Modeling Approaches for Nanomanufacturing Risk Assessment

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Proceedings of the 2009 Industrial Engineering Research Conference

Modeling Approaches for Nanomanufacturing Risk Assessment Zeynep D. Ok, Jacqueline A. Isaacs, James C. Benneyan Department of Mechanical & Industrial Engineering Northeastern University, Boston, MA 02115, USA

Abstract Given the significant uncertainty about environmental, health, and safety risks of nanomaterials, modeling their relative risks versus benefits is especially important. Several risk assessment methods exist in a variety of industries to investigate similar issues, depending on the nature of the problem and specific research needs. Using occupational exposure in carbon nanotube manufacturing processes as an example, we discuss and illustrate possible modeling approaches that might be useful for nanomanufacturing risk assessment, including Monte Carlo, multi-criteria, stochastic programming, and desirability function models.

Keywords Carbon nanotubes, SWNT, occupational health, uncertainty

1. Introduction Although nanotechnology holds enormous promise in energy, technology, medicine, electronics, consumer products, and other applications, significant uncertainty exists regarding associated occupational, consumer, and environmental health and safety (EHS) risks. Of the few toxicity studies to date, several suggest engineered nanomaterials may pose potential risks to human health, due to their small size and large surface area, allowing them to penetrate dermal barriers, cross cell membranes, breach gas exchange regions in lungs, travel throughout the body, and interact at the molecular level [1]. For example, critical reviews of single wall carbon nanotubes (SWNTs) toxicity found damage to mice lung tissue [2, 3], although further research is necessary to understand risks to humans. In response, several authors and regulatory bodies have advocated more research on nanotechnology EHS [4], including the U.S Environmental Protection Agency and National Institute for Occupational Safety and Health [5, 6]. The U.S National Nanotechnology Initiative also outlined an overall strategy for needed nanomaterial EHS research [7-9]. Until proposed studies develop a sufficient risk understanding to inform safe handling of engineered nanomaterials, nanomaterial researchers, policy makers, and businesses have little guidance for safe operating practices. Several risk assessment methods, however, exist in a variety of other industries that also should be useful in nanomanufacturing, including Monte Carlo, multi-criteria, stochastic programming, and desirability function models. These methods differ in the manner by which they handle uncertainty, multiple criteria, and risk-benefits trade-offs, with Table 1 summarizing potential nano applications, advantages, and disadvantages. Each approach is illustrated below, using occupational health risks associated with carbon nanotube manufacturing processes as an example. More broadly, until more is known about EHS risks of any nanotechnology or nanomaterial, these models can help decision-makers develop better understandings of risks, costs, and inherent trade-offs. Table 1: Summary of possible risk assessment methods useful in nanomanufacturing Method

Advantages & Disadvantages

Example of Potential Application

Monte Carlo simulation

+ Allows modeling uncertainty – No tradeoff framework 

Comparison of alternate occupational health protection strategies for HiPco nanomanufacturing process

Multi criteria decision making

+ Tradeoff frontiers – Deterministic

Goal programming model for balancing reliability, exposure, and throughput in a nanomanufacturing process

Stochastic programming

+ Allows stochastic parameters – Computational time

Chance-constrained models for reliability and safety analysis of a specific nanomanufacturing process

Desirability functions

+ Can compare discrete alternatives, robust – Abstract approach, arbitrary weights

Optimal selection of the most preferred product

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2. Potential Risk Assessment Modeling Approaches 2.1 Monte Carlo Models Monte Carlo (MC) simulation models are widely used in risk assessment because they very realistically can capture process complexities, chance events, and probabilistic outcomes, with Table 2 summarizing potential nanomanufacturing applications. MC results are computed from randomly generated data that emulate model input uncertainty (e.g., exposure amount or impact, regulatory requirements, associated costs), with results re-computed a large number of times to develop distributions and ranges of true (one-time) outcomes. These models can be run on a wide range of assumptions, help identify optimal decisions, and provide other useful information, such as guiding research priorities in order to minimize result uncertainty and make better decisions. Table 2: Potential nanomanufacturing applications of Monte Carlo risk assessment models Problem Type

Potential Application

Human health risk assessment

Exposure assessment of occupational health protection strategies Modeling of a dose-response curve of a specific engineered nanomaterial

Ecological risk assessment

Estimating nanomaterial accumulation in ecosystem Risk modeling for environmental policy issues

As one example, Ok, Isaacs, and Benneyan [10] developed a preliminary MC risk model to assess cost-exposure trade-offs in high pressure carbon monoxide (HiPco) processes, a common SWNT production method. Uncertainties associated with the process (e.g., costs and occupational health risks) and the regulatory environment (e.g., EHS standards timing, requirements, and costs) are modeled as probabilistic events, with results including distributions, expected values, and standards deviations of production costs and occupational health exposure. As the MC model executes, it generates manufacturing costs, occupational exposure amounts, and regulatory requirements according to context logic and computes total 10-year costs and exposure, repeating this computation 10,000 times to obtain accurate sampling distributions. For example, Figure 1 illustrates the (left) joint distribution of the production cost and exposure and (right) resultant total production and exposure cost distribution under certain process, regulatory, and cost assumptions, the latter producing interesting and counter-intuitive multi-modality.

Figure 1: Examples of results from MC nano-risk model. (Left) Joint distribution of production cost and exposure, (Right) Total production and exposure cost under different cost structures and regulatory policy assumptions, illustration of inability to identify optimal occupational protection decision due to overlapping distributions 2.2 Multi-Criteria Methods While the above approach helps analyze tradeoffs or optimize single-objective problems (or aggregate objective functions), multi-criteria decision making (MCDM) methods help optimize decisions with multiple conflicting objectives. Because all criteria usually cannot be optimized simultaneously, trade-off solutions that somehow optimally balance all objectives are computed or identified. Many MCDM methods exist and can be classified as having either a continuous or discrete number of solutions (i.e., selecting decision variable values or particular alternatives). Discrete methods most commonly include multi-attribute utility, analytic hierarchy process (AHP), and outranking models, whereas continuous methods most commonly include goal programming, weighted-sum, and vector maximum approaches. Each of these methods might be applicable to a wide range of nanomanufacturing applications, with some summarized in Table 3.

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Ok, Isaacs, Benneyan Table 3: Potential nano applications of multi criteria decision making methods Method

Alternatives

Potential Application

Multi-attribute utility theory

Discrete

Comparison of environmental risks of candidate nanotechnologies Choosing among business strategies for commercialization of nanotechnology

Analytic hierarchy process

Discrete

Material selection for a nanomanufacturing application Ranking environmental and health practices for safe nanotechnology

Outranking methods

Discrete

Selection of a fume hood for a nanotechnology research lab from a set of alternatives Prioritization of nanomaterials used in nanotechnology research labs

Weighted-sum method

Continuous

Balancing engineering objectives in the nanomanufacturing process development Choosing specific process settings for a nanomanufacturing process

Vector maximum approach

Continuous

Development of responsible nanomanufacturing processes by balancing benefits and risks Design of nanotechnology research lab conditions to avoid nanoparticle exposure

Goal programming

Continuous

Balancing reliability, exposure, and throughput in a nanomanufacturing process Production planning for a nanomanufacturing plant

The below example illustrates a potential use of goal programming (GP) to balance three criteria in a nanomanufacturing process – reliability, throughput, and occupational safety – with goals and priorities for each factor summarized in Table 4. The overall GP objective in this case is to identify values of the decision variables pH (x1), conductivity (x2), and temperature (x3) that minimize total deviation from these goals. Here, the highest priority is given to maintaining 90% reliability, with the two remaining goals (production and exposure) being secondary priorities, although goals or priority levels can be updated as knowledge about emerging technologies evolve. Table 4: Data summary for goal programming example Priority Level

Factor

Goal

First-priority Second-priority

Reliability rate Production rate Exposure level

≥ 90% ≥ 10 grams ≤ 5 units

Penalty Weights M 5 3

Under the GP method, the highest priority goal is considered infinitely more important than others and a large penalty weight M is assigned for deviations from this goal. Positive or negative deviations from any goal i are denoted by d+i or d-i (i.e., corresponding to lower or upper bounds), respectively, with the general GP formulation on the left and an example on the right being (1) (2) (3) (4) (5) (6) (7) where the ci terms are constraint vectors and x is the decision variables vector. Constraint relationships might be developed from first principles or experimental designs, although a purely hypothetical example is illustrated here. For sake of illustration, the optimal solution in this case is x1 (pH) = 10.68, x2 (conductivity) = 100, and x3 (temperature) = 151.49, satisfying the first two goals (reliability and production) but not the third (exposure) – but none-the-less optimal – and thereby resulting in values of d-1 = 0, d-2 = 0, and d+3 = 1.12. A related type of multi-objective optimization model uses one criteria (e.g., maximize yield) in the (univariate) objective function subject to constraints that other criteria meet some thresholds (e.g., cost ≤ threshold). By then iterating across a range of constraint thresholds, the optimal tradeoff frontier is mapped out (i.e., the lowest cost can be to achieve any desired yield level), leaving it to decision makers to determine where they want to locate on this optimized surface.

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Ok, Isaacs, Benneyan 2.3 Stochastic Programming Models Stochastic programming (SP) models include either probabilistic objective functions (such as to minimize expected exposure or the probability that cost exceeds some amount) or probabilistic constraints (such as not allowing total random exposure to exceed some value), often with uncertainty represented by probability distributions [11-12] and often treating secondary objectives as probabilistic constraints (somewhat extending the above idea). Two standard types of SP models are recourse and chance-constrained models, with Table 5 summarizing potential nano applications of each. Recourse models are used when sequential decisions over multiple time periods are possible, producing a schedule of optimal decisions both presently and in subsequent time periods in the form of optimal corrective (recourse) actions dependent on which specific random events occur in the interim. An example might be a strategic capacity planning problem in a manufacturing industry under uncertain market, technology, and manufacturing conditions. Table 5: Potential nano applications of stochastic programming Problem Type

Potential Application

Multi-period recourse models

Investment planning for a nanomanufacturing plant Technology choices for a nanomanufacturing process Capacity planning for a small start-up company

Chance-constrained models

Selection of optimal EHS strategy Yield/cost optimization for a nanomanufacturing process Material selection for a nanomanufacturing application

Chance-constrained programs are used to make decisions that ensure certain constraints will be satisfied with some specified probability, such as a risk-based portfolio selection example for investment decisions. The below example illustrates a chance-constrained model of the reliability of a nanomanufacturing process, again with the general formulation on the left and a hypothetical example on the right. As new technologies are developed, initially some processes might be extremely costly and tolerances might be relaxed to some point to reduce costs but still be able to meet a reliability target with some probability. The objective function finds the values of four decision variables – pH (x1), conductivity (x2), temperature (x3), and occupational health protection level (x4) – that minimize cost while satisfying each constraint with specified probabilities. (8) (9) (10) (11) (12) (13) where the ci terms are constraint vectors, x is the decision variables vector, and α1, α2, and α3 are user-specified probabilities of satisfying each constraint – for example, maintaining a yield rate of 60% ≥ 95% of the time, a production rate of 10 grams per hour ≥ 90% of the time, and cumulative exposure less than the ‘no observable effect’ level ≥ 95% of the time. As previously, constraint relationships, appropriate probability distributions, means, and standard deviations might be developed experimentally, however for illustration purposes a normal distribution and a coefficient of variation of 0.5 are assumed for all responses, producing optimal decision variable values of x1 (pH) = 11, x2 (conductivity) = 292.5, x3 (temperature) = 97.9, and x4 (occupational health protection level) = 3. Alternately, a stochastic programming recourse (SPR) model might be formulated to map out a schedule of optimal decisions for a multistage planning problem, such as for a nanomanufacturing plant, where decisions are dependent not only on random variables in the traditional SPR sense such as future regulatory occupational health and safety requirements but possibly also on ‘degrees of belief’ or ‘probabilistic knowledge’ such as true health risks. 2.4 Desirability Functions Another multi-criteria approach, based on desirability functions [13], can be used to either choose between a finite number of alternatives (e.g., fume hood selection) or identify the optimal settings of continuous process variables (e.g., flow rate, hood height, solution concentration), similar to multi-attribute methods and GP or SP models, respectively. Each criteria’s value, Yi, (which depends on the alternative selected or process variable settings) is

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Ok, Isaacs, Benneyan transformed to a dimensionless desirability value, di, where 0 ≤ di ≤ 1, the value of di increases as the desirability of the corresponding Yi increases, and di = 0.00 and di = 1.00 correspond to completely unacceptable (undesirable) and acceptable (desirable or ideal) results, respectively. These di values are combined into an overall desirability value (objective function), D, of achieving each possible combination of results for the K measures of interest. The optimum solution then is found as that which maximizes D. While weights used in DF (and GP) models are somewhat subjective, sensitivity and what-if analysis are easily conducted by examining plots of the desirability surface, and as such also can provide practical process improvement insights (e.g., moving in steepest ascent directions). Table 6: Potential nano applications of desirability functions Problem Type

Potential Application

Discrete problems (selecting among several alternatives)

Selection of an equipment for a research lab from a set of alternatives Determine the most preferred process from alternate nanomanufacturing processes Material selection for a nanomanufacturing application

Continuous problems (finding optimum variable values)

Balancing reliability, exposure, and throughput in the development of a nanomanufacturing process Development of specific nanomanufacturing processes by balancing benefits and risks

The below example illustrates a discrete use of desirability functions to select nanotechnology laboratory equipment with other possible nano applications summarized in Table 6. In this case, three criteria are important for an effective fume hood – cost (Y1), air flow (Y2), and ease of use (Y3). For illustration, standard Derringer and Suich (DH) desirability transformations are used [14], illustrated in Figure 2, with the importance weights for each criteria based on expert judgment (and here implying air flow is four and two times more important than ease of use and cost, respectively).

Figure 2: Fume hood desirability functions for cost (left), air flow (center), and ease of use (right) Table 7: Individual desirability values and overall desirability for each candidate Candidate Fume Hood

Cost

d1

Air Flow

d2

Ease of Use

d3

Desirability (D)

F1 F2 F3

$7,500 $9,500 $6,000

0.56 0.30 0.81

145 120 110

0.2 0.8 0.4

4 5 2

0.75 1 0.25

0.32 0.62 0.46

The individual criteria di desirabilities and overall D desirabilities of each of three candidate fume hoods are summarized in Table 7, with the overall desirability D calculated most commonly as a sort of weighted geometric mean (14) In this case, fume hood F2 has the largest D value and is the best candidate in terms of balancing cost, air flow, and ease of use, although a different weighting scheme or functional forms for di and D could produce different results, underscoring the importance of sensitivity analysis. Alternately, a continuous problem might be formulated to find the values of three decision variables – fume hood height (x1), sash position (x2), and volume flow rate (x3) that optimizes fume hood effectiveness against nanomaterials. The overall D desirability then is maximized for four criteria that are important for fume hood performance – face velocity (Y1), turbulence (Y2), particle size distribution (Y3), and particle number concentration (Y4) – by searching through the levels of controllable factors (i.e., x1, x2, and x3).

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3. Conclusions Assessing tradeoffs between nanomanufacturing production, cost, and safety concerns is both difficult and important given the significant uncertainty that exists about exposure effects. A variety of risk assessment models can be developed within this context (used separately and together) to help decision-makers with the difficult task of identifying appropriate or optimal process design, equipment selection, and regulatory policy decisions. As more becomes known about nanomaterial exposure risks, these models can be updated to reflect the current knowledge base, suggesting optimal decisions likely will change over time.

Acknowledgements The first and second authors are supported by National Science Foundation grants SES-0404114 and EEC-0425826 through the Nanoscale Science and Engineering Center for High-Rate Nanomanufacturing.

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