Environ. Sci. Technol. 2010, 44, 8704–8711
Application of Stochastic Multiattribute Analysis to Assessment of Single Walled Carbon Nanotube Synthesis Processes L A U R E C A N I S , † I G O R L I N K O V , * ,† A N D THOMAS P. SEAGER‡ U.S. Army Corps of Engineers, Engineer Research and Development Center, 696 Virginia Road, Concord, Massachusetts 01742, United States, and, Center for Earth Systems Engineering & Management, School of Sustainable Engineering and the Built Environment, Ira A. Fulton Schools of Engineering, Arizona State University, Tempe, Arizona 85287, United States
Received June 23, 2010. Revised manuscript received September 16, 2010. Accepted September 27, 2010.
The unprecedented uncertainty associated with engineered nanomaterials greatly expands the need for research regarding their potential environmental consequences. However, decisionmakers such as regulatory agencies, product developers, or other nanotechnology stakeholders may not find the results of such research directly informative of decisions intended to mitigate environmental risks. To help interpret research findings and prioritize new research needs, there is an acute need for structured decision-analytic aids that are operable in a context of extraordinary uncertainty. Whereas existing stochastic decision-analytic techniques explore uncertainty only in decisionmaker preference information, this paper extends model uncertainty to technology performance. As an illustrative example, the framework is applied to the case of single-wall carbon nanotubes. Four different synthesis processes (arc, high pressure carbon monoxide, chemical vapor deposition, and laser) are compared based on five salient performance criteria. A probabilistic rank ordering of preferred processes is determined using outranking normalization and a linearweighted sum for different weighting scenarios including completely unknown weights and four fixed-weight sets representing hypothetical stakeholder views. No single process pathway dominates under all weight scenarios, but it is likely that some inferior process technologies could be identified as low priorities for further research.
1. Introduction Engineered nanomaterials present a serious challenge to regulators, product developers, consumers, or other groups concerned about potential risks associated with nanomaterial production and use. The pace of innovation with regard to new materials far outstrips the pace of environmental, health, and safety research (1). As a result, there is considerable * Corresponding author phone: (978)318-8197; e-mail: igor.linkov@ usace.army.mil. † U.S. Army Corps of Engineers. ‡ Arizona State University. 8704
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concern that nanotechnology workers, consumers, or ecological receptors could be exposed prior to implementation of risk management alternatives or mitigation strategies. To date, environmental health and safety research regarding nanotechnology has focused primarily on hazard identification, exposure, and dose-response effects associated with nanomaterials in the environment and work place (2). For example, the USEPA (3) research strategy explicitly calls for characterization of health risks at all nanomaterial life-cycle stages, including raw material production, manufacturing, use, and end-of-life. Nonetheless, it is now widely accepted that the unprecedented variability and uncertainty associated with engineered nanomaterials presents a serious challenge to traditional models of risk assessment (4). Most obviously, there is a paucity of data with regard to the fate of nanomaterials in the environment, the response of human or ecological receptors to exposure, as well as the energy and material requirements regarding production of nanoenabled components. In fact, the data requirements regarding nanomaterials may be so great that the standards of precision or certainty expected in a conventional materials context may never be achieved in the case of many economically significant nanomaterials. Consequently, there is an acute need to more closely relate nanotechnology risk research to the needs of decision-makers operating in a context of extraordinary uncertainty (4, 5). Historically, research efforts regarding conventional materials of environmental interest may have been focused on occupational, consumer, or disposal settings separately. However, interest in nanomaterials comes at a time when the value of a more comprehensive approach that includes all life-cycle stages is now well recognized (6). To this end, the Environmental Protection Agency (EPA) calls for nanomaterial risk research to be informed by life-cycle thinking, if not life cycle assessment (LCA), per se. The potential synergies achievable via integration of risk assessment (RA) and LCA have been elucidated previously (7-10), but the relationship of these tools to structured decision processes has only rarely been the subject of detailed study. Whereas RA and LCA are methods of creating data, but limited in their capacity to interpret or prioritize information for decision makers, multicriteria decision analysis (MCDA) complements RA and LCA by providing the necessary decision-analytical framework (11-13). Similarly, where MCDA is perceived as practical tool, but vulnerable to subjective influences, RA and LCA are grounded in scientific objectivity. Taken in isolation, any of the three analytic approaches is insufficient. However, taken collectively they can stand many of the criticisms that have been directed at each singular approach. Previous work on life-cycle impact assessment in the context of decision analysis has focused on biofuels and the uncertainty inherent in subjective, value-laden aspects of weighing the trade-offs among different technological alternatives (12). However, in this previous approach, only the uncertainty in environmental impact criteria weightings (and not the emissions inventory) is explored stochastically. In the case of nanotechnology, extraordinarily high levels of uncertainty necessitate novel decision-analytic structures that are more robust in handling different types of uncertainty (14). This paper expands upon the Stochastic Multi-Attribute Analysis for Life-Cycle Impact Assessment (SMAA-LCIA) method described previously (12) by modeling uncertainty in both technology performance assessments and stakeholder or decision-maker priorities. 10.1021/es102117k
2010 American Chemical Society
Published on Web 10/22/2010
To illustrate the proposed approach, a comparative analysis of processes for synthesis of purified single walled carbon nanotubes (SWCNT) is presented. The goal is to identify the manufacturing technology that maximizes manufacturing efficiencies and minimizes life cycle environmental risks. Four widely used technological approaches to the synthesis of SWCNT are studied, including laser vaporization, arc discharge, chemical vapor deposition, and high pressure carbon monoxide. Each process is expected to have a unique life cycle environmental profile and end-use functionality (14-16). However, there is little or no information regarding the life-cycle environmental implications or health risks of SWCNT in specific applications. Given these uncertainties in risk assessment and LCA with regard to SWCNT, prioritizing an environmental research agenda is a considerable challenge. From a risk analytic perspective, study of the functional characteristics and biological mechanisms that explain toxicity may seem to be a high priority. Alternatively, the life cycle perspective may focus on improving material and energy consumptions in SWCNT manufacturing processes, thereby reducing emissions of carbon dioxide, acid rain precursors, or fine particles to the atmosphere per mass of SWCNT produced. Both the risk assessment and LCA perspectives might also prioritize characterization of source term scenarios for specific applications in use or disposal stages of the life-cycle (17). While the case for any of these investigative threads may seem compelling on a scientific basis, in relation to a specific decision problem, any one of them is unlikely to result in specific policy, design, or risk management prescriptions. This paper represents an incremental step toward remedying that deficiency.
2. Methods and Case Study The case study discussed in this paper relates to a product development problem of selecting the most advantageous technology for synthesizing and purifying SWCNT. No single criterion, such as lowest cost or greatest productivity, is likely to be decisive. Typically, multiple criteria are brought to bear in problems of product development or manufacturing technology selection that include cost, efficiency, environmental, and/or health risks. Therefore, MCDA represents an appropriate structure for informing the decision problem. The general approach involves several steps: defining the alternatives, selecting the criteria, eliciting criteria weights, and scoring alternatives to result in a final preference ordering (18). However, traditional MCDA approaches do little to facilitate exploration of the eventual rank ordering sensitivity to critical uncertainties, such as technology performance or criteria weightings. Monte Carlo Analysis (MCA) has previously been used to study the economy of mitigation measures in a nanomanufacturing occupational health setting without the benefit of MCDA (19). We present a novel application of MCDA that samples multiple uncertainties simultaneously and presents the final results in probabilistic, multicriteria terms. 2.1. Alternatives Description. Four different feasible process technologies have been identified: High Pressure Carbon Monoxide (HiPCO), arc discharge (Arc), chemical vapor deposition (CVD), and laser vaporization (Laser). Each of these processes involves production of a carbonaceous vapor, condensation of carbon in the presence of a metal catalyst to form SWCNT and amorphous carbon, and subsequent purification steps. The material and energy yields of each process (and thus, the life-cycle environmental consequences) vary greatly, as do the cost, purity, and characteristic qualities (including, perhaps, toxicity) of the different tubes. That is, even though each product may be classified as SWCNT, the fact that they are produced in different ways creates a high degree of variability (e.g., in
physical and electrochemical properties and in life-cycle environmental impacts) even when the tubes are purified. 2.2. Criteria Definition. In LCA, it is essential to understand the economic functionality of the material in question. Unlike risk assessment, which is concerned primarily with calculation of an absolute probability of harm (and the severity of that harm), LCA normalizes emissions (i.e., source term) data relative to the functional unit so as to facilitate comparison of multiple technological pathways for satisfying the economic demand. SWCNT have a myriad of real or imagined applications. One of these is as a conductive additive or electrode support in advanced Li-ion batteries plug-in electric hybrid vehicles (20). The requisite performance characteristics of the SWCNT themselves in this case would include high specific thermal and electrical conductivity (relative to mass and/or volume). From a risk perspective, a type of SWCNT that is particularly problematic in manufacture (e.g., in terms of manufacturing yields, safety concerns, or quality expectations) may be disadvantageous. However, from a life-cycle perspective, the same SWCNT could be advantageous, if enhanced functionality (e.g., increased power or energy density) results in environmental savings in the use phase that justify additional impacts during manufacture. To select a preferred material processing pathway, product developers must formulate criteria that represent the most important goals, constraints, or other measurable consequences of the decision in this application. While these criteria may be industry or application specific, there are several that are mentioned often enough in science or environmental management literature that they may be selected here for illustrative purposes. Namely, energy intensity and materials (or atom) efficiency are typically of interest to process engineers (21). An aggregated life-cycle impact assessment score (e.g., carbon footprint) may be of interest to product managers, customers, or dealer/retail networks, and cost is typically a consideration throughout the supply chain. Lastly, the toxicological health risks of the SWCNT themselves may be of considerable importance to product developers and/ or regulators (22, 23). Assessment of the technological alternatives in relation to these criteria may be problematic, due to a lack of information. It is unlikely that these criteria are entirely independent, even though the units, boundaries of analysis, and analytic methods for each criterion may be different. Ideally, the number of criteria should be reduced to the point that any further aggregation would result in loss of some incommensurate attribute that is important to at least one public or stakeholder group. 2.3. Assessment of Alternatives. The approach selected here is an adaptation of SMAA-LCIA that has previously been applied to comparative assessment of biofuel technologies, in which alternatives are compared pairwise on individual performance criteria using an outranking algorithm and criteria weights are explored stochastically (12). The novel method differs from the previous paper principally in the treatment of uncertainty, which is of considerable importance to issues of nanomaterials. Previous decision analytic algorithms rely on point estimates of technology performance, in which uncertainty in performance is represented solely as indifference thresholds - i.e., a range in which no preference can be expressed via pairwise comparison due to a lack of precision in performance estimates compared to decisionmaker sensitivity. The current approach adopts a more rigorous view of performance uncertainty, in which estimates are represented either as probability distributions or ordinal rankings (such as “High”, “Medium”, or “Low”). The additional flexibility of the current approach allows explicit exploration of the sensitivity of final rank-ordering of alternatives to increased confidence in performance assessment (represented as a narrowing of uncertainty in the VOL. 44, NO. 22, 2010 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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TABLE 1. Performance Assessments of Each Alternative with Respect to Decision Criteria, Represented As Frequency Plots
probability distribution). This is an advantage that will be important in later studies focused on prioritization of research programs from a value-of-information perspective. Wherever available, assessment data incorporated in this study are culled from literature sources. However, existing reports on process yields or efficiencies are few, uncertainty information is entirely absent, and information on health effects in a real-world setting may amount to little more than speculation. Therefore, performance assessments are represented in different ways, meaning that the results are subject to revision as new data become available. Table 1 depicts probabilistic performance assessments for each of the four different SWCNT synthesis pathways. Data for energy intensity and material yields for Laser is estimated from Ganter et al. (24), where a value of 0.13-0.19 GWh/kg (on a cradle-to-gate basis) is reported. Total cradeto-gate energy for HiPCO, CVD, and Arc is extrapolated from point estimates for electricity consumption in Healy et al. (15), based upon the assumption that the fraction of total embodied energy that is due to electricity consumption in these processes is similar to the 60%-85% reported in Ganter et al. (24). Material yields are reported in the literature solely as point estimates. Therefore, we assign uncertainty intervals in a triangular distribution that are comparable to the uncertainty reported in Ganter et al. (24) for energy - i.e., between 50% and 150% of the point estimate, which is taken as the mode. (When values in the middle of a range are expected to be more likely than the extremes, a triangular distribution is often considered adequate approximation (25)). For HiPCO, CVD, and Arc, Healy et al. (15) report both synthesis reaction yield and purification yields, which are multiplied together to result in a point estimate for total process yield. Data with regard to life cycle impact assessment (LCIA) is typically reported as a normalized, weighted aggregation of the entire inventory of chemical releases to the environment that has been characterized with respect to several different impact categories such as global warming, airborne particulates, stratospheric ozone depletion, eutrophication, acid rain, human health, and others. The focus in LCIA is ordinarily conventional chemical releases, such as carbon dioxide produced in the generation of electricity consumed 8706
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in the synthesis of SWCNT, rather than the environmental properties of nanomaterials themselves (for which no impact data exist in standard life-cycle inventory or impact databases). Impact results may be reported in a dimensionless, arbitrary scale such as “ecopoints” (or some other relative ranking system) that facilitates comparison of different technologies or allows prioritization of different aspects of the life cycle for improvement. Data in Table 1 for HiPCO, CVD, and Arc are approximated as triangular distributions ranging from 50% to 150% of point estimates reported in Healy et al. (15). LCIA estimates for Laser are unavailable and are therefore modeled as a uniform distribution between the low and high values reported for the other processes. The cost of SWCNT produced from different sources is highly variable and dropping rapidly as commercial synthesis processes evolve from small-scale, low-rate batch processes to larger-scale, high rate, continuous processes. Typically, HiPCO produced tubes are available comparatively inexpensively and can even be purchased through Internet-based retailers (such as www.cheaptubes.com). However, purified SWCNT that are sorted for specific chirality (i.e., metallic or semiconducting) cost about $500,000 per gram. Typical pricing for acid-purified SWCNT (without regard to chirality) is more likely several hundred dollars a gram, with commercial producers targeting future costs as low at $100 per kilogram. Healy et al. (15) report point estimates of $485, $1706, and $1906 per gram for HipCO, CVD, and Arc, respectively. Although price data are subject to revision based upon changing markets, 50% and 150% uncertainty intervals have been applied to create triangular distributions for the purposes of this study. As of this writing, laser-produced tubes are not commercially available. Nonetheless, the NanoPower Research Lab at Rochester Institute of Technology has previously bartered purified laser-produced SWCNT at an exchange rate equivalent to $1000 per gram (26). To represent this uncertainty for the purposes of this study, the cost of laser-produced tubes has been represented as a uniform distribution from the lower to upper bound represented by all other alternatives. The health risks associated with SWCNT are extraordinarily uncertain, especially in real environments, where the state or fate of the SWCNT in the body is unknown. For
FIGURE 1. Hypothetical stakeholder views are represented as contrasting weight vectors. example, agglomerated or bundled tubes may have different toxicological effects, depending on their fate in the environment and the exposure pathways particular to a specific receptor. Research to date has focused primarily on identifying hazards (e.g., mesothelioma in lung tissues) or characterizing dose-response relationships. However, there is currently no quantitative scale (such as a minimum no effect dosage or maximum exposure limit) on which to construct a comparative basis for assessment of relative health risks of SWCNT produced from different processes. Therefore, for the purposes of illustrating how the MCDA framework presented is capable of working with semiquantitative data, health risks are represented on an ordinal scale corresponding to high, medium, or low. Without data regarding comparative health risks, all alternatives are assessed equal probabilities of being at low, medium, or high initially. 2.4. Normalization and Exploration of Weights. Aggregation of incommensurate decision criteria requires normalization of data into uniform or dimensionless units that can subsequently be compared based on minimization or maximization preferences. In LCA, if normalization occurs at all, the standard practice is to employ an external normalization that divides characterized midpoint inventories associated with a particular process by the total inventory of emissions extant in a geographic region (e.g., national or European Union data) or industry. However, in this case, national or industry data are both unavailable and inappropriate. Moreoever, in problems of technology comparison, external normalization has previously been found to potentially mask aspects of a decision that may be important (12). Therefore, we employ an internal normalization algorithm known as outranking, in which performance assessments for different alternatives are compared pairwise based on decision-maker maximization or minimization preferences.
Because there is little or no public information on appropriate weight sets with regard to nanomaterials, it is reasonable to explore all feasible weights sets stochastically, thereby resulting in a probabilistic rank-ordering depicting the likelihood that any given alternative is preferred (12, 27, 29). Such an approach can be used to screen underperforming alternatives, prioritize high-ranking alternatives for further research, or to facilitate further valueelicitation from decision-makers and stakeholders. Nevertheless, we may hypothesize that stakeholder groups exist that can narrow their preferred weight set in accordance with subjective values representative of decision goals. Therefore, we also construct four hypothetical weighting scenarios for the purpose of exploring the sensitivity of the rank ordering results to different value systems. Figure 1 depicts the weight vectors that describe each scenario as a bar chart. Manufacturers are modeled as emphasizing cost, material and energy process efficiency, and health risks -- but not life-cycle considerations. End Users are modeled as agreeing with manufacturers on cost, but placing greater emphasis on health risks and life-cycle impacts, without separate consideration of process efficiency. (It should be noted that these are not fully independent assessments. It is entirely possible that alternatives with high efficiency may also have advantageous LCIA scores, but it is not necessarily the case.) Environmentalists are assumed to have a more advanced view about the protection of natural resources and environmental quality without concern for costs. Therefore, they are modeled as emphasizing the LCIA score, material and energy efficiency, and health risks. Regulators are modeled as sharing the environmentalists’ concern for health risks but not necessarily without consideration of cost. Whereas regulations in the US rarely take an explicit life-cycle perspective, there are instances in which material and energy VOL. 44, NO. 22, 2010 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 2. Frequency distribution graph of the ranking of each alternative with absence of knowledge regarding stakeholder preferences. efficiency are within the purview of regulatory or policy concern - such as programs that emphasize pollution prevention, waste minimization, nontraditional pollutants (e.g., carbon dioxide), and non-nano regulated emissions. These broader regulatory issues are modeled as concern for material and energy efficiency. 2.5. MCDA Application. The last step involves extension of the SMAA-LCIA method to aggregate different criteria scores and to obtain a probabilistic preference ordering of the different technological alternatives based on the criteria weights. Whereas in a previous application of SMAA-LCIA (12), performance data were represented as point estimates, in this study performance data are sampled from the probability distributions presented in Table 1. The resulting data are then normalized using outranking and combined with weight vectors sampled stochastically in the manner previously described (12). In this case, we ignore preference and indifference thresholds such that a complete preference c ) 1 may be expressed in the pairwise comparison of the performance of two alternatives on a single criteria when a > b, and c ) 0 otherwise. The aggregated weighted preference function c (a>b) is the linear-weighted sum of all pairwise comparisons over k number of criteria, where wk is a vector representing the relative weights assigned to each criterion c(a g b) )
∑w
k
· ck(a g b)
k
The pairwise comparison process of (a>b) is repeated for b in comparison to a. The net weighted preference function is then computed as ∑b*a[c(agb) - c(bga)]. Alternatives are then ranked according to net flow, from highest to lowest. A total of 10,000 simulations were used, which yielded sufficient precision for the purpose of our analysis and exceeded the recommended 9604 simulations cited previously as necessary to achieve 95% confidence on error limits of (0.01 for the eventual rank ordering using a similar method (28). A single simulation consists of a final ranking computed by independent Monte Carlo selection of the performance assessments ak, bk, etc. from the probability distributions represented in Table 1 and stochastic sampling of the weight vector wk in accordance with a previously published algorithm (12). Although we first pledge total ignorance on the value of the weights so as to explore the sensitivity of preference in 8708
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the absence of advance knowledge of decision maker or stakeholder preferences, it is also interesting to compare different value perspectives to discover whether additional information regarding the weights could result in increased confidence in the eventual rank ordering or identification of potential conflicts between different stakeholder groups. Therefore, we repeated 10,000 Monte Carlo simulations for each of four hypothetical stakeholder groups represented by fixed weight vectors and compared the resulting probabilistic rank orderings.
3. Results 3.1. Technology Selection with No Knowledge of Stakeholder Preferences. Figure 2 depicts a frequency table representing the proportion of simulations each alternative is ranked-ordered as first, second, third, or fourth. The result may be interpreted as the probability that each alternative occupies each rank. Although HiPCO is most likely to be the preferred alternative, a decision-maker with a preference for process yield efficiencies over cost may prefer Laser to HiPCO. Arc is secondarily interesting, and CVD is clearly the least preferable alternative, with almost no chance of ranking first. (The results are illustrative of the method. New information may result in significant changes in rank order.) Although the frequency graph is easy to interpret, the information communicated is inconclusive. Figure 3 presents the same results in terms of a cumulative distribution function (CDF), which plots the data from the same simulations with respect to the net flows for each alternative. Net flows calculated for each alternative are assumed to be representative of the alternative values in this analysis. It is assumed that, even though the calculation of the new flows is not a rational process (the net flow for one alternative might depend on other alternatives), once these net flows are calculated, the decision-maker is rational in the sense that greater net flow is always preferred in comparison to less. To interpret those CDFs, we use the concept of first-order and second-order stochastic dominance (25). Alternative A is said to dominate Alternative B in the first order if the CDF function for A is smaller than that of B at any point, which means that the CDFs never cross. No rational decision-maker should ever prefer a first-order stochastically dominated alternative. Similarly, Alternative A is said to dominate Alternative B in the second order if, at any point, the integral of the CDF function until that point for A is smaller than that
FIGURE 3. Cumulative distribution functions of the rankings for each alternative. of B. In this case, the CDFs do not cross and we can infer a rank-ordering from first-order stochastic dominance. That is, a decision-maker with completely uncertain weighting preference would have an overall ranking from Figure 3 as HiPco> Laser> Arc > CVD, which corresponds to the ordering of the CDFs (read from right to left). A decision-maker with more certain preferences (i.e., a narrowing of weight-set distributions) may nevertheless have a different preference ordering. 3.2. Technology Selection for Hypothetical Stakeholders. To explore the sensitivity of the rank-orderings to more definitive information of stakeholder preferences, the performance simulations are rerun by fixing weight vectors for each of the four stakeholders. Figure 4 presents frequency diagrams showing the likely rank-orderings that result for each of the hypothetical stakeholder scenarios. With more information regarding stakeholder preference, the frequency diagrams show larger differences between the alternative rankings than the uncertain weight set; i.e., increased confidence in the weights results in increased confidence in the eventual rank-ordering. Indeed, the HiPco alternative is almost always preferred for the Manufacturer. The presence for HiPco is still strong for the End User and grows more and more uncertain for the Regulator. However, the stakeholder results also highlight the potential for disagreement among stakeholders with different views. The Environmentalist seems to slightly prefer the Laser alternative, although uncertainty is high.
Assuming each stakeholder has perfect information about their own preferences, the frequency diagrams in Figure 4 show the likelihood that any one alternative would occupy the first, second, third, or least preferred rank. In this case, the uncertainty in the rank orderings reflects only the uncertainty in the performance of each alternative. Figure 5 presents the same results in the form of a CDF, which demonstrates that the Manufacturer, End User, and the Regulator groups would prefer HiPco, while the Environmentalist prefers Laser. However, Figure 4 shows that the strength of the Environmentalist and Regulator preferences are weak. New information (such as may be obtained through research or experience) regarding technology performance may result in a change of mind toward HiPco or Arc and a slightly lower chance for the End User to switch to laser. It is unlikely that the Manufacturer group will ever change their minds.
4. Discussion The incorporation of stochastic MCDA techniques like SMAALCIA allows for explicit uncertainty analysis and makes a decision model especially suitable for cases where information to evaluate criteria scores is limited, as well as to handle multistakeholder situations with varying preference information on criteria weights. The presented case study is an example of a stochastic MCDA-based method for situations where knowledge of the weights is lacking and uncertainty about criteria scores is significant. The results may be used VOL. 44, NO. 22, 2010 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 4. Frequency distribution graph of the ranking of each alternative for each stakeholder.
FIGURE 5. Cumulative distribution functions illustrating the preference of each stakeholder for each alternative. Those alternatives plotted furthest to the right are the most preferred. to screen technology alternatives, prioritize new research programs, or identify potential controversies. In this case, the role of Health information is not obvious in any of the results. Without specific information on Health that is capable of making a distinction among different technology alternatives, the overall effect of including Health in the decision problem is to reduce confidence in the eventual rank-ordering. If Health information were not included in the analysis simply because it is not available, the results may lead to a false sense of confidence among decision-makers represented by increased likelihood of firstor second-order stochastic dominance. Another advantage 8710
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of including the Health criterion is that it allows the analyst to test the sensitivity of preference to new information. That is, it may be interesting to explore whether the preference of the Manufacturer or other groups is robust enough to persist even if new Health information is represented in a hypothetical scenario analysis. The critically important aspect of an integrated decisiondirected approach toward research in a rapidly evolving field such as nanomaterials is that it enables exploration of different types of uncertainty and variability in an integrated, systematic way, ultimately identifying those that are most relevant to the decision. Without considering the entire system
in a specific decision context, it is impossible to ascertain whether additional research efforts into reducing uncertainty or characterizing uncertainty would be relevant to the final outcome. Informed by an example such as the one presented in this paper, a product developer might justifiably focus research and development attention on improved understanding of HiPCO and laser processes to better differentiate a preference for one process over the other. Gathering new information - for example, by performing new tests or conducting further research - may only be useful for the decision if there are cases where a rank ordering reversal may result from the effort. In the described decision-directed approach, research hypotheses can be tested as a change in the probability distributions represent in Table 1. If a change in the preferred rank ordering of the first two alternatives results from the new hypothesis, the research may be directly informative of the decision. However, if the preferred alternative remains unchanged, then the information that might be generated by the new research would be of little value to the decision maker. Another revealing aspect of this study is that uncertainties exist both in the domain of performance assessment (e.g., the cost of laser-produced SWCNT) and in the domain of decision-maker or stakeholder preferences. Modeling weight vectors as point estimates can potentially disaggregate these two types of uncertainties to highlight the sensitivity of an eventual rank-ordering to both the objective information resulting from scientific study and the value-laden information elicited from stakeholders. Only by exploring the sensitivity of the decision outcome to all types of uncertainty in concert can those with the greatest influence be discovered, as uncertainties in one aspect of the analysis may overwhelm those in other areas that may have otherwise been considered important areas to investigate further. The overall results of this process are a better understanding of the sensitivity of the system to important design variables or parameters, a reprioritization of research and development efforts, a better understanding of decision-maker preferences, better decisions, and ultimately, environmentally advantageous technologies.
Acknowledgments Comments provided by Brian Landi, Matthew Ganter, and Chris Schauermann at the Nanopower Research Laboratory, Rochester Institute of Technology, as well as Christy Foran and Charles Welch of the US Army Engineer Research and Development Center were especially helpful in the preparation of this article. Editorial and technical assistance was provided by John Vogel and Benjamin Trump of the US Army Engineer Research and Development Center. Permission was granted by the Chief of Engineers to publish this information.
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