Deciding with Thresholds: Importance Measures and Value of Information

Risk‐informed decision making is often accompanied by the specification of an acceptable level of risk. Such target level is compared against the value of a risk metric, usually computed through a probabilistic safety assessment model, to decide about the acceptability of a given design, the launch of a space mission, etc. Importance measures complement the decision process with information about the risk/safety significance of events. However, importance measures do not tell us whether the occurrence of an event can change the overarching decision. By linking value of information and importance measures for probabilistic risk assessment models, this work obtains a value‐of‐information‐based importance measure that brings together the risk metric, risk importance measures, and the risk threshold in one expression. The new importance measure does not impose additional computational burden because it can be calculated from our knowledge of the risk achievement and risk reduction worth, and complements the insights delivered by these importance measures. Several properties are discussed, including the joint decision worth of basic event groups. The application to the large loss of coolant accident sequence of the Advanced Test Reactor helps us in illustrating the risk analysis insights.     

Optimal Tracking and Testing of U.S. and Canadian Herds for BSE: A Value-of-Information (VOI) Approach

The U.S. Department of Agriculture (USDA) tests a subset of cattle slaughtered in the United States for bovine spongiform encephalitis (BSE). Knowing the origin of cattle (U.S. vs. Canadian) at testing could enable new testing or surveillance policies based on the origin of cattle testing positive. For example, if a Canadian cow tests positive for BSE, while no U.S. origin cattle do, the United States could subject Canadian cattle to more stringent testing. This article illustrates the application of a value-of-information (VOI) framework to quantify and compare potential economic costs to the United States of implementing tracking cattle origins to the costs of not doing so. The potential economic value of information from a tracking program is estimated to exceed its costs by more than five-fold if such information can reduce future losses in export and domestic markets and reduce future testing costs required to reassure or win back customers. Sensitivity analyses indicate that this conclusion is somewhat robust to many technical, scientific, and market uncertainties, including the current prevalence of BSE in the United States and/or Canada and the likely reactions of consumers to possible future discoveries of BSE in the United States and/or Canada. Indeed, the potential value of tracking information is great enough to justify locating and tracking Canadian cattle already in the United States when this can be done for a reasonable cost. If aggressive tracking and testing can win back lost exports, then the VOI of a tracking program may increase to over half a billion dollars per year.     

Integrating Software into PRA: A Test-Based Approach

Probabilistic risk assessment (PRA) is a methodology to assess the probability of failure or success of a system's operation. PRA has been proved to be a systematic, logical, and comprehensive technique for risk assessment. Software plays an increasing role in modern safety critical systems. A significant number of failures can be attributed to software failures. Unfortunately, current probabilistic risk assessment concentrates on representing the behavior of hardware systems, humans, and their contributions (to a limited extent) to risk but neglects the contributions of software due to a lack of understanding of software failure phenomena. It is thus imperative to consider and model the impact of software to reflect the risk in current and future systems. The objective of our research is to develop a methodology to account for the impact of software on system failure that can be used in the classical PRA analysis process. A test-based approach for integrating software into PRA is discussed in this article. This approach includes identification of software functions to be modeled in the PRA, modeling of the software contributions in the ESD, and fault tree. The approach also introduces the concepts of input tree and output tree and proposes a quantification strategy that uses a software safety testing technique. The method is applied to an example system, PACS.     

The Value of Improved National Exposure Information for Perchloroethylene (Perc): A Case Study for Dry Cleaners

Opportunities to improve our information about risk continue to arise and lead decision makers to indirectly address the issue of the value of improved information through resource allocation decisions. Statistical decision analysis techniques provide an analytical framework for valuing information explicitly in the context of regulatory decision making. This paper provides estimates of the value of improved national estimates of perchloroethylene (perc) exposure from U.S. dry cleaners in the context of EPA's recently promulgated National Emissions Standard for Hazardous Air Pollutants (NESHAP) with emphasis on exposure information. Consistent with the NESHAP decision, we relied on EPA's technology and economic assessments. In this first cut analysis, estimates of the exposures of workers, consumers of dry cleaning services, and the general public are probabilistically characterized to reflect uncertainty about exposure and potency. We consider the net benefits of the different control options by assessing the associated changes in the total annual population risks and valuing them in monetary terms, with no constraints placed on maximum individual risks. The results suggest that the expected value of perfect information (EVPI) about potency exceeds the EVPI about exposure. Sensitivity analyses demonstrate how the choices of the valuation parameters and distributions used to characterize uncertainty in the model affect the estimates of the value of information.     

Risk-Based Environmental Remediation: Bayesian Monte Carlo Analysis and the Expected Value of Sample Information

A methodology that simulates outcomes from future data collection programs, utilizes Bayesian Monte Carlo analysis to predict the resulting reduction in uncertainty in an environmental fate-and-transport model, and estimates the expected value of this reduction in uncertainty to a risk-based environmental remediation decision is illustrated considering polychlorinated biphenyl (PCB) sediment contamination and uptake by winter flounder in New Bedford Harbor, MA. The expected value of sample information (EVSI), the difference between the expected loss of the optimal decision based on the prior uncertainty analysis and the expected loss of the optimal decision from an updated information state, is calculated for several sampling plan. For the illustrative application we have posed, the EVSI for a sampling plan of two data points is $9.4 million, for five data points is $10.4 million, and for ten data points is $11.5 million. The EVSI for sampling plans involving larger numbers of data points is bounded by the expected value of perfect information, $15.6 million. A sensitivity analysis is conducted to examine the effect of selected model structure and parametric assumptions on the optimal decision and the EVSI. The optimal decision (total area to be dredged) is sensitive to the assumption of linearity between PCB sediment concentration and flounder PCB body burden and to the assumed relationship between area dredged and the harbor-wide average sediment PCB concentration; these assumptions also have a moderate impact on the computed EVSI. The EVSI is most sensitive to the unit cost of remediation and rather insensitive to the penalty cost associated with under-remediation.     

A value of information framework for assessing the trade-offs associated with uncertainty,duration, and cost of chemical toxicity testing

A number of investigators have explored the use of value of information (VOI) analysis to evaluate alternative information collection procedures in diverse decision-making contexts. This paper presents an analytic framework for determining the value of toxicity information used in risk-based decision making. The framework is specifically designed to explore the trade-offs between cost, timeliness, and uncertainty reduction associated with different toxicity-testing methodologies. The use of the proposed framework is demonstrated by two illustrative applications which, although based on simplified assumptions, show the insights that can be obtained through the use of VOI analysis. Specifically, these results suggest that timeliness of information collection has a significant impact on estimates of the VOI of chemical toxicity tests, even in the presence of smaller reductions in uncertainty. The framework introduces the concept of the expected value of delayed sample information, as an extension to the usual expected value of sample information, to accommodate the reductions in value resulting from delayed decision making. Our analysis also suggests that lower cost and higher throughput testing also may be beneficial in terms of public health benefits by increasing the number of substances that can be evaluated within a given budget. When the relative value is expressed in terms of return-on-investment per testing strategy, the differences can be substantial.     

Value of Information in Closed Loop Supply Chains

We explore the value of information (VOI) in the context of a firm that faces uncertainty with respect to demand, product return, and product recovery (yield). The operational decision of interest in matching supply with demand is the quantity of new product to order. Our objective is to evaluate the VOI from reducing one or more types of uncertainties, where value is measured by the reduction in total expected holding and shortage costs. We start with a single period model with normally distributed demands and returns, and restrict the analysis to the value of full information (VOFI) on one or more types of uncertainty. We develop estimators that are predictive of the value and sensitivity of (combinations of) different information types. We find that there is no dominance in value amongst the different types of information, and that there is an additional pay‐off from investing in more than one type. We then extend our analysis to the multi‐period case, where returns in a period are correlated with demands in the previous period, and study the value of partial information (VOPI) as well as full information. We demonstrate that our results from the single period model (adapted for VOPI) carry‐over exactly. Furthermore, a comparison with uniformly distributed demand and return show that these results are robust with respect to distributional assumptions.     

The Value of Environmental Information without Control of Subsequent Decisions

The standard value of information approach of decision analysis assumes that the individual or agency that collects the information is also in control of the subsequent decisions based on the information. We refer to this situation as the “value of information with control (VOI‐C).” This paradigm leads to powerful results, for example, that the value of information cannot be negative and that it is zero, when the information cannot change subsequent decisions. In many real world situations, however, the agency collecting the information is different from the one that makes the decision on the basis of that information. For example, an environmental research group may contemplate to fund a study that can affect an environmental policy decision that is made by a regulatory organization. In this two‐agency formulation, the information‐acquiring agency has to decide, whether an investment in research is worthwhile, while not being in control of the subsequent decision. We refer to this situation as “value of information without control (VOI‐NC).” In this article, we present a framework for the VOI‐NC and illustrate it with an example of a specific problem of determining the value of a research program on the health effects of power‐frequency electromagnetic fields. We first compare the VOI‐C approach with the VOI‐NC approach. We show that the VOI‐NC can be negative, but that with high‐quality research (low probabilities of errors of type I and II) it is positive. We also demonstrate, both in the example and in more general mathematical terms, that the VOI‐NC for environmental studies breaks down into a sum of the VOI‐NC due to the possible reduction of environmental impacts and the VOI‐NC due to the reduction of policy costs, with each component being positive for low environmental impacts and high‐quality research. Interesting results include that the environmental and cost components of the VOI‐NC move in opposite directions as a function of the probability of environmental impacts and that VOI‐NC can be positive, even though the probability of environmental impacts is zero or one.     

The Value of Information for Managing Retail Inventory Remotely

An important difference between both manufacturing and wholesaling vs. retail is the information available concerning inventory. Typically, far less information characterizes retail. Here, an extreme environment of information shortfall is examined. The environment is technically termed “unattended points of sale,” but colloquially called vending machines. Once inventory is loaded into a machine, information on demand and inventory level is not observed until the scheduled reloading date. Technological advances and business process changes have drawn attention to the value of information (VOI) in retail inventory in many venues. Moreover, technology is now available that allows unattended points of sale to report inventory information. Capturing the value of this information requires changes in current business practice. We demonstrate the value of capturing information analytically in an environment with restrictive demand assumptions. Experiments in an environment with realistic demand assumptions and parameter values show that the VOI depends greatly on operating characteristics and can range from negligible effects to increasing profitability 30% or more in actual practice.     

The Risk Criteria for Assessment of Temporary Changes in a Nuclear Power Plant

Risk criterion is a term that may distinguish between what is considered as an acceptable level of safety and what is not. One of the ways of determining quantitative risk criteria for temporary changes in a nuclear power plant considering probabilistic safety assessment is presented. Risk criteria are based on timing and on time duration of the change. Several examples of temporary changes in a nuclear power plant were examined to evaluate the criteria. Results show that it is possible to determine a set of risk criteria for temporary changes. Risk criteria can represent a standpoint for risk-informed decision making.     

The Value of Animal Test Information in Environmental Control Decisions

Value of information (VOI)analytic techniques are used to evaluate the benefit of performing animal bioassays to provide information about the cancer potency of specific chemical compounds. These tools allow the identification of the conditions in which the cost of reducing uncertainty about potency, by performing a subchronic or chronic bioassay, is justified by the benefit of having improved information for making control decisions. The decision analytic results are readily scaled to apply to a range of human contact rates (exposures)and a variety of control strategies. The sensitivity of results to uncertainty about animal to human extrapolation and the design of the bioassay is explored. An evaluation of the possible gains in general understanding about the mechanisms of carcinogenicity resulting from chronic bioassays is beyond the scope of this approach.     

基于ARMA（1，1）需求的供应链历史订单量信息价值的分析

牛鞭效应和供应链成本是目前供应链管理中值得关注的两个问题,本文通过分析ARMA(1,1)需求条件下的供应链历史订单量信息对牛鞭效应和制造商平均成本的影响,得出历史订单量信息的充分利用可以减小牛鞭效应、降低供应链成本.本文研究表明,如果充分利用历史订单量信息,则需求信息共享对供应链的贡献就不会有目前所认为的那么显著,其中的部分贡献可以由历史订单量信息来承担.因此,历史订单量信息的充分利用可以在一定程度上减少为寻求供应链需求信息共享而付出的投资费用.     

Stochastic Dominance: An Approach to Decision Making Under Risk

This paper introduces stochastic dominance as a technique to reduce the set of possible actions that a decision maker must consider in a decision problem under risk. The procedure usually does not choose an optimal action, but instead eliminates certain actions as unacceptable. Very little need be known about the decision maker's utility function. Two possible applications are presented: upgrading buildings to better withstand an earthquake; and choosing a site for a LNG facility.     

Multicriteria Decision Analysis: A Comprehensive Decision Approach for Management of Contaminated Sediments

Contaminated sediments and other sites present a difficult challenge for environmental decisionmakers. They are typically slow to recover or attenuate naturally, may involve multiple regulatory agencies and stakeholder groups, and engender multiple toxicological and ecotoxicological risks. While environmental decision-making strategies over the last several decades have evolved into increasingly more sophisticated, information-intensive, and complex approaches, there remains considerable dissatisfaction among business, industry, and the public with existing management strategies. Consequently, contaminated sediments and materials are the subject of intense technology development, such as beneficial reuse or in situ treatment. However, current decision analysis approaches, such as comparative risk assessment, benefit-cost analysis, and life cycle assessment, do not offer a comprehensive approach for incorporating the varied types of information and multiple stakeholder and public views that must typically be brought to bear when new technologies are under consideration. Alternatively, multicriteria decision analysis (MCDA) offers a scientifically sound decision framework for management of contaminated materials or sites where stakeholder participation is of crucial concern and criteria such as economics, environmental impacts, safety, and risk cannot be easily condensed into simple monetary expressions. This article brings together a multidisciplinary review of existing decision-making approaches at regulatory agencies in the United States and Europe and synthesizes state-of-the-art research in MCDA methods applicable to the assessment of contaminated sediment management technologies. Additionally, it tests an MCDA approach for coupling expert judgment and stakeholder values in a hypothetical contaminated sediments management case study wherein MCDA is used as a tool for testing stakeholder responses to and improving expert assessment of innovative contaminated sediments technologies.     

A Tiered Approach for Risk‐Benefit Assessment of Foods

Risk‐benefit analyses are introduced as a new paradigm for old problems. However, in many cases it is not always necessary to perform a full comprehensive and expensive quantitative risk‐benefit assessment to solve the problem, nor is it always possible, given the lack of required date. The choice to continue from a more qualitative to a full quantitative risk‐benefit assessment can be made using a tiered approach. In this article, this tiered approach for risk‐benefit assessment will be addressed using a decision tree. The tiered approach described uses the same four steps as the risk assessment paradigm: hazard and benefit identification, hazard and benefit characterization, exposure assessment, and risk‐benefit characterization, albeit in a different order. For the purpose of this approach, the exposure assessment has been moved upward and the dose‐response modeling (part of hazard and benefit characterization) is moved to a later stage. The decision tree includes several stop moments, depending on the situation where the gathered information is sufficient to answer the initial risk‐benefit question. The approach has been tested for two food ingredients. The decision tree presented in this article is useful to assist on a case‐by‐case basis a risk‐benefit assessor and policymaker in making informed choices when to stop or continue with a risk‐benefit assessment.     

非对称信息下供应链应急管理和信息价值研究

研究了非对称信息下供应链在突发事件下的应急管理和信息价值问题。当供应链生产计划已经完成后,突发事件发生并导致零售商所面临的市场需求规模以及供应商的生产成本同时发生突变,而且这些突变信息对于供应链成员而言是非对称的。分析了非对称信息对应急管理的影响以及相应的管理对策,发现非对称信息下的最优生产量不超过对称信息下的最优生产量,导致供应链系统收益减少并产生了信息价值,分析了非对称信息下供应链系统的信息价值规律以及影响因素。最后给出数值算例说明了信息在供应链中的重要价值,同时也说明了突发事件情况下实施应急管理的必要性和重要性。     

The Value of Information in Decision‐Analytic Modeling for Malaria Vector Control in East Africa

Decision analysis tools and mathematical modeling are increasingly emphasized in malaria control programs worldwide to improve resource allocation and address ongoing challenges with sustainability. However, such tools require substantial scientific evidence, which is costly to acquire. The value of information (VOI) has been proposed as a metric for gauging the value of reduced model uncertainty. We apply this concept to an evidenced‐based Malaria Decision Analysis Support Tool (MDAST) designed for application in East Africa. In developing MDAST, substantial gaps in the scientific evidence base were identified regarding insecticide resistance in malaria vector control and the effectiveness of alternative mosquito control approaches, including larviciding. We identify four entomological parameters in the model (two for insecticide resistance and two for larviciding) that involve high levels of uncertainty and to which outputs in MDAST are sensitive. We estimate and compare a VOI for combinations of these parameters in evaluating three policy alternatives relative to a status quo policy. We find having perfect information on the uncertain parameters could improve program net benefits by up to 5–21%, with the highest VOI associated with jointly eliminating uncertainty about reproductive speed of malaria‐transmitting mosquitoes and initial efficacy of larviciding at reducing the emergence of new adult mosquitoes. Future research on parameter uncertainty in decision analysis of malaria control policy should investigate the VOI with respect to other aspects of malaria transmission (such as antimalarial resistance), the costs of reducing uncertainty in these parameters, and the extent to which imperfect information about these parameters can improve payoffs.     

Equity in Social Risk: Some Empirical Observations

In societal risk analysis the equity of the distribution of risks is often an important consideration owing to the special nature of health risks. We empirically validate some assumptions about equity that have been discussed in the decision analytic literature. Our results show that the way fatalities are distributed throughout a society is considered along with the number of fatalities in evaluating alternative policies involving mortality risks. The concepts of ex ante equity and ex post equity are both shown to be important in judgments of fairness. We next present a decision model based on multiattribute preference theory incorporating the number of fatalities, as well as ex ante equity and ex post equity. When ex ante equity and ex post equity are positively weighted in this fair-risk model , options with more equal risk distributions are ranked higher. Next we empirically show that the distribution of benefits has an impact on judgments of fairness. The fair-risk model does not include information on the benefits distribution, so it would apply when benefits are distributed equally or when the decision maker wishes to not include benefits in the model. We briefly discuss how the notion of proportional equity can incorporate benefits into judgments of the fairness of risk distributions. We then include benefits in a more general model in which fair risk-benefit combinations are those that are exchange equitable. A key implication of this envy-free risk–benefit model is that an unequal distribution of risks may be preferred if it is accompanied by a compensatory differential in benefits consistent with peoples' preference tradeoffs between received benefits and assumed risks. Finally, we discuss how perceived deservedness may influence judgments about equity. We conclude with a discussion of the implications of research on alternative notions of equity for policy makers dealing with social risks.