment decisions. This problem is challenging to solve due to non‐convexity and high dimensionality. However, we find that under the Bernoulli shrinkage process, the optimal inventory inspection policy has a simple threshold structure that depends on the number of consecutive zero‐sales periods since the last inspection, while the optimal inventory replenishment policy is the same as the optimal policy without inventory shrinkage. Our numerical studies further demonstrate that this simple and intuitive policy can be an effective heuristic for more general shrinkage processes.

Optimal multi-type inspection policy for systems with imperfect online monitoring

Both online monitoring and manual inspection are widely used in identifying a system’s health state, based on which proper preventive maintenance (PM) can be carried out. The existing maintenance optimization models typically consider only online monitoring or a single type of inspection and assume they can perfectly reveal the system’s state. However, the information provided by online monitoring is never perfect, and it needs to be combined with the inspection to identify the system’s health state. Besides, there are usually many types of inspections with different costs and detecting capabilities in real applications. It is hence equally important to decide on when operators should make an inspection and which kind of inspection should be performed based on the information from online monitoring. In this paper, we formulate the multi-type inspection decision-making problem within the partially observable Markov decision process (POMDP) framework. We establish some structural properties for the optimal multi-type inspection policy. The value iteration and the λ-minimization algorithm are combined to obtain the optimal solution. A case study is provided to illustrate the optimal inspection policy and its advantage over some existing policies.

Joint pricing and lot sizing model with statistical inspection and stochastic lead time

In many real-world situations, there are a fraction of defective items in a received lot whose quality should be evaluated before storage. In this article, we address the joint ordering, pricing, and inspection planning problem for a retailer facing price-sensitive demand and stochastic supply lead-time. The fraction of nonconforming items in a received lot follows a beta distribution and the buyer considers different kinds of inspection policies that include no inspection, inspection and sampling. Moreover, a novel non-linear optimization model is developed in order to determine optimal ordering, pricing and inspection policies. An analytical solution procedure based on mathematical properties of the model is proposed to find optimal decision variables. Numerical studies are conducted in order to show the applicability of the developed model and effectiveness of the proposed algorithms.

Optimal inspection models with minimal repair

Although the logistics support is indispensable in maintaining defense systems, there may exist some situations that systems have to be operated in no logistics support and maintenances of systems are performed with constraint stocks. Although repairing by brand-new parts improve system reliability, repairing by degraded parts may not disturb the system failure rate and such maintenance is called minimal repair. The minimal repair maintenance is common for warships in the long voyage because their repair parts inventories are limited and degraded parts have to be exploited. Although system failures can be detected because the system operates peculiarly that the operator does not wish, some failures cannot be detected in operation and they are detected only by diagnoses. In this paper, these two types of failures should be considered when we plan the military system maintenance. Optimal inspection policies of two types of failures with minimal repair are proposed.

Integrated production and maintenance scheduling for a single degrading machine with deterioration-based failures

In production lines, several factors contribute to the manufacturing of final products. Among these factors, the production time, machine status, and energy consumption, before and during production, need to be investigated further. In this paper, we present a mathematical model which jointly optimizes production scheduling and maintenance planning in a single-machine production environment. The performance of the machine deteriorates with time, and the machine is subject to stochastic deterioration-based failures. We assume that the transitions between the machine’s deterioration states follow an exponential distribution. We consider that processing times and energy consumption are affected by machine deterioration and failures. The main contribution of the paper is that maintenance and scheduling decisions are made based on the machine’s degradation level (i.e., the machine’s condition). We address the machine’s deterioration as a discrete multi-state degradation process; and model the effects of the machine’s deterioration and failures on the duration of job processing and the machine’s energy consumption. Then, we develop a stochastic mixed-integer programming model that integrates decisions about maintenance and production scheduling. The model generates the optimal maintenance action for each degradation state, as well as the optimal inspection policy and job sequence, with the overall aim being to minimize the total cost, including: inspection costs, repair costs, machine energy consumption costs, and the makespan penalty for exceeding a predetermined threshold. Due to the complexity of the developed model, an effective genetic algorithm (GA) based on the properties of the considered problem is proposed. Finally, through a comparative numerical study, we show that making decisions according to the deterioration level of the machine results in more integrated and cost-effective plans compared to the current method of repairing the machine only once it has reached its failure state.

Operational Risk Management: Optimal Inspection Policy

Operational risk is one of the major risks in the financial industry; major banks around the world lost nearly $210 billion from operational risk events between 2011 and 2016 (Huber and Funaro 2018) and inspection on operational risk is required by the Basel Committee on Banking Supervision. Motivated by the importance of operational risk and its current industry regulation, we study how a financial firm can optimally design inspection policies to manage operational risk losses. Specifically, we propose a continuous-time principal-agent model framework to examine a financial firm's (principal) optimal inspection policy and their employees' (agent) effort towards lowering the risk event occurrences. We first consider two commonly used inspection policies, namely, random and periodic policies, and characterize the optimal inspection strategy under each policy. We identify conditions for two different modes of inspection (effort inducement and error correction) as well as nuanced interactions among inspection frequency, penalty charged on errors, and wage paid to employees. We then compare the performances of random and periodic policies. We find that, contrary to conventional wisdom, the random policy is not always optimal; it is dominated by the periodic policy if the inspection cost is sufficiently low. Furthermore, we construct a hybrid policy that strictly dominates random policy and weakly dominates periodic policy, which suggests that a proper reduction of the random element in the inspection policy can always improve its performance. Finally, calibrating model parameters using operational risk data from a major bank in China, we numerically show that our key insights about random, periodic, and hybrid policies are robust to various model extensions.

Dynamic Maintenance, Production and Inspection Policies, for a Single-Stage, Multi-State Production System

Over the past 20 years, integrated decision making for production systems has gained the interest of researchers and practitioners. Many studies have shown that integrated decision making can lead to substantial amount of savings. Yet, a few research work has been conducted on the areas of integrated maintenance, production and quality in dynamic environments. This paper provides an integrated multi-period, maintenance, production and quality-inspection scheduling model, which is formulated as a Markov decision process. The model minimizes the total expected maintenance, production and quality inspection costs. The structural properties of the proposed model are mathematically investigated and with using sensitivity analysis, practical insights are also provided. We mathematically provide conditions to guarantee that the optimal inspection policy is monotone non-decreasing in the state of the machine. Furthermore, we show that the optimal production policy decreases by one unit as the state of inventory increases by one unit. Sensitivity analysis demonstrates that the production parameters affect both, maintenance and inspection decisions. In addition, the maintenance parameters affect inspection decisions. Finally, it is found that among the inspection parameters (i.e., cost-of-inspection and inspection-errors), type-II error mainly affects maintenance decisions.

Optimal job scheduling and inspection of a machine with delayed failure

In this paper, we consider a single machine, which must process n jobs in sequence. The machine's failure process follows the two-stage Delay Time Model, i.e. it starts with an initial defect, and will lead to eventual failure if the defect is left unattended. An inspection may be performed before starting a job to detect a defect. We improve the machine's maintenance decision making process by considering the possibility of performing minimal repair or replacement at any event time with regard to the age of the machine. This assumption affects the complexity of the problems in terms of executing loops in MATLAB excessively. The objective is to find the optimal inspection policy and the jobs sequence, which minimise the total expected makespan. We will develop two models and derive their corresponding recursive formulas. For the optimisation of the first model, we will combine the Genetic Algorithm with the recursive equations to jointly optimise the job sequence and inspection policy. In the second model, due to cumbersome recursive equations, we will adopt a simulation algorithm to obtain the required expected values in the objective function. We will provide numerical examples to present the application of the models, and study the influence of various input parameters on the best-obtained policies. We conduct extensive computational experiments on randomly generated problems with different configurations to evaluate the efficiency of models.

Efficient self-control device based on inspection model for Pitot sensors system

This paper proposes a new inspection model for a multi-component system, subject to a deterioration process which impacts its efficiency. To control the deterioration process, several inspections are carried out after which various decisions are made on how to evaluate the functioning of the system. The proposed inspection model is applied on the case of Pitot sensors system for aircraft. This study is derived from an aeronautic problem defined following the crash of the Airbus 330 in the Rio-Paris flight. Since the Pitot sensors system is non-self-announcing, the paper proposes a technical solution which consists in setting up an additional self-control device in order to inspect and calibrate the already installed Pitot sensors measurements.The objective of this paper is to determine an optimal inspection policy which minimizes the total measurement quality degradation per unit of time in a finite time horizon. Numerical examples and a comparative study are provided to illustrate the proposed analytic model and to highlight the contribution of the paper.

Two-stage failure modeling and optimal periodic inspection policy during the extended warranty period

ABSTRACTThe increased complexity of products and failure-induced costs add more pressure on the dealers of extended warranty (EW) contracts. In such conditions, conducting periodic inspection over the EW time-span may provide an opportunity to identify and repair defects before product failure. In this study, for a product with a two-stage failure process, the delay time model is applied to derive the failure process of the product. Considering a periodic inspection policy, the effects of identifying and removing defects on the failure process of the product and its corresponding cost are modeled. Then, a mathematical optimization model is derived to minimize the expected servicing cost for the dealer over the EW period. In the presented model, the number of inspections is assumed to be the dealer’s decision variable. Adopting a real case study from the literature, a numerical example is presented to clarify the model. Moreover, an extensive sensitivity analysis is conducted to study the effect of parameters on the optimal solution. The results show that considering periodic inspection may help pinpoint and remove defects, reduce failures, and minimize the expected servicing cost for the dealer.

Inspection location in capacity-constrained lines

We consider the effects of inspection and repair stations on the production capacity and product quality in a serial garments production line with possible inspection and repair following each operation. We construct a profit function that takes into account inspection, repair, scrap, and goodwill costs, as well as the capacity of each station. Then we discuss how the profit function can be maximized and provide properties of the optimal inspection plan. Our analysis captures the possibility of increasing production capacity by scrapping or repairing defective items before a bottleneck operation station, and hence reducing the waste of operation capacity on defective products. Our numerical results show that incorporating such capacity considerations can have substantial impact on the optimal inspection policy and that optimal inspection allocations can be identified quickly even for large problem instances.

Availability analysis and optimal inspection policy for systems with neglected down time

Many practical systems are subject to neglected down time, i.e., if the down time is less than a given threshold, then the system can be considered as working during the down time. Otherwise, the system is considered as in the failure state. This paper investigates the availability and maintenance policy for inspected systems with neglected down time. The instantaneous and steady-state availabilities of the system are derived analytically. Furthermore, a maintenance model is developed to find the optimal inspection interval, , which minimizes the long-run average cost rate. Based on the developed maintenance model, the analytical properties of the optimal inspection policy are explored. Numerical examples on ventilator system calculating the availability and optimal inspection policy are given to illustrate the applicability of the proposed model.