Risk-Based Integrity and Inspection Modeling (RBIIM) of Process Components/System

Process plants deal with hazardous (highly flammable and toxic) chemicals at extreme conditions of temperature and pressure. Proper inspection and maintenance of these facilities is paramount for the maintenance of safe and continuous operation. This article proposes a risk-based methodology for integrity and inspection modeling (RBIIM) to ensure safe and fault-free operation of the facility. This methodology uses a gamma distribution to model the material degradation and a Bayesian updating method to improve the distribution based on actual inspection results. The method deals with the two cases of perfect and imperfect inspections. The measurement error resulting from imperfect inspections is modeled as a zero-mean, normally distributed random process. The risk is calculated using the probability of failure and the consequence is assessed in terms of cost as a function of time. The risk function is used to determine an optimal inspection and replacement interval. The calculated inspection and replacement interval is subsequently used in the design of an integrity inspection plan. Two case studies are presented: the maintenance of an autoclave and the maintenance of a pipeline segment. For the autoclave, the interval between two successive inspections is found to be 19 years. For the pipeline, the next inspection is due after 5 years from now. Measurements taken at inspections are used in estimating a new degradation rate that can then be used to update the failure distribution function.     

Production lot sizing with process deterioration and machine breakdown under inspection schedule

The paper develops integrated production, inventory and maintenance models for a deteriorating production system in which the production facility may not only shift from an ‘in-control’ state to an ‘out-of-control’ state but also may break down at any random point in time during a production run. In case of machine breakdown, production of the interrupted lot is aborted and a new production lot is started when the on-hand inventory is depleted after corrective repair. The process is inspected during each production run to examine the state of the production process. If it is found in the ‘in-control’ state then either (a) no action is taken except at the time of last inspection where preventive maintenance is done (inspection policy-I) or (b) preventive maintenance is performed (inspection policy-II). If, however, the process is found to be in the ‘out-of-control’ state at any inspection then restoration is done. The proposed models are formulated under general shift, breakdown and repair time distributions. As it is, in general, difficult to find the optimal production policy under inspection policy-I, a suboptimal production policy is derived. Numerical examples are taken to determine numerically the optimal/suboptimal production policies of the proposed models, to examine the sensitivity of important model parameters and to compare the performance of inspection and no inspection policies.     

具有隐藏故障的多状态竞争失效系统检测策略研究

复杂工业系统的故障中有40%属于隐藏故障,若隐藏故障得不到及时消除,则可能导致巨大的经济损失。本文针对具有隐藏故障的多状态竞争失效系统,在考虑不完全检测的基础上,对其进行了维修建模。首先,基于制定的视情维修策略,分析了系统的更新情形;然后,基于所推导出的各种系统更新情形的发生概率,建立了以期望成本率为目标函数,以检测间隔时间为决策变量的维修模型。最后,以电容器组为例对所构建维修模型的适用性和有效性进行了验证,研究结果表明,检测质量对检测策略的制定有重要影响,因此研究具有隐藏故障的多状态竞争失效系统的检测策略时,有必要考虑检测误差。本文提出的维修建模方法不仅能在一定程度上丰富多状态竞争失效系统的维修策略理论与方法,还能为工程实际中复杂工业系统的维修工作提供理论基础与决策依据。     

Optimal policy for imperfect inspection in discrete time

Abstract

The problem of finding the optimal inspection interval for a fallible system that operates in discrete time when inspection is subject to errors was addressed. A Markov chain model of the system state was developed to formulate the objective function, which is the minimum expected total cost per lime unit. A numerical search procedure was used to find local minima for a representative range of parameter values. The objective function turned out to be quite insensitive to deviations in the inspection interval in the neighbourhood of the minimum, so an approximate method based on curve fitting was developed and tested, yielding good results in the representative range.     

Application of load-oriented manufacturing control in industry

This paper deals with multi-stage lotsizing models for imperfect production processes. The effect of imperfect quality on lotsizing decisions and effect ofinspection errorsare taken into consideration in the proposed models. Numerical examples are presented for illustration purposes. The developed models are very helpful for justifying quality assurance and quality improvement efforts.     

Information‐Sensitive Replenishment when Inventory Records Are Inaccurate

Inspired by recent empirical work on inventory record inaccuracy, we consider a periodic review inventory system with imperfect inventory records and unobserved lost sales. Record inaccuracies are assumed to arrive via an error process that perturbs physical inventory but is unobserved by the inventory manager. The inventory manager maintains a probability distribution around the physical inventory level that he updates based on sales observations using Bayes Theorem. The focus of this study is on understanding, approximating, and evaluating optimal forward‐looking replenishment in this environment. By analyzing one‐ and two‐period versions of the problem, we demonstrate several mechanisms by which the error process and associated record inaccuracy can impact optimal replenishment. Record inaccuracy generally brings an incentive for a myopic manager to increase stock to buffer the added uncertainty. On the other hand, a forward‐looking manager will stock less than a myopic manager, in part to improve information content for future decisions. Using an approximate partially observed dynamic programming policy and associated bound, we numerically corroborate our analytical findings and measure the effectiveness of an intelligent myopic heuristic. We find that the myopic heuristic is likely sufficiently good in practical settings targeting high service levels.     

Detecting nuclear materials smuggling: performance evaluation of container inspection policies

In recent years, the United States, along with many other countries, has significantly increased its detection and defense mechanisms against terrorist attacks. A potential attack with a nuclear weapon, using nuclear materials smuggled into the country, has been identified as a particularly grave threat. The system for detecting illicit nuclear materials that is currently in place at U.S. ports of entry relies heavily on passive radiation detectors and a risk-scoring approach using the automated targeting system (ATS). In this article we analyze this existing inspection system and demonstrate its performance for several smuggling scenarios. We provide evidence that the current inspection system is inherently incapable of reliably detecting sophisticated smuggling attempts that use small quantities of well-shielded nuclear material. To counter the weaknesses of the current ATS-based inspection system, we propose two new inspection systems: the hardness control system (HCS) and the hybrid inspection system (HYB). The HCS uses radiography information to classify incoming containers based on their cargo content into "hard" or "soft" containers, which then go through different inspection treatment. The HYB combines the radiography information with the intelligence information from the ATS. We compare and contrast the relative performance of these two new inspection systems with the existing ATS-based system. Our studies indicate that the HCS and HYB policies outperform the ATS-based policy for a wide range of realistic smuggling scenarios. We also examine the impact of changes in adversary behavior on the new inspection systems and find that they effectively preclude strategic gaming behavior of the adversary.     

ASME Risk-Based Inservice Inspection and Testing: An Outlook to the Future

Significant research work has been completed in the development of risk-based inservice inspection (ISI) and testing (IST) technology for nuclear power plant applications through the ASME Center For Research and Technology Development. This paper provides technology that has been developed for these engineering applications. The technology includes risk-based ranking methods, beginning with the use of plant probabilistic risk assessment (PRA), for the determination of risk-significant and less risk-significant components for inspection and the determination of similar populations for pumps and valves for inservice testing. Decision analysis methods are outlined for developing ISI and IST programs. This methodology integrates nondestructive examination data, structural reliability/risk assessment results, PRA results, failure data, and expert opinion to evaluate the effectiveness of ISI programs. Similarly, decision analysis uses the output of failure mode and causes analysis in combination with data, expert opinion, and PRA results to evaluate the effectiveness of IST programs. Results of pilot applications of these ASME methods to actual nuclear plant systems and components are summarized. The results of this work are already being used to develop recommended changes in ISI and IST requirements by the ASME Section XI and the ASME Operation and Maintenance Code organizations. A perspective on Code and regulatory adoption is also outlined. Finally, the potential benefits to the nuclear industry in terms of safety, person-rem exposure, and costs are summarized.     

ON-LINE QUALITY MANAGEMENT: INTEGRATION OF PRODUCT INSPECTION AND PROCESS CONTROL

A growing recognition that quality management is an important factor in defining a firm's competitive position has led to renewed attention to this function and has resulted in implementation of elaborate systems for on-line quality control comprising product inspection and process control. Traditionally, these functions have been treated independently, with very little interaction. In this paper we examine, in detail, a scheme that integrates the two functions, and we demonstrate that such an approach can result in significant cost savings. The motivation for this work comes from our experience in a wafer fabrication facility that suggested that exchange of quality information between different stages of production could result in significant performance improvements. To illustrate this approach, we consider a specific environment characterized by a single-stage continuous production process whose status is monitored by an X̄ control chart. We assume that quality-related costs may be described as a function of the process output. This is analogous to Taguchi's quality loss function and may be interpreted as a generalization of conventional classification of process output as either acceptable or defective units. The integrative scheme essentially relies on utilization of the process status information (based on process control) in making product inspection decisions. For this system we derive a cost model and develop a solution procedure to determine optimal decision parameters. Limited computational results indicate that the scheme has significant potential for reducing quality-related costs.     

风险质检行为下的模糊生产-库存决策

本文研究在风险质检行为下需求与生产率具有模糊属性的由一个制造商与一个零售商构成的生产-库存问题。在假设制造商生产的产品存在质量缺陷,零售商在质检过程中存在质检风险的基础上,分别建立了需求模糊下的生产-库存总成本模型,需求与生产率模糊下的总成本模型,运用符号距离法进行了逆模糊化处理,将模糊化的生产-库存总成本转化为确定性成本。证明了两类情形下的总成本均是关于最优订购量与最优缺货量的联合凸函数。数值分析结果表明：随着期望缺陷率的增加,最优订购量增加,最优缺货量减少,最优成本增加,且最优成本增加的速度越来越快。一类质检风险增大引起总成本增加,二类质检风险增大引起总成本减少。最优订购策略对质检一类风险敏感,对质检二类风险不敏感。     

Income Maintenance and Labor Force Participation

The paper studies the optimal tax‐subsidy schedules in an economy where the only decision of the agents is to work, or not, with an application to the case of France. Given an income guarantee provided by the welfare state, the tax schedule that maximizes government revenue provides a benchmark, the Laffer bound, above which it is inefficient to tax. In fact, under mild conditions, a feasible allocation is second best optimal if and only if the associated taxes are lower than the Laffer bound. The only restriction that efficiency puts on the shape of the tax scheme is this upper Laffer bound. The Laffer tax scheme itself can be computed from the joint distribution of the agents' productivities and work opportunity costs. Depending on the economy, it can take widely different forms, and exhibit, for instance, negative marginal tax rates. After estimating the joint distribution of productivities and work opportunity costs on French data, I compute the Laffer bound for two subpopulations, single women and married women with two children or more. Quite surprisingly, the actual incentives to work appear to be very close to the bound.     

Robustness analysis methodology for multi-objective combinatorial optimization problems and application to project selection

Multi-objective combinatorial optimization (MOCO) problems, apart from being notoriously difficult and complex to solve in reasonable computational time, they also exhibit high levels of instability in their results in case of uncertainty, which often deviate far from optimality. In this work we propose an integrated methodology to measure and analyze the robustness of MOCO problems, and more specifically multi-objective integer programming ones, given the imperfect knowledge of their parameters. We propose measures to assess the robustness of each specific Pareto optimal solution (POS), as well as the robustness of the entire Pareto set (PS) as a whole. The approach builds upon a synergy of Monte Carlo simulation and multi-objective optimization, using the augmented ε-constraint method to generate the exact PS for the MOCO problems under examination. The usability of the proposed framework is justified through the identification of the most robust areas of the Pareto front, and the characterization of every POS with a robustness index. This index indicates a degree of certainty that a specific POS sustains its efficiency. The proposed methodology communicates in an illustrative way the robustness information to managers/decision makers and provides them with an additional supplement/tool to guide and support their final decision. Numerical examples focusing on a multi-objective knapsack problem and an application to academic capital budgeting problem for project selection, are provided to verify the efficacy and added value of the methodology.     

Process improvement by variance reduction for a single filling operation with rectifying inspection

Recently, there has been a great interest in the economics of quality control. Process mean targeting is one of the quality control problems which has attracted many researchers. Many papers have been written on finding the optimal mean setting of the process, but very few papers have considered the value of variance reduction. In this paper, we consider a single filling operation with rectifying inspection. We study the effect of the variance on the process performance. We analyse the cost saving which results from reduction in the process variance. We also provide a numerical example.     

DESIGNING INSPECTION STRATEGIES FOR UNCERTAIN ENVIRONMENTS

This paper considers the problems of designing inspection strategies for production systems terms in the presence of environmental uncertainty. The framework for determining information priorities to support inspection system planning is presented in the contaxt of a generic production system that encompasses the characteristics of many real-world serial production systems. The impact on the design decision of five key variables is considered: quality of producton processes, quality of inspection procedures, penalty cost for undetected defective units, relative cost of improving process vs. inspection, and shape of the cost functions for process and inspection enhancement. The framework for analysis involves varying factors over two or three orders of magnitude to determine optimal inspection strategies across a wide range of environments These results are used to compare design decisions made in the presence of environmental uncertainty using expected-opportunity-cost and minimization-of-maximum-opportunity-cost approaches. Design strategies are identified for situations ranging from complete lack of knowledge about the environment through increasing levels of information. Information-gathering priorities are established, and the impact on the design decision of this additional information is assayed.     

基于时间延迟理论的预防维修模型及案例研究

本文旨在解决设备维修决策过程中预防维修检查数据缺乏情况下如何确定出合理的维修间隔期问题。首先,通过预防维修技术经济分析,提出了有关维修间隔期和总的停机时间之间关系的预防维修模型。其次,根据时间延迟维修理论,利用故障记录数据和预防维修检查数据的估计值,建立了统计模型并用来计算维修间隔期内故障次数的期望值。计算机仿真检验证明统计模型正确后,采用最大拟然法估计有关参数,这些参数包括缺陷发生率、时间延迟分布、检查出缺陷的概率等。最后是案例分析,应用估计参数和预防维修模型,计算出最佳的维修间隔期。     

Exact closed-form solutions for “optimal inventory model for items with imperfect quality and shortage backordering”

Wee et al. [Optimal inventory model for items with imperfect quality and shortage backordering. Omega 2007;35(1):7–11] recently contributed an optimal inventory model for items with imperfect quality and shortage backordering. This article revisits their study and applies the well-known renewal-reward theorem to obtain a new expected net profit per unit time. We derive the exact closed-form solutions to determine the optimal lot size, backordering quantity and maximum expected net profit per unit time, specifically without differential calculus. We also solve the same model algebraically from another direction, which has been mentioned, but the process has not been finished yet. The problem parameter effects upon the optimal solutions are examined analytically and numerically.     

Scheduling Problems in a Practical Allocation Model

A parallel computational model is defined which addresses I/O contention,latency, and pipe-lined message passing between tasks allocated to differentprocessors. The model can be used for parallel task-allocation on either anetwork of workstations or on a multi-stage inter-connected parallel machine.To study performance bounds more closely, basic properties are developed forwhen the precedence constraints form a directed tree. It is shown that theproblem of optimally scheduling a directed one-level precedence tree on anunlimited number of identical processors in this model is NP-hard. Theproblem of scheduling a directed two-level precedence tree is also shown tobe NP-hard even when the system latency is zero. An approximation algorithm is then presented for scheduling directedone-level task trees on an unlimited number of processors with anapproximation ratio of 3. Simulation results show that this algorithm is, infact, much faster than its worst-case performance bound. Better simulationresults are obtained by improving our approximation algorithm usingheusistics. Restricting the problem to the case of equal task executiontimes, a linear-time algorithm is presented to find an optimal schedule.     

知识流动模式与非正式知识网络结构特征的滞后效应

探讨了知识的不同流动模式,并利用多主体仿真初步研究了其对非正式知识网络结构的影响。结果表明,从小世界网络主要结构特征角度,群体显/隐性知识比值存在一个最优区间,在此区间内,网络集聚系数的增长较网络平均最短路径长度要快得多;从演化角度,网络平均最短路径的下降较集聚系数存在滞后效应,当群体显/隐性知识比值落在此最优区间内时,该滞后效应更加明显。     

Bounding Optimal Expected Revenues for Assortment Optimization under Mixtures of Multinomial Logits

We consider assortment problems under a mixture of multinomial logit models. There is a fixed revenue associated with each product. There are multiple customer types. Customers of different types choose according to different multinomial logit models whose parameters depend on the type of the customer. The goal is to find a set of products to offer so as to maximize the expected revenue obtained over all customer types. This assortment problem under the multinomial logit model with multiple customer types is NP‐complete. Although there are heuristics to find good assortments, it is difficult to verify the optimality gap of the heuristics. In this study, motivated by the difficulty of finding optimal solutions and verifying the optimality gap of heuristics, we develop an approach to construct an upper bound on the optimal expected revenue. Our approach can quickly provide upper bounds and these upper bounds can be quite tight. In our computational experiments, over a large set of randomly generated problem instances, the upper bounds provided by our approach deviate from the optimal expected revenues by 0.15% on average and by less than one percent in the worst case. By using our upper bounds, we are able to verify the optimality gaps of a greedy heuristic accurately, even when optimal solutions are not available.     

The Retail Planning Problem Under Demand Uncertainty

We consider the retail planning problem in which the retailer chooses suppliers and determines the production, distribution, and inventory planning for products with uncertain demand to minimize total expected costs. This problem is often faced by large retail chains that carry private‐label products. We formulate this problem as a convex‐mixed integer program and show that it is strongly NP‐hard. We determine a lower bound by applying a Lagrangian relaxation and show that this bound outperforms the standard convex programming relaxation while being computationally efficient. We also establish a worst‐case error bound for the Lagrangian relaxation. We then develop heuristics to generate feasible solutions. Our computational results indicate that our convex programming heuristic yields feasible solutions that are close to optimal with an average suboptimality gap at 3.4%. We also develop managerial insights for practitioners who choose suppliers and make production, distribution, and inventory decisions in the supply chain.