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.     

Reducing Drinking Water Supply Chemical Contamination: Risks from Underground Storage Tanks

Drinking water supplies are at risk of contamination from a variety of physical, chemical, and biological sources. Ranked among these threats are hazardous material releases from leaking or improperly managed underground storage tanks located at municipal, commercial, and industrial facilities. To reduce human health and environmental risks associated with the subsurface storage of hazardous materials, government agencies have taken a variety of legislative and regulatory actions—which date back more than 25 years and include the establishment of rigorous equipment/technology/operational requirements and facility‐by‐facility inspection and enforcement programs. Given a history of more than 470,000 underground storage tank releases nationwide, the U.S. Environmental Protection Agency continues to report that 7,300 new leaks were found in federal fiscal year 2008, while nearly 103,000 old leaks remain to be cleaned up. In this article, we report on an alternate evidence‐based intervention approach for reducing potential releases from the storage of petroleum products (gasoline, diesel, kerosene, heating/fuel oil, and waste oil) in underground tanks at commercial facilities located in Rhode Island. The objective of this study was to evaluate whether a new regulatory model can be used as a cost‐effective alternative to traditional facility‐by‐facility inspection and enforcement programs for underground storage tanks. We conclude that the alternative model, using an emphasis on technical assistance tools, can produce measurable improvements in compliance performance, is a cost‐effective adjunct to traditional facility‐by‐facility inspection and enforcement programs, and has the potential to allow regulatory agencies to decrease their frequency of inspections among low risk facilities without sacrificing compliance performance or increasing public health risks.     

Modeling Finite‐Time Failure Probabilities in Risk Analysis Applications

In this article, we introduce a framework for analyzing the risk of systems failure based on estimating the failure probability. The latter is defined as the probability that a certain risk process, characterizing the operations of a system, reaches a possibly time‐dependent critical risk level within a finite‐time interval. Under general assumptions, we define two dually connected models for the risk process and derive explicit expressions for the failure probability and also the joint probability of the time of the occurrence of failure and the excess of the risk process over the risk level. We illustrate how these probabilistic models and results can be successfully applied in several important areas of risk analysis, among which are systems reliability, inventory management, flood control via dam management, infectious disease spread, and financial insolvency. Numerical illustrations are also presented.     

Quality Management in Multi‐Level Supply Chains with Outsourced Manufacturing

Outsourcing stretches supply chains longer with added contract manufacturers responsible for the manufacturing of parts and final products. Should a firm change its quality management approach as its supply chain becomes longer with outsourced manufacturing? This paper studies a brand owner's optimal choice between two commonly used quality management approaches: an inspection‐based approach and an external failure‐based approach, in two supply chains – a dyadic supply chain and a multi‐level supply chain where the brand owner outsources manufacturing to an independent contract manufacturer. Our study finds that the brand owner's optimal choice between the two quality management approaches could be opposite in the two supply chains. Specifically, we show that if agency costs exist between the contract manufacturer and the brand owner, the brand owner may prefer an inspection‐based approach in the multi‐level supply chain in contrast to preferring an external failure‐based approach in the dyadic supply chain. In particular, inspections can be effective for the brand owner to limit the manufacturer's profit by excluding defective finished products and components, which in turn reduce agency costs in the multi‐level supply chain. Hence, the efficiency of an inspection‐based approach relative to an external failure‐based approach can be higher in the multi‐level supply chain as compared to the dyadic one. Our findings suggest that firms should adjust to changes in supply chain structures and re‐evaluate the efficiencies of different quality management approaches accordingly.     

Optimal Inspection of Imports to Prevent Invasive Pest Introduction

The United States imports more than 1 billion live plants annually—an important and growing pathway for introduction of damaging nonnative invertebrates and pathogens. Inspection of imports is one safeguard for reducing pest introductions, but capacity constraints limit inspection effort. We develop an optimal sampling strategy to minimize the costs of pest introductions from trade by posing inspection as an acceptance sampling problem that incorporates key features of the decision context, including (i) simultaneous inspection of many heterogeneous lots, (ii) a lot‐specific sampling effort, (iii) a budget constraint that limits total inspection effort, (iv) inspection error, and (v) an objective of minimizing cost from accepted defective units. We derive a formula for expected number of accepted infested units (expected slippage) given lot size, sample size, infestation rate, and detection rate, and we formulate and analyze the inspector's optimization problem of allocating a sampling budget among incoming lots to minimize the cost of slippage. We conduct an empirical analysis of live plant inspection, including estimation of plant infestation rates from historical data, and find that inspections optimally target the largest lots with the highest plant infestation rates, leaving some lots unsampled. We also consider that USDA‐APHIS, which administers inspections, may want to continue inspecting all lots at a baseline level; we find that allocating any additional capacity, beyond a comprehensive baseline inspection, to the largest lots with the highest infestation rates allows inspectors to meet the dual goals of minimizing the costs of slippage and maintaining baseline sampling without substantial compromise.     

Risk‐Based Sampling: I Don't Want to Weight in Vain

Recently, there has been considerable interest in developing risk‐based sampling for food safety and animal and plant health for efficient allocation of inspection and surveillance resources. The problem of risk‐based sampling allocation presents a challenge similar to financial portfolio analysis. Markowitz (1952) laid the foundation for modern portfolio theory based on mean‐variance optimization. However, a persistent challenge in implementing portfolio optimization is the problem of estimation error, leading to false “optimal” portfolios and unstable asset weights. In some cases, portfolio diversification based on simple heuristics (e.g., equal allocation) has better out‐of‐sample performance than complex portfolio optimization methods due to estimation uncertainty. Even for portfolios with a modest number of assets, the estimation window required for true optimization may imply an implausibly long stationary period. The implications for risk‐based sampling are illustrated by a simple simulation model of lot inspection for a small, heterogeneous group of producers.     

Adversarial Risk Analysis with Incomplete Information: A Level‐k Approach

This article proposes, develops, and illustrates the application of level‐k game theory to adversarial risk analysis. Level‐k reasoning, which assumes that players play strategically but have bounded rationality, is useful for operationalizing a Bayesian approach to adversarial risk analysis. It can be applied in a broad class of settings, including settings with asynchronous play and partial but incomplete revelation of early moves. Its computational and elicitation requirements are modest. We illustrate the approach with an application to a simple defend‐attack model in which the defender's countermeasures are revealed with a probability less than one to the attacker before he decides on how or whether to attack.     

Dynamic Impacts of a Catastrophic Production Event: The Foot‐and‐Mouth Disease Case

In foot‐and‐mouth disease (FMD) free countries, the occurrence of an FMD outbreak is a rare event with potentially large economic losses. We explore the dynamic effects of an FMD outbreak on market variables and economic surplus taking into account the largely neglected issue of farm bankruptcy. Simulations are performed on a stylized agricultural economy, which is a net exporter before the outbreak. We find complex dynamic market effects when the farm credit market suffers from information imperfections leading to farm closure. Welfare effects are also dramatically altered. Domestic consumers may lose in the long run from an FMD outbreak because domestic supply contracts. On the other hand, farmers able to resist this event may ultimately gain. Our analysis also shows that these effects are not monotone, making any efficient policy response to this catastrophic event quite challenging.     

Inspecting a Vital Component Needed upon Emergency

We consider a stochastically failing component that will be needed at a random future time when an emergency occurs. If the component is not operational at that time, the system incurs a large penalty, which we want to avoid through inspections and replacements. We propose a model and solution algorithm for finding an inspection policy that minimizes the infinite horizon discounted expected penalty, replacement, and inspection costs. We also discuss structural properties of the solution, as well as insights based on numerical results.     

A Stochastic Model to Assess the Effect of Meat Inspection Practices on the Contamination of the Pig Carcasses

The objective of meat inspection is to promote animal and public health by preventing, detecting, and controlling hazards originating from animals. With the improvements of sanitary level in pig herds, the hazards profile has shifted and the inspection procedures no longer target major foodborne pathogens (i.e., not risk based). Additionally, carcass manipulations performed when searching for macroscopic lesions can lead to cross‐contamination. We therefore developed a stochastic model to quantitatively describe cross‐contamination when consecutive carcasses are submitted to classic inspection procedures. The microbial hazard used to illustrate the model was Salmonella, the data set was obtained from Brazilian slaughterhouses, and some simplifying assumptions were made. The model predicted that due to cross‐contamination during inspection, the prevalence of contaminated carcass surfaces increased from 1.2% to 95.7%, whereas the mean contamination on contaminated surfaces decreased from 1 logCFU/cm² to ?0.87 logCFU/cm², and the standard deviations decreased from 0.65 to 0.19. These results are explained by the fact that, due to carcass manipulations with hands, knives, and hooks, including the cutting of contaminated lymph nodes, Salmonella is transferred to previously uncontaminated carcasses, but in small quantities. These small quantities can easily go undetected during sampling. Sensitivity analyses gave insight into the model performance and showed that the touching and cutting of lymph nodes during inspection can be an important source of carcass contamination. The model can serve as a tool to support discussions on the modernization of pig carcass inspection.     

Structure of Uncertainty and Decision Making: An Experimental Investigation*

Decisions in the real world usually involve imprecise information or uncertainty about the precesses by which outcomes may be determined. This research reports the results of a laboratory experiment which examined whether the structure of uncertainty, namely, both the center and the range of the probability distribution describing the uncertainty, is an important determinant of choice. Specifically, it examines how the uncertainty of audit by the Internal Revenue Service of income tax returns affects taxpayers' decisions about intentional noncompliance. The context is relevant as almost nothing is known about how taxpayers assess detection risks using the probability information they have. The study focuses on intentional noncompliance. The factors affecting it are distinct and separate from those affecting unintentional noncompliance. Other factors that affect intentional tax noncompliance, such as risk, tax rates, and penalty rates, were controlled in the experiment. It was hypothesized that the lower the mean and the lesser the range (ambiguity) of the perceived audit probability, the greater the international noncompliance. As hypothesized, the analysis indicates that both the mean and the range of the perceived audit probability rate affect intentional noncompliance, though the effect of ambiguity is greater at a relatively higher level of mean. This result suggests that the strength of the information describing an uncertain event is captured better by both the mean and the range of the uncertainty than either of those components singly.     

Optimal Mission Abort Policy for Systems Operating in a Random Environment

Many real‐world critical systems, e.g., aircrafts, manned space flight systems, and submarines, utilize mission aborts to enhance their survivability. Specifically, a mission can be aborted when a certain malfunction condition is met and a rescue or recovery procedure is then initiated. For systems exposed to external impacts, the malfunctions are often caused by the consequences of these impacts. Traditional system reliability models typically cannot address a possibility of mission aborts. Therefore, in this article, we first develop the corresponding methodology for modeling and evaluation of the mission success probability and survivability of systems experiencing both internal failures and external shocks. We consider a policy when a mission is aborted and a rescue procedure is activated upon occurrence of the m th shock. We demonstrate the tradeoff between the system survivability and the mission success probability that should be balanced by the proper choice of the decision variable m . A detailed illustrative example of a mission performed by an unmanned aerial vehicle is presented.     

Sample Size Allocation for Food Item Radiation Monitoring and Safety Inspection

The objective of this study is to identify a procedure for determining sample size allocation for food radiation inspections of more than one food item to minimize the potential risk to consumers of internal radiation exposure. We consider a simplified case of food radiation monitoring and safety inspection in which a risk manager is required to monitor two food items, milk and spinach, in a contaminated area. Three protocols for food radiation monitoring with different sample size allocations were assessed by simulating random sampling and inspections of milk and spinach in a conceptual monitoring site. Distributions of ¹³¹I and radiocesium concentrations were determined in reference to ¹³¹I and radiocesium concentrations detected in Fukushima prefecture, Japan, for March and April 2011. The results of the simulations suggested that a protocol that allocates sample size to milk and spinach based on the estimation of ¹³¹I and radiocesium concentrations using the apparent decay rate constants sequentially calculated from past monitoring data can most effectively minimize the potential risks of internal radiation exposure.     

Inferring an Augmented Bayesian Network to Confront a Complex Quantitative Microbial Risk Assessment Model with Durability Studies: Application to Bacillus Cereus on a Courgette Purée Production Chain

The Monte Carlo (MC) simulation approach is traditionally used in food safety risk assessment to study quantitative microbial risk assessment (QMRA) models. When experimental data are available, performing Bayesian inference is a good alternative approach that allows backward calculation in a stochastic QMRA model to update the experts’ knowledge about the microbial dynamics of a given food‐borne pathogen. In this article, we propose a complex example where Bayesian inference is applied to a high‐dimensional second‐order QMRA model. The case study is a farm‐to‐fork QMRA model considering genetic diversity of Bacillus cereus in a cooked, pasteurized, and chilled courgette purée. Experimental data are Bacillus cereus concentrations measured in packages of courgette purées stored at different time‐temperature profiles after pasteurization. To perform a Bayesian inference, we first built an augmented Bayesian network by linking a second‐order QMRA model to the available contamination data. We then ran a Markov chain Monte Carlo (MCMC) algorithm to update all the unknown concentrations and unknown quantities of the augmented model. About 25% of the prior beliefs are strongly updated, leading to a reduction in uncertainty. Some updates interestingly question the QMRA model.     

Impact of Acquired Immunity and Dose‐Dependent Probability of Illness on Quantitative Microbial Risk Assessment

Dose‐response models in microbial risk assessment consider two steps in the process ultimately leading to illness: from exposure to (asymptomatic) infection, and from infection to (symptomatic) illness. Most data and theoretical approaches are available for the exposure‐infection step; the infection‐illness step has received less attention. Furthermore, current microbial risk assessment models do not account for acquired immunity. These limitations may lead to biased risk estimates. We consider effects of both dose dependency of the conditional probability of illness given infection, and acquired immunity to risk estimates, and demonstrate their effects in a case study on exposure to Campylobacter jejuni. To account for acquired immunity in risk estimates, an inflation factor is proposed. The inflation factor depends on the relative rates of loss of protection over exposure. The conditional probability of illness given infection is based on a previously published model, accounting for the within‐host dynamics of illness. We find that at low (average) doses, the infection‐illness model has the greatest impact on risk estimates, whereas at higher (average) doses and/or increased exposure frequencies, the acquired immunity model has the greatest impact. The proposed models are strongly nonlinear, and reducing exposure is not expected to lead to a proportional decrease in risk and, under certain conditions, may even lead to an increase in risk. The impact of different dose‐response models on risk estimates is particularly pronounced when introducing heterogeneity in the population exposure distribution.     

A Probabilistic Transmission Model to Assess Infection Risk from Mycobacterium Tuberculosis in Commercial Passenger Trains

The objective of this article is to characterize the risk of infection from airborne Mycobacterium tuberculosis bacilli exposure in commercial passenger trains based on a risk‐based probabilistic transmission modeling. We investigated the tuberculosis (TB) infection risks among commercial passengers by inhaled aerosol M. tuberculosis bacilli and quantify the patterns of TB transmission in Taiwan High Speed Rail (THSR). A deterministic Wells‐Riley mathematical model was used to account for the probability of infection risk from M. tuberculosis bacilli by linking the cough‐generated aerosol M. tuberculosis bacilli concentration and particle size distribution. We found that (i) the quantum generation rate of TB was estimated with a lognormal distribution of geometric mean (GM) of 54.29 and geometric standard deviation (GSD) of 3.05 quantum/h at particle size ≤ 5 μm and (ii) the basic reproduction numbers (R₀) were estimated to be 0.69 (0.06–6.79), 2.82 (0.32–20.97), and 2.31 (0.25–17.69) for business, standard, and nonreserved cabins, respectively. The results indicate that commercial passengers taking standard and nonreserved cabins had higher transmission risk than those in business cabins based on conservatism. Our results also reveal that even a brief exposure, as in the bronchoscopy cases, can also result in a transmission when the quantum generation rate is high. This study could contribute to a better understanding of the dynamics of TB transmission in commercial passenger trains by assessing the relationship between TB infectiousness, passenger mobility, and key model parameters such as seat occupancy, ventilation rate, and exposure duration.     

Risk‐Based Probabilistic Approach to Assess the Impact of False Mussel Invasions on Farmed Hard Clams

The purpose of this article is to provide a risk‐based predictive model to assess the impact of false mussel Mytilopsis sallei invasions on hard clam Meretrix lusoria farms in the southwestern region of Taiwan. The actual spread of invasive false mussel was predicted by using analytical models based on advection‐diffusion and gravity models. The proportion of hard clam colonized and infestation by false mussel were used to characterize risk estimates. A mortality model was parameterized to assess hard clam mortality risk characterized by false mussel density and infestation intensity. The published data were reanalyzed to parameterize a predictive threshold model described by a cumulative Weibull distribution function that can be used to estimate the exceeding thresholds of proportion of hard clam colonized and infestation. Results indicated that the infestation thresholds were 2–17 ind clam^?1 for adult hard clams, whereas 4 ind clam^?1 for nursery hard clams. The average colonization thresholds were estimated to be 81–89% for cultivated and nursery hard clam farms, respectively. Our results indicated that false mussel density and infestation, which caused 50% hard clam mortality, were estimated to be 2,812 ind m^?2 and 31 ind clam^?1, respectively. This study further indicated that hard clam farms that are close to the coastal area have at least 50% probability for 43% mortality caused by infestation. This study highlighted that a probabilistic risk‐based framework characterized by probability distributions and risk curves is an effective representation of scientific assessments for farmed hard clam in response to the nonnative false mussel invasion.     

General Probability‐Time Tradeoff and Intertemporal Risk‐Value Model

This article proposes an intertemporal risk‐value (IRV) model that integrates probability‐time tradeoff, time‐value tradeoff, and risk‐value tradeoff into one unified framework. We obtain a general probability‐time tradeoff, which yields a formal representation form to reflect the psychological distance of a decisionmaker in evaluating a temporal lottery. This intuition of probability‐time tradeoff is supported by robust empirical findings as well as by psychological theory. Through an explicit formalization of probability‐time tradeoff, an IRV model taking into account three fundamental dimensions, namely, value, probability, and time, is established. The object of evaluation in our framework is a complex lottery. We also give some insights into the structure of the IRV model using a wildcatter problem.     

Risk and Planning in Agriculture: How Planning on Dairy Farms in Ireland Is Affected by Farmers’ Regulatory Focus

This article examines how planning on dairy farms is affected by farmers' motivation. It argues that farmers' choice of expansion strategies can be specified in terms of risk decision making and understood as either prevention‐focused or promotion‐focused motivation. This relationship was empirically examined using mediated regression analyses where promotion/prevention focus was the independent variable and its effect on total milk production via planned expansion strategies was examined. The results indicate that promotion focus among farmers has an indirect effect on farm expansion via planning strategies that incur greater risk to the farm enterprise. Regulatory focus on the part of farmers has an influence on farmers' planning and risk management activities and must be accounted for in the design and implementation of policy and risk management tools in agriculture.