the design of a sustainability assessment standard using life cycle information

M E T H O D S TO O L S A N D S O F T WA R E

The Design of a Sustainability AssessmentStandard Using Life Cycle InformationDi Lu and Matthew J Realff

Keywords

industrial ecologylife cycle assessment (LCA)life cycle impact assessment (LCIA)multiattribute decision makingpoint allocationstandards design

Summary

Sustainability assessment standards are currently being developed for a range of buildingproducts This activity has been stimulated through the considerable success of the USGreen Building Councilrsquos (USGBC) LEEDTM standard Transparent life cyclendashbased standardscan guide manufacturers to design products that have reduced environmental impact Theuse of a sustainability standard can certify performance and avoid green washing In thisarticle we present a logical framework for designing a sustainability assessment standardthrough the creation of tables that award points in the standard to be consistent with lifecycle information Certain minimum principles of consistency are articulated In the casethat the life cycle impact assessment method maps the life cycle inventory to impact througha linear weighting two design approachesmdashimpact category and activity substitutionmdashareconstructed to be consistent with these principles The approach is illustrated in a casestudy of a partial redesign of a carpet sustainability assessment standard (NSFANSI-140)

Introduction

Standards are tools to measure and calibrate product or sys-tem performance and are often used to regulate and certifythem An emerging area for standards development is sustain-ability assessment Sustainability assessment standards have sev-eral features that are common to many product standards Firstas with many standards the stakeholders interested in the stan-dard come from diverse groups with different values and in-terests In the American National Standards Institute (ANSI)process these stakeholders are represented on a joint commit-tee that formulates and revises the standard The committeemust follow rules of balanced representation from stakeholdergroups and one group cannot dominate the committee Sec-ond the dimensions along which the product or system hasto be measured are numerous However unlike many productperformance standards the underlying metrics for sustainabil-ity are not well understood agreed upon or defined by the

Address correspondence to Matthew J Realff School of Chemical and Biomolecular Engineering Georgia Institute of Technology 311 Ferst Drive NW Atlanta GA30332-0100 USA Email MatthewRealffchbegatechedu

ccopy 2012 by Yale UniversityDOI 101111j1530-9290201200539x

Volume 17 Number 4

stakeholder groups who are often not experts in sustainabilitybut in the underlying product domain The metrics encom-pass technical product performance often for reasons of safetyand longevity company or facility performance such as socialmetrics of corporate responsibility or use of environmental man-agement systems and production process performance such asenergy resource use and waste In addition product categoryrules (PCRs) are often used for environmental product decla-rations (EPDs) which enable the transparent comparison ofdifferent products within the same product category

Standard-setting processes are discussed by Twing and col-leagues (2010) in the context of educational performance Stan-dard formulation relies heavily on stakeholdersrsquo experiences butmay be inadequate for judging the quality of standard-setting re-sults Since the ad hoc character of standard setting is widely ac-knowledged by researchers and practitioners studies are carriedout to validate the standard-setting outcomes McGinty (2005)states that to set defensible standards work needs to be done

wwwwileyonlinelibrarycomjournaljie Journal of Industrial Ecology 493


to understand the influence of cognitive social political andemotional factors during the decision-making process There-fore qualitative research methods such as naturalistic observa-tion and quantitative research methods that draw on researchoutside the measurement area such as research in cognitivepsychology are used to try to understand the standard-settingprocess These aspects of standard setting will not be furtherdiscussed in this article They are important but it is equallyimportant to establish a credible basis for connecting availablescience to the form of the standard Similarly another body ofliterature that is relevant to connecting the results of this arti-cle to overall life cycle decision making is multiattribute deci-sion making and utility theory Churchman and Ackoff (1954)analyze the method of simple additive weighting (SAW) fordecision-making processes with multiple attributes Fishburn(1967) discusses the approach for multiattribute decision mak-ing (MADM) In addition Keeney and Raiffa (1976) discuss theMulti-Attribute Utility Theory (MAUT) for the comparison ofmany diverse measures In the context of life cycle assessment(LCA) Koffler et al (2008) discusses how to apply voting rulesto panel-based decision making MAUT and MADM are im-portant topics for taking the next step to find the weightingbetween different attributes and provide the underlying theoryfor how and why the attributes are scaled with respect to eachother

In sustainability assessment the diversity of product processand company performance metrics creates unique problems inhow to balance the rewards across this diversity and how to syn-thesize a single measure of performance This latter point theconversion of a set of categories into a single multicategory mea-sure is a feature of the sustainability standards such as LEEDTM

(2008) NSF-140 (2007 the Carpet Sustainability AssessmentStandard) and other emerging standards for products For ex-ample the Business and Institutional Furniture ManufacturersAssociation (BIFMA) levelTM sustainability standard (2012)is a multifaceted approach The BIFMA levelTM standard pro-vides manufacturers with valuable resources for evaluating andcommunicating the environmental and social impacts of theirfurniture products and processes based on criteria includingmaterials use of energy atmospheric impacts human healthand ecosystems and social responsibility Therefore manufac-turers now have a methodology to present the environmentalcharacteristics in a clear easily understood manner with a ver-nacular that gives end users the ability to make a fair compari-son Scheuer and Keoleian (2002) discuss how to evaluate theLEED standard using LCA methods The study revealed a va-riety of discrepancies that were in the version of the standardat the time The LCA results compared with the LEED rat-ings showed that these were not always aligned because of thechoice of metrics to reward performance improvements TheLEED and NSF-140 standards resolve the problem of synthesiz-ing a single measure of performance by using points awarded forperformance along each dimension and then adding the pointsto give a total score This creates an interesting challenge forthe development of this type of points-based standard how bestto determine the point allocations across the performance di-

mensions The goal of this article is to lay a foundation for arational allocation of points for the life cycle component of asustainability assessment standard

An ideal but not the only approach for points-based stan-dard setting can be summarized as follows The stakeholdergroup agrees on a category set that they feel reflects the sustain-ability of the system For example the toxicity of the materialsthe amount of waste the energy use in manufacturing the safetyand health of workers and the social and financial performanceof the company The group then decides how many points in to-tal the standard will have The points are then divided betweenthe categories reflecting the importance they assign to themFinally they decide how many points a given performance levelshould receive and allocate the points to the different levels ofachievement Unfortunately this is very difficult to do Oftenthe division or allocation is implicit arrived at by developing aset of activities that can be undertaken to improve a categoryand then allocating points to the activities The points are thentotaled for the activities

For example the current carpet sustainability assessmentstandard in its first version was developed with substantial in-sights from the Joint Committee of this ANSI standard on whatproduct changes might lead to sustainability improvement Ingeneral these potential product changes were simply intuitiveconcepts by which points were subsequently awarded Someof the sustainability improvements (and points) were relatedto organizational-level categories (such as for environmentalmanagement systems) which are vital to achieve change Theother improvements (and points) were directed at material andenergy improvements (such as for bio-based materials) Othernational standards such as LEED also began as intuitive pointsystems to drive change However these organizations have rec-ognized that a science-based approach is ultimately needed forthe improvements related to material and energy changes Thiswill help to avoid creating incentives for activities that maynot provide substantial improvement to the overall life cycle ofthe system A science-based approach requires substantial lifecycle information and the life cycle field has reached sufficientmaturity in many areas to enable this approach to the life cyclecomponent of these standards For example it is possible toevaluate the congruency of an existing standard with life cycleprinciples by optimizing a product design either to maximizethe points awarded in the standard or to minimize the life cycleimpact measures (Lu and Realff 2010)

Methodology

Definitions

We start with definitions of terms used in this article thatcould have different interpretations in other contexts

1 An impact category is an environmental impact suchas global warming acidification or eco-toxicity For ex-ample there are ten impact categories in the TRACI

494 Journal of Industrial Ecology


(Tool for the Reduction and Assessment of Chemicaland Other Environmental Impacts) method (Bare 2002)

2 An impact categoryndashbased standard rewards improve-ments in the environmental profile of a product as mea-sured by its impacts within the different categories

3 An activity substitution is defined as a chemical or physi-cal process that substitutes certain materials such as bio-based postconsumer and postindustrial materials intoexisting products or substitutes renewable energy or im-proves the energy efficiency of existing processes or whichreclaims end-of-life materials

4 An activity-based standard rewards decreases or in-creases with respect to different activities for examplereducing energy consumption or emissions and increas-ing bio-based content or recycled content

5 A points-based standard rewards greater improvementsin environmental profiles or the undertaking of differentlevels of activity with points that reflect either crossinga particular threshold or on a sliding scale These pointsare added together for an overall score and are sometimescompared to particular thresholds to determine the prod-uct rating such as ldquoplatinumrdquo or ldquobronzerdquo

Principles and Requirements in Points-based StandardsDesign

We start with the basic assumption that overall productswith a lesser life cycle impact should be rewarded with morepoints in the life cycle component of the standard than a productwith a greater life cycle impact all other things being equalThis does not mean that overall the product with a lower totalimpact will achieve a higher point total since there are oftenmany impacts outside those considered Two formal principlesshould be enforced in the design of the points-based standardto ensure our method of standard design is consistent with thenotion that we prefer products with overall lower life cycleimpacts

Principle 1 If an activity aj causes the same or an improve-ment in every impact category compared to activity aprime

j ac-tivity aj should be awarded the same or more points in thestandard

If this principle is not enforced then it is possible for a prod-uct that improves the environmental performance of a productthe same or more in every category than another to have a worsepoint total This principle avoids inconsistencies in the rewardscheme and strengthens the standardrsquos claims to be moving agiven product in the direction of improved environmental per-formance This implies that certain relationships between ac-tivity rewards must be implicitly obeyed within activity-basedstandards Therefore the mapping from category or activity lev-els to points must be designed a certain way in order to avoid acontradiction of Principle 1

Principle 2 There must be an agreed upon reference stateor baseline life cycle impact assessment (LCIA) for eachproduct platform

This is necessary in the case of the percentage reductionfrom the baseline or where an absolute standard is used wherethe baseline plays a role in defining the minimum or maximumvalues of the impact The standard may be applied to productswhere there are many different subcategories such as in furni-ture or in the case of carpet broadloom and tile In this casethe baseline product can be defined for each subcategory Oneapproach to defining a baseline has been to choose a historicalproduct design such as one from a decade ago which representsthe industry product segment

If the standard allows for companies to make improvementsrelative to their own products rather than those of the entireindustry then it is possible to have products that have higherimpacts earning more points in the standard This demonstratesthat agreed product platform baselines for a company are in-sufficient to guarantee that products with lower environmen-tal impacts are preferred in a standard compared with otherproducts

It is of course possible to design a points-based standard thatviolates these principles but it should be recognized from theoutset that this will lead to the potential mismatch of environ-mental impacts and points Allowing this mismatch may be areasonable course of action when first designing standards sinceit can be important to reward organizations for progress eventhough they are starting from a position of greater environmen-tal impacts for their products relative to their competitors

Process Life Cycle Inventory and Life Cycle ImpactAssessment Representations

First we give a formal definition of a process-based life cycleinventory (LCI) block Figure 1 shows all information includedin the LCI block where me is the amount of emissions mp isthe amount of the final product P mraw is the amount of rawmaterial mby is the amount of by-product and E is the energyconsumption In general mraw mby and me are vectors of mate-rial throughput quantities in appropriate units (eg kilograms[kg]) and mp is a material flow that defines the functional unit ofthe LCI such as 1000 kg The by-product flows are included toenable allocation schemes of impacts to products to be used Ecan be a vector of energy types that are used in the process suchas natural gas electricity and fuel oils Since the focus of thisstudy is on the materials and energy the other measurementssuch as land use and nonenvironmental impact indicators havenot been included in the LCI block below However these mea-surements could be included in this block ndash as the quantitativemethods to measure the indicators evolve

For the rest of this article we assume a linear relationshipbetween LCI and LCIA to illustrate the design of a sustain-ability assessment standard This assumption does limit the useof certain LCIA categories and assessment strategies Howeverthere are many assessment categories for which this assumptioncan be made For example the LCIA approach of TRACI uti-lizes linear relationships such as NV( j ) = sum

xs CF ( j )xs lowast exs where NV(j) is the normalized value for impact category j exs

is the emission or resource depletion of stressor x for the spatial

Lu and Realff Sustainability Assessment Standard Design Using Life Cycle Information 495


Figure 1 General product cradle-to-gate life cycle inventory (LCI) block

scale s and CF(j)xs is the characterization factor for impactcategory j for stressor x within spatial scale s

Given that one impact category j has a linear relationshipwith emission meq in mass then the impact can be expressedin equation (1)

I j =sum

q

Cj q lowast meq (1)

given the coefficient Cjq transforming the data from LCI toLCIA where Ij is the value of impact category j Cjq is the char-acterization factor of emission substance q for impact categoryj that transforms the LCI of emission q to its LCIA in impactcategory j and meq is the amount of emission substance q anelement of the me vector Similarly elements of mraw and E canbe included in this relationship

The rest of this article will focus on how to design the stan-dard tables using life cycle information Category-based andactivity-based standards will be discussed The use of the sus-tainability assessment standard design procedure in the prelim-inary study of the NSF-140 carpet standard will be illustratedFinally we will conclude the article with a discussion of theresults and conclusions

Category-based Standard Design

Category-based standard design is based on the stakeholdersrsquoviews on the relative importance of LCIA categories For eachimpact category j a weight wj is given from stakeholders and aset of n LCIA categories has weights w1 w2 wn where thesum of the weights is 1 Each impact category will be allocatedto certain points according to the given total points and weightswj Then the standard tables will be created

It is anticipated that the stakeholders will be able to con-struct a set of weights for each of the impact categories This willrequire substantial effort and is subject to all the same pitfallsof aggregating preferences as all social choice situations (Arrow1951 Arrow et al 1997) However we take the position that itis better that the stakeholders attempt to arrive at weighting onthe categories and then translate their preferences in a princi-pled way to points in a standard rather than attempt to allocatethe points directly within the tables themselves

Design of Category-based Tables

In order to design the tables that map improvements in im-pacts to points there are two coupled decisions that need to bemade These are the total points in the standard and the gran-ularity of the tables as expressed by the interval range requiredto earn a point Clearly the higher the total points (TP) in thestandard the finer the resolution can be within each categoryto earn a point However the intervals for an impact categoryshould not be made so small as to imply a false sense of precisionin determining the impact Thus the point total should balancethe desire to allow incremental improvement with the precisionwith which that improvement can be measured

Given the weights w1 w2 wn the points allocatedto each impact category can be calculated as w1lowastTP w2lowastTP wnlowastTP The category tables can be generated systemati-cally given the total points in the standard Figure 2 shows thecategory-based standard framework where Kj is usually the per-centage improvement interval to have a single point awardedin category j

One alternative design for category-based tables is to rewardthe performance based on the impact percentage in a givenabsolute range of values that one impact category j can take[Ijmin Ijmax] Essentially the LCI can be found for a productand then the value for each impact category can be computedusing equation (1) The fraction of those points awarded to theproduct will be based on equation (2)

Percentage = I j minus I j min

I j max minus I j min (2)

Then the category tables with a structure like table 1 willbe generated based on the impact percentage of the productachieved in the impact category The difficulty with this designis that finding the appropriate values for the minimum andmaximum impacts is challenging Zero could be taken for theminimum although there may be good reasons that zero impactmay be unachievable in the time frame in which the standardis to be used

The maximum impact can often be defined through a base-line product These choices of the minimum and maximumwould then lead to a standard based on the fraction of impact ofthe baseline product The impact of a baseline or reference state



Figure 2 Category-based standard framework See text for a full description of terms

Table 1 Awarded points according to equivalent percentagereduction among different activities

Activity 0 Activity 1 Activity m

Coefficient 1 a1 am

Improvement togain 1 point

x a1lowastx am

lowastx

Maximumachievable

b0 b1 bm

for category j I j is shown in equation (3) The percentage

of impact improvement from the baseline can be computed us-ing equation (4) The resulting table is very similar to table 1with the percentages now representing improvements from thebaseline

I j =

sumq

Cj q lowast meq (3)

Percentage = I j minus I j

I j

(4)

In summary the information required to design LCIAcategory-based standards is as follows

1 Impact category set Ij j = 1 2 n2 Relative weights on categories wj j = 1 2 n3 Total number of LCIA-based standard points

If we want to use an LCI-based framework then we will need

4 Relationships to translate LCI measures to LCIA mea-sures

If it is required to use percentage reductions then in additionyou will need

5 Baselinereference LCIA measures

Discussion of Category-based Designs

Category-based standards are easy to update and expandFor example new categories of impacts can be introduced andeither the point total expanded or the points refactored overthe tables If the points are increased then any threshold levelsthat are established for performance will have to be similarlyadjusted If the baseline product is updated to reflect the con-tinuous improvement of the industry as a whole this requiresno changes in the standard Overall category-based standardsare clear to stakeholders who are experts in life cycle impactsbut less transparent to those stakeholders that are focused ontaking actions to conform to the standard The category-basedstandard gives no guidance as to how to achieve points There-fore a manufacturer must be able to translate their possibleactions into the impacts often a nontrivial task which mustbe repeated by each manufacturer This could be regarded asboth a strength and a weakness depending on the stakeholderperspective This leads to the second type of standards thosebased on activities rather than measures of performance

Adding Activity Substitution toConsiderations of Impact Category-basedStandard Design

This section addresses two aspects of activity-based standarddesign First the problems of designing these standards are high-lighted Then despite these problems it is demonstrated thatit is possible to design standards according to the principles laidout earlier

There are at least two significant problems that arise from thegeneration of points-based standards on an activity basis Firstallocating points to activities shifts the focus from improvingthe categories to rewarding specific activities These activitiesmay actually improve (or worsen) several of the categories thatwere originally of interest to the stakeholders but this will not



be transparent to the standard because the activity receives thepoints not the improvement of the category In other words anactivity-based standard mixes the rewards for improving cate-gories together in the rewards for the activities which may thenbe much harder to interpret For example recycling may lowermaterial resource use energy consumption and landfill wastebut may receive points that do not reflect the original concernof the stakeholders for each of these categories Second newactivities that could improve the original categories such asreducing the material use of the product may receive no pointsat all because this activity was not considered as part of theoriginal stakeholder discussion For example recycling of theproduct may not change the recycled content of the productitself if the material is used in some other secondary stream yetthe recycling is saving material resources overall However thestandard may reward only the activity of increasing the recycledcontent of the product

In general it seems unlikely that we will think of all theactivities that might be taken to improve categories Thus itwill be difficult to avoid constant adjustment of the standardmaking sure that activities are rewarded appropriately becausenew activities may require adjustments to the existing activityrewards This has to be done to avoid inflating the total numberof points available in the standard for achieving the same re-duction in final impacts However if the activities are mutuallyexclusive then this does not pose a problem

Despite the limitations of activity-based standards there isstill a strong driving force to have them because adoption of thestandard by industry becomes much easier if it is focused on ac-tivities rather than forcing companies to calculate the impactsof their activities The extra effort involved in measuring cal-culating documenting and reporting the impact values shouldnot be underestimated Small and medium-size enterprises maynot have the resources to undertake these efforts and hence acategory-based standard would become a barrier to competition

The goal of this section is to develop a more scientific ap-proach to the generation of activity-based standards that ad-dresses these two concerns First the approach keeps the focuson rewarding product category improvements that reflect theoriginal values of the stakeholders Second it admits many dif-ferent forms of activity and constructs the points reward schemeto ensure that different activities are rewarded proportionatelyto their improvement of impact categories The focus will beon those components of LCA that are directly related to LCImeasures such as global warming potential and other emissionsor resource use categories We describe our approach to allo-cating the point-based standard from two different scenariossingle category and multicategory We illustrate how to employthe mechanism in the preliminary study of the NSF-140 carpetstandard

Case 1 Single Category Activity-based Design

For ease of exposition we start with the case of a singleenvironmental attribute or category to which activities con-tribute For a standard to be consistent with Principle 1 the

same number of points earned by each activity should reflectan equivalent environmental impact To achieve this goal twoassumptions are made First the points should be awarded inlinear proportion to the category This is the same as the pointallocation in the category-based tables The second assumptionis that the relative impact on the category for each activityis known Assume there are m + 1 activities the relations ofimpact improvement among different activities for the samecategory impact are shown in table 1 where a1 a2 am

are coefficients that represent the equivalent improvement per-centage of each activity i compared with the baseline activity0 For example if using 10 recycled materials is equal to a 5electricity reduction from an environmental perspective thecoefficient for using recycled materials is 2 if we use electricityreduction as the baseline activity 0 This ratio can be establishedthrough the life cycle information as explained later

Activity 0 is taken as the baseline We define that x percentof improvement from activity 0 will earn 1 point Then a1lowastxpercent of improvement from activity 1 will earn 1 point aswell Therefore from equation (1) the points of each activityn will be allocated as follows

b0

a0 lowast x+ b1

a1 lowast x+ b2

a2 lowast x+ middot middot middot + bm

am lowast x= Total Points

(5)

where bi represents the maximum improvement percentage thatan activity can achieve in the category For example supposeactivity 1 stands for using recycling materials and in somesystem the maximum percentage of recycled materials beingused cannot exceed 25 Therefore b1 is equal to 25 and theupper bound of the threshold in the recycling materials table is25 The constructed table will have the same structure as thecategory-based standard as shown in table 2

The coefficients are considered known and are determined inone of two ways The preferred method is to use LCI informationto determine the relation coefficients ai for those categories forwhich relationships between LCI and LCIA are known and forwhich the activitiesrsquo LCI values can be calculated The secondmethod is to use stakeholder experience to judge the relativechange in impact by different activities This has been the onlyway to proceed with the design of such standards in the absenceof LCI and LCA information The bi are based on the productsystemrsquos condition which means only the bi of the limit canbe reached The bis are typically determined by manufacturerperformance specifications for material content or can be setas goals for the system to reach or by direct knowledge ofthe maximum The bi values can be adjusted as the ability ofmanufacturers to meet the current goals improves such as byincreasing the compatibility of material generated by a recyclingprocess and hence its maximum percentage content The ai

and bi values have been explained in terms of percentagesIt is possible to use absolute amounts in the original activityunits instead Then the ai values represent the amount of agiven activity relative to the baseline activity required to havethe same impact The bi value represents the maximum in the



Table 2 Standard table structure

Activity 0rsquos table structure Activity irsquos table structure

Improvement for activity 0 Points awarded Improvement for activity i Points awarded

(0 x] 1 (0 amlowastx] 1

(x 2lowastx] 2 (amlowastx 2lowastam

lowastx] 2

(b0 minus x b0] b0x (bi minus amlowastx bi] bi(am

lowastx)

original activity units and x is the amount of activity 0 requiredto earn a point

Case 2 Multiple Categories Activity-based Design

Case 1 represents the single-category standard which canhave different activities but they impact only one categoryHowever normally one activity affects multiple impact cate-gories instead of just one This raises the issue of how to con-struct multicategory tables in the standard To normalize theprocess of creating a standard a four-step procedure based onimpact level and activity level is proposed as shown in figure 3

The first step is to generate the matrix with the categories(the number of impacts is n) as columns and the activity (thenumber of activities is m) as rows

The second step is to allocate points within each impactcategory through the same stakeholder process as for category-based designs

The third step is to construct the individual tables Pointswithin the same impact category will be allocated through dif-ferent activities for the single-category activity-based designThis step will generate a matrix of tables with the categories(the number of impacts is n) as columns and the activity (thenumber of activities is m) as rows

The fourth step is to check the mlowastn tables with respect toeach impact and each activity In some cases it may be possi-

ble to merge the different category tables for a single activityinto one table This is based on whether the point intervalsare of common size or the intervals can be interleaved with-out creating too fine distinctions to earn a point The merg-ing does not affect the point allocation but makes check-ing the points for undertaking an activity more convenientWhen this merging is impossible the tables can be left un-merged and tables similar to table 3 can be constructed for eachcategory

Dealing with Uncertainty in Activity Impact

Often it is difficult to get the exact values for the LCIsor for the way that these inventories translate into impactsThis causes uncertainty in the values of ai for the relativeimprovements that are created by different activities We willassume that we can characterize the ai values by an upper boundand lower bound The range will introduce uncertainty intothe system and make it more difficult to specify the standardthreshold values However one approach to understandingthe impact of the uncertainty and to continue with the designprocess is to use interval arithmetic operations as shown inequations (6) through (9) For example assume there are threeactivities activity 0 where the percentage of improvementwill gain one point is known from previous studies andactivities 1 through n with the lower bound and upper bound

Figure 3 Multiple category-based standard framework See text for a full description of terms



Table 3 Selected tables from the NSF-140 carpet standard

Manufacturerrsquos use of renewable energy andor energy reduction (a)Points awarded for manufacturerrsquos use of bio-based

recycled content or EPP (b)

Percentage of energy reduction Points awarded Percentage of recycled content Points awarded

ge1 2 ge5 2ge2 3 ge10 3ge5 4 ge15 4ge8 5 ge20 5ge10 6 ge25 6Increments of 5 per point until ge35 +1 ge30 7ge50 11 Increments of 5 per point +1ge75 12 ge95 20

Note EPP = environmentally preferable product

of their activitiesrsquo improvement Consider two activities(a1 isin [a1 a1] a2 isin [a2 a2]) compared with activity 0

Assume

a1 isin [a1 a1] a2 isin [a2 a2]

[a1 a1] + [a2 a2] = [(a1 + a2) (a1 + a2)] (6)

[a1 a1] minus [a2 a2] = [(a1 minus a2) (a1 minus a2)] (7)

[a1 a1] lowast [a2 a2] = [(a1 lowast a2) (a1 lowast a2)] (8)

Then

[a1 a1]

[a2 a2]= [a1 a1]lowast

[1a2

1a2

] if a2 = 0 a2 = 0 (9)

In general starting with equation (10) the interval of xcan be found as shown in equation (11) Therefore the newpercentage of improvement for getting one point for activity 0can be estimated as in a range [x x ]

b0

a0 lowast x+ b1

a1 lowast x+ middot middot middot + bn

an lowast x= Total (10)

[x x ] =[

1Total

lowast(

b0

a0+

nsumi =1

bi

ai

)

1Total

lowast(

b0

a0+

nsumi =1

bi

ai

)]

(11)

The next step is for stakeholders to choose the percentageimprovement value xprime from the range [x x ] for activity 0 to getone point where the maximum amount of points for activity 0to gain is b0

x prime0 Take activity 1 as an example [a1 lowast x0

prime a1 lowast x0prime]

will be the percentage improvement range of activity 1 toget one point The ambiguity in the percentage improvementrepresented by the range will give a sense of the uncertainty inthe allocation This ambiguity must be resolved by the stake-holders but this discussion will be framed by the range ratherthan being completely open After establishing x0

prime for activity 0and xi

prime for activity i from 1 to n minus 1 xnprime for activity n can be cal-

culated through the equation b0x0prime + b1

x1prime + middot middot middot + bnxn prime = Total

Case Study

The NSF-140 standard (NSF 2007) is an example of a points-based standard that incorporates elements of both category- andactivity-based design The standard awards points according toseveral different criteria

bull Criterion 1 Processdocumentationmdashthe standardawards points for following certain processes in document-ing product activities and in managing the product suchas using an environmental quality control system

bull Criterion 2 Threshold propertiesmdashthe standard awardspoints for crossing certain thresholds such as eliminat-ing toxics from the product Once the specific thresh-old is crossed no more points can be earned in thecategory

bull Criterion 3 Tabular threshold propertiesmdashthe standardawards points on the basis of crossing thresholds but anincreasing number of points are awarded according to thehighest threshold crossed This is typically applied to ma-terials and energy usage in the product Greater use ofdesirable materials and energy content and lower overallenergy usage are rewarded

From the perspective of this article the points in criterion1 do not interact significantly with other decisions and are fo-cused more around company policy than the actual materialsand energy content of the product To achieve a threshold incriterion 2 you can increase or decrease the inclusion of spe-cific materials in the product and this may interact with otherlife cycle category improvements These tables are essentiallycategory tables with values of k of 1 or 2 If the material car-ries substantial energy burdens these tables will interact withpoints awarded for reducing energy use if included as a categoryHowever most potentially harmful materials are not includedin products at substantial volumes and thus the impact of theirremoval on categories such as energy use is relatively minorcompared with other material changes in the product Crite-rion 3 is the one that overlaps most clearly the approach ofthis article In the NSF-140 standard these points are earned in



Table 4 Case study of awarded points according to equivalent percentage reduction of energy among different activities

Using postconsumer face Using postconsumer Using postindustrialfiber material backing material fiber

Coefficient 1 0537 0065Use of material to gain 1 point x 0537lowastx 0065lowastxMaximum use of material 0894 1321 0278

three major areas product reclamation recycled or bio-basedcontent and renewable energy and energy efficiency

Carpet Energy Use and Recycling Table Reconstruction

In the NSF-140 standard the total awarded points is 114among which 32 points are awarded for changes in materialand energy use Our focus is on the lattermdash32mdashpoints awardedwith threshold values as shown in table 3 reproduced from theNSF-140 carpet standard (NSF 2007)

Two issues are apparent in this table First table 3 column(a) does not maintain a linear relationship between renewableenergy and awarded points given the allocation of points forless than 10 use of renewable energy or energy reduction Thereason that more points are distributed at the beginning of theenergy percentage reduction in table 3 column (a) is to initiateactivities that improve energy use It does mean that radicalinnovations that dramatically improve energy use would not beas highly rewarded Moreover since the last 2 points are rarelyor never going to be earned 35 probably represents the bvalue for this table Second the implicit assumption is thatthe activities of use of renewable energy and energy reductionare equivalent This is an oversimplification since renewableenergy has a different set of impacts from the energy that wouldbe avoided by reducing energy use

In table 3 column (b) manufacturers can earn 1 point per5 of recycled content except exceeding 5 is required Thepoints are still distributed linearly after this initial offset andso if impacts are monotonic functions of the content this stillcomplies with the first principle

In order to consider specific activities that can be undertakenby a manufacturer and translate them into point rewards weuse recycling activities and their impact on the cradle-to-gateenergy consumption as an example We will assume for thepurposes of illustration that there are three activities that canbe undertaken We choose to reallocate the 32 points in therecycled content and energy reduction tables

Carpet consists of two main elements the face fiber andbacking The face fiber is almost always a synthetic polymersuch as nylon polyester or polypropylene The backing itselfhas a polymer component consisting of thermoplastic fabricsand thermoset glue and a filler We consider the activities ofreplacing the face fiber with a 100 recycled postconsumer(PC) face fiber a 100 postindustrial (PI) recycled fiber and a100 PC backing material

To calculate the change in the inventory of energy use forthese three activities we use an optimization tool for carpet

design for LCI reduction (Lu et al 2011) This tool starts bybuilding the pathways from natural resources to the final prod-uct and cataloging the resource use (including energy) alongeach path The paths that use one of the recycled materi-als but none of the others can be used to calculate the in-ventory reduction from the baseline product with all virginmaterials

Table 4 contains the information from the pathway calcu-lations that is relevant to the table construction The replace-ment of carpet fiber by PC fiber is taken as the base activity witha0 = 1 The amount of equivalent backing and PI fiber is givenin the first row The absolute amounts in kilograms are usedrather than percentages Therefore ai represents the kilogramsof material per kilogram of PC face fiber The maximum useof material is different for these three activities First this isbecause of the different mass of filler in the backing comparedto face fiber Second it is because the PI material can only beused at a fixed percentage in the face fiber and other minorcomponents of the backing fabric x represents the kilograms ofPC face fiber per point Equation (12) gives a value of x = 0239kg The points in table 5 are then created yielding a total pointallocation of 32

0894x

+ 13210537 lowast x

+ 02780065 lowast x

= 32 (12)

Case Study Discussion

The case study reveals several important features of redesign-ing tables according to the goal of rewarding environmentalimpact equally across different activities First PI recycling gar-ners the majority 18 of 32 of the points This is because ofits relatively low energy input to produce the recycled contentthat replaces a high-energy virgin life cycle input Howevermany stakeholders might view this as a perverse outcome be-cause PI material is already widely recycled and is often easierto recycle This is not the problem of the table constructionbut of the initial baseline This could be addressed by reducingthe maximum amount of PI fiber allowed to reflect its presencein the baseline product At the same time the ai coefficientsshould be changed to reflect the differences in the inclusion ofthe recycled materials relative to the new baseline Second theinclusion of the PC face fiber does not garner many points amaximum of 4 of 32 because it is relatively energy intensiveThe stakeholders might be dismayed by this lack of reward foran often highly regarded activity This should not be addressedby ldquofiddlingrdquo with the rewards for life cycle impacts It would bemore transparent for the stakeholders to recognize they value



Table 5 The constructed new standard tables

Postconsumer face fiber materials table Postconsumer backing materials table Postindustrial materials table

Usage of postconsumer face Usage of postconsumer Usage of postindustrialfiber (kgkg of product) Points backing (kgkg of product) Points material (kgkg of product) Points

(0 0238] 1 (0 0129] 1 (0 0015] 1(0238 0476] 2 (0129 0258] 2 (0015 0030] 2(0476 0714] 3 (0258 0387] 3 (0030 0045] 3(0714 0894] 4

(1161 1321] 10 (0255 0278] 18

PC recycling for its own merit and put a weight on this directlyThis would lead to another table in which PI recycling couldgain no points and then the points from this new table areadded back into the two PC activity rewards Third the maxi-mum reduction that can be achieved by the activity does playan important role in the assignment of points Two activitieswith similar relative impacts will be assigned different points ifone can only be undertaken at a rate half that of another Thereduction in the maximum extent of the activity reduces thenumber of points allocated to it in the table This is consistentwith the notion that less activity should lead to fewer pointsOnly the x value changes so the equivalent amount of eachactivity required to earn a point is preserved

Discussion

Standards are general tools to measure product or systemperformance and are used to drive industry toward superior out-comes In a growing body of standards this multidimensionalassessment problem has been approached by allocating pointsto the various activities and impacts considered relevant bythe product stakeholders The point allocation across differentcategories is mostly based on the stakeholdersrsquo previousexperience and may not reflect empirical evidence as to theimpacts of different product activities

The stakeholdersrsquo experiences are indeed valuable andshould be used to shape which categories are included and therelative weights that are placed on different impact categoriesHowever there is a desire to have a more scientifically basedstandard that aligns the standard with environmental impactsparticularly when points are assigned to undertaking differentactivities Moreover since these points are rewarded cumula-tively according to corresponding thresholds how to award thepoints across different activities to equally reward the same im-pact is a key issue

This article has presented a mechanism for point allocationthat can be broadly utilized for many points-based standards Itbuilds on the stakeholder experience and values through spe-cific weightings of impact categories It highlights that thereare two basic approaches to the way points are allocated thosebased on the reduction in impacts and those based on the ac-tivities that are undertaken to generate impact reductions In

the former case the point allocation depends on establishingeither baseline impacts or maximum and minimum impacts Inthe latter case the allocation is more complex The specific ta-bles that map activities to points are constructed to ensure thatpoints are distributed to reward activities appropriate to theirimpacts In addition the other factors that are not directly re-lated to the point allocations for the threshold tables are alsorequired to be defined and included in the standard (eg theindirect impact the time and location impact the LCI datasources and the LCIA methods)

From the standards design point of view activity-basedstandards and category-based standards have their own advan-tages and disadvantages For instance manufacturers may pre-fer activity-based standards because they can most easily maptheir corporate decisions to activities And it is clear how man-ufacturers earn points by improving their activities directlyHowever if a category-based standard is used the manufacturerwould have to do extra work such as LCI and LCIA analysisto translate its activities to each environmental category to getpoints In contrast there are other stakeholders who participatein standards design who might prefer a category-based standardbecause they understand the categories better than the specificactivities of a given industry

An advantage for category-based standards is that it is rel-atively straightforward and practicable to expand the standardwhen including a new category in the standard But for activity-based standards introducing a new activity to the standard di-lutes the points awarded for other activities Overall the majordifference between the two kinds of standards is that eithermanufacturers or the standards developer performs the trans-formation from LCI to LCIA measures However since thetransformation is feasible for mature areas where well-acceptedLCI and LCIA measures and data exist then the developmentof category-based standards is relatively simple In addition it isrecommended that the stakeholders either create activity-onlystandards or category-only standards since a mixture will causepoint double counting for improvements in the same category

A case study for the NSF-140 carpet standard was carriedout to demonstrate the ability to reconstruct tables based onlife cycle information In the NSF-140 standard two tables(manufacturerrsquos use of renewable energy andor energy reduc-tion and manufacturerrsquos use of bio-based recycled content orenvironmentally preferable product [EPP] materials) with 32



points were targeted for refactoring into activity-based tablesIn the case study three tables (using PI material PC backingmaterial and PC face fiber material) instead of two were cre-ated The set of new tables enable the manufacture to use thestandard straightforwardly and encourage them to earn pointsby performing product redesign

Throughout the article we assumed a linear relationship be-tween points and percentage of improvement to ensure an equalpoints allocation of the standard Nevertheless stakeholderswill often desire to deviate from this linear design For exam-ple the initial points awarded may be increased in order toencourage adoption of the standard and the points for greaterimprovements may be reduced since there will be a negligiblechance of these being achieved For thresholds this is best han-dled separately by an ldquoall or nothingrdquo point award For stronglycurved responses it is possible to reward equal increments in theresponse space and use the inventory to impact function to mapback to unequal intervals in the activity or category space

Acknowledgements

The authors would like to acknowledge partial funding bythe State of Georgia USA through its Traditional IndustriesProgram

References

Arrow K J 1951 Social choice and individual values New York NYUSA Wiley

Arrow K J K A Sen and K Suzumura 1997 Social choice re-examined New York NY USA St Martinrsquos Press

Bare J C 2002 TRACI The tool for the reduction and assessment ofchemical and other environmental impacts Journal of IndustrialEcology 6(3) 49ndash78

BIFMA 2012 levelTM Sustainability standard httplevelcertifiedorg Accessed March 2012

Churchman C W and R L Ackoff 1954 An approximate measureof value Journal of the Operational Research Society of America 2(2)172ndash187

Fishburn P C 1967 Additive utilities with incomplete product set Applica-tions to priorities and assignments Baltimore MD USA AmericanSociety of Operations Research

Keeney R L and H Raiffa 1976 Decision with multiple objectivesPreference and value trade-offs New York NY USA Wiley

Koffler C L Schebek and S Krinke 2008 Applying voting rules topanel-based decision making in LCA International Journal of LifeCycle Assessment 13 456ndash467

Lu D M Overcash and M J Realff 2011 A mathematical program-ming tool for LCI-based product design and case study for a carpetproduct Journal of Cleaner Production 19(12) 1347ndash1355

Lu D and M J Realff 2010 Point-based standard optimization withlife cycle assessment for product design Computers amp ChemicalEngineering 34(9) 1356ndash1364

McGinty D 2005 Illuminating the ldquoblack boxrdquo of standard setting Anexploratory qualitative study Applied Measurement in Education18(3) 269ndash287

NSF International 2007 NSFANSI standard 140-2007 wwwnsforgbusinessnewsroompdfSustainability2pdf Accessed March2012

Scheuer C W and A G Keoleian 2002 Evaluation ofLEED using life cycle assessment methods NIST GCR02-836 wwwfirenistgovbfrlpubsbuild02PDFb02170pdf Ac-cessed March 2012

Twing J D D Mueller and K OrsquoMalley 2010 Standard-settingmethods as measurement processes Educational Measurement29(1) 14ndash24

About the Authors

Di Lu is a senior engineer of research and development atBecton Dickinson amp Company (BD) Franklin Lakes NJ USAMatthew J Realff is a professor of chemical and biomolecularengineering at the Georgia Institute of Technology AtlantaGeorgia USA



to understand the influence of cognitive social political andemotional factors during the decision-making process There-fore qualitative research methods such as naturalistic observa-tion and quantitative research methods that draw on researchoutside the measurement area such as research in cognitivepsychology are used to try to understand the standard-settingprocess These aspects of standard setting will not be furtherdiscussed in this article They are important but it is equallyimportant to establish a credible basis for connecting availablescience to the form of the standard Similarly another body ofliterature that is relevant to connecting the results of this arti-cle to overall life cycle decision making is multiattribute deci-sion making and utility theory Churchman and Ackoff (1954)analyze the method of simple additive weighting (SAW) fordecision-making processes with multiple attributes Fishburn(1967) discusses the approach for multiattribute decision mak-ing (MADM) In addition Keeney and Raiffa (1976) discuss theMulti-Attribute Utility Theory (MAUT) for the comparison ofmany diverse measures In the context of life cycle assessment(LCA) Koffler et al (2008) discusses how to apply voting rulesto panel-based decision making MAUT and MADM are im-portant topics for taking the next step to find the weightingbetween different attributes and provide the underlying theoryfor how and why the attributes are scaled with respect to eachother

In sustainability assessment the diversity of product processand company performance metrics creates unique problems inhow to balance the rewards across this diversity and how to syn-thesize a single measure of performance This latter point theconversion of a set of categories into a single multicategory mea-sure is a feature of the sustainability standards such as LEEDTM

(2008) NSF-140 (2007 the Carpet Sustainability AssessmentStandard) and other emerging standards for products For ex-ample the Business and Institutional Furniture ManufacturersAssociation (BIFMA) levelTM sustainability standard (2012)is a multifaceted approach The BIFMA levelTM standard pro-vides manufacturers with valuable resources for evaluating andcommunicating the environmental and social impacts of theirfurniture products and processes based on criteria includingmaterials use of energy atmospheric impacts human healthand ecosystems and social responsibility Therefore manufac-turers now have a methodology to present the environmentalcharacteristics in a clear easily understood manner with a ver-nacular that gives end users the ability to make a fair compari-son Scheuer and Keoleian (2002) discuss how to evaluate theLEED standard using LCA methods The study revealed a va-riety of discrepancies that were in the version of the standardat the time The LCA results compared with the LEED rat-ings showed that these were not always aligned because of thechoice of metrics to reward performance improvements TheLEED and NSF-140 standards resolve the problem of synthesiz-ing a single measure of performance by using points awarded forperformance along each dimension and then adding the pointsto give a total score This creates an interesting challenge forthe development of this type of points-based standard how bestto determine the point allocations across the performance di-

mensions The goal of this article is to lay a foundation for arational allocation of points for the life cycle component of asustainability assessment standard

An ideal but not the only approach for points-based stan-dard setting can be summarized as follows The stakeholdergroup agrees on a category set that they feel reflects the sustain-ability of the system For example the toxicity of the materialsthe amount of waste the energy use in manufacturing the safetyand health of workers and the social and financial performanceof the company The group then decides how many points in to-tal the standard will have The points are then divided betweenthe categories reflecting the importance they assign to themFinally they decide how many points a given performance levelshould receive and allocate the points to the different levels ofachievement Unfortunately this is very difficult to do Oftenthe division or allocation is implicit arrived at by developing aset of activities that can be undertaken to improve a categoryand then allocating points to the activities The points are thentotaled for the activities

For example the current carpet sustainability assessmentstandard in its first version was developed with substantial in-sights from the Joint Committee of this ANSI standard on whatproduct changes might lead to sustainability improvement Ingeneral these potential product changes were simply intuitiveconcepts by which points were subsequently awarded Someof the sustainability improvements (and points) were relatedto organizational-level categories (such as for environmentalmanagement systems) which are vital to achieve change Theother improvements (and points) were directed at material andenergy improvements (such as for bio-based materials) Othernational standards such as LEED also began as intuitive pointsystems to drive change However these organizations have rec-ognized that a science-based approach is ultimately needed forthe improvements related to material and energy changes Thiswill help to avoid creating incentives for activities that maynot provide substantial improvement to the overall life cycle ofthe system A science-based approach requires substantial lifecycle information and the life cycle field has reached sufficientmaturity in many areas to enable this approach to the life cyclecomponent of these standards For example it is possible toevaluate the congruency of an existing standard with life cycleprinciples by optimizing a product design either to maximizethe points awarded in the standard or to minimize the life cycleimpact measures (Lu and Realff 2010)

Methodology

Definitions

We start with definitions of terms used in this article thatcould have different interpretations in other contexts

1 An impact category is an environmental impact suchas global warming acidification or eco-toxicity For ex-ample there are ten impact categories in the TRACI



























I j =sum

q

Cj q lowast meq (1)



















Coefficient 1 a1 am


x a1lowastx am

lowastx

Maximumachievable

b0 b1 bm



I j =

sumq

Cj q lowast meq (3)


I j

(4)























b0

a0 lowast x+ b1

a1 lowast x+ b2



(5)











lowastx] 2


lowastx)





















Assume


[a1 a1] + [a2 a2] = [(a1 + a2) (a1 + a2)] (6)



Then

[a1 a1]


[1a2

1a2

] if a2 = 0 a2 = 0 (9)


b0

a0 lowast x+ b1



[x x ] =[

1Total

lowast(

b0

a0+

nsumi =1

bi

ai

)

1Total

lowast(

b0

a0+

nsumi =1

bi

ai

)]

(11)









Case Study





















0894x

+ 13210537 lowast x

+ 02780065 lowast x

= 32 (12)








(0 0238] 1 (0 0129] 1 (0 0015] 1(0238 0476] 2 (0129 0258] 2 (0015 0030] 2(0476 0714] 3 (0258 0387] 3 (0030 0045] 3(0714 0894] 4

(1161 1321] 10 (0255 0278] 18


Discussion












Acknowledgements


References















About the Authors




























I j =sum

q

Cj q lowast meq (1)



















Coefficient 1 a1 am


x a1lowastx am

lowastx

Maximumachievable

b0 b1 bm



I j =

sumq

Cj q lowast meq (3)


I j

(4)























b0

a0 lowast x+ b1

a1 lowast x+ b2



(5)











lowastx] 2


lowastx)





















Assume


[a1 a1] + [a2 a2] = [(a1 + a2) (a1 + a2)] (6)



Then

[a1 a1]


[1a2

1a2

] if a2 = 0 a2 = 0 (9)


b0

a0 lowast x+ b1



[x x ] =[

1Total

lowast(

b0

a0+

nsumi =1

bi

ai

)

1Total

lowast(

b0

a0+

nsumi =1

bi

ai

)]

(11)









Case Study





















0894x

+ 13210537 lowast x

+ 02780065 lowast x

= 32 (12)








(0 0238] 1 (0 0129] 1 (0 0015] 1(0238 0476] 2 (0129 0258] 2 (0015 0030] 2(0476 0714] 3 (0258 0387] 3 (0030 0045] 3(0714 0894] 4

(1161 1321] 10 (0255 0278] 18


Discussion












Acknowledgements


References















About the Authors







Coefficient 1 a1 am


x a1lowastx am

lowastx

Maximumachievable

b0 b1 bm



I j =

sumq

Cj q lowast meq (3)


I j

(4)























b0

a0 lowast x+ b1

a1 lowast x+ b2



(5)











lowastx] 2


lowastx)





















Assume


[a1 a1] + [a2 a2] = [(a1 + a2) (a1 + a2)] (6)



Then

[a1 a1]


[1a2

1a2

] if a2 = 0 a2 = 0 (9)


b0

a0 lowast x+ b1



[x x ] =[

1Total

lowast(

b0

a0+

nsumi =1

bi

ai

)

1Total

lowast(

b0

a0+

nsumi =1

bi

ai

)]

(11)









Case Study





















0894x

+ 13210537 lowast x

+ 02780065 lowast x

= 32 (12)








(0 0238] 1 (0 0129] 1 (0 0015] 1(0238 0476] 2 (0129 0258] 2 (0015 0030] 2(0476 0714] 3 (0258 0387] 3 (0030 0045] 3(0714 0894] 4

(1161 1321] 10 (0255 0278] 18


Discussion












Acknowledgements


References















About the Authors













b0

a0 lowast x+ b1

a1 lowast x+ b2



(5)











lowastx] 2


lowastx)





















Assume


[a1 a1] + [a2 a2] = [(a1 + a2) (a1 + a2)] (6)



Then

[a1 a1]


[1a2

1a2

] if a2 = 0 a2 = 0 (9)


b0

a0 lowast x+ b1



[x x ] =[

1Total

lowast(

b0

a0+

nsumi =1

bi

ai

)

1Total

lowast(

b0

a0+

nsumi =1

bi

ai

)]

(11)









Case Study





















0894x

+ 13210537 lowast x

+ 02780065 lowast x

= 32 (12)








(0 0238] 1 (0 0129] 1 (0 0015] 1(0238 0476] 2 (0129 0258] 2 (0015 0030] 2(0476 0714] 3 (0258 0387] 3 (0030 0045] 3(0714 0894] 4

(1161 1321] 10 (0255 0278] 18


Discussion












Acknowledgements


References















About the Authors









lowastx] 2


lowastx)





















Assume


[a1 a1] + [a2 a2] = [(a1 + a2) (a1 + a2)] (6)



Then

[a1 a1]


[1a2

1a2

] if a2 = 0 a2 = 0 (9)


b0

a0 lowast x+ b1



[x x ] =[

1Total

lowast(

b0

a0+

nsumi =1

bi

ai

)

1Total

lowast(

b0

a0+

nsumi =1

bi

ai

)]

(11)









Case Study





















0894x

+ 13210537 lowast x

+ 02780065 lowast x

= 32 (12)








(0 0238] 1 (0 0129] 1 (0 0015] 1(0238 0476] 2 (0129 0258] 2 (0015 0030] 2(0476 0714] 3 (0258 0387] 3 (0030 0045] 3(0714 0894] 4

(1161 1321] 10 (0255 0278] 18


Discussion












Acknowledgements


References















About the Authors











Assume


[a1 a1] + [a2 a2] = [(a1 + a2) (a1 + a2)] (6)



Then

[a1 a1]


[1a2

1a2

] if a2 = 0 a2 = 0 (9)


b0

a0 lowast x+ b1



[x x ] =[

1Total

lowast(

b0

a0+

nsumi =1

bi

ai

)

1Total

lowast(

b0

a0+

nsumi =1

bi

ai

)]

(11)









Case Study





















0894x

+ 13210537 lowast x

+ 02780065 lowast x

= 32 (12)








(0 0238] 1 (0 0129] 1 (0 0015] 1(0238 0476] 2 (0129 0258] 2 (0015 0030] 2(0476 0714] 3 (0258 0387] 3 (0030 0045] 3(0714 0894] 4

(1161 1321] 10 (0255 0278] 18


Discussion












Acknowledgements


References















About the Authors

















0894x

+ 13210537 lowast x

+ 02780065 lowast x

= 32 (12)








(0 0238] 1 (0 0129] 1 (0 0015] 1(0238 0476] 2 (0129 0258] 2 (0015 0030] 2(0476 0714] 3 (0258 0387] 3 (0030 0045] 3(0714 0894] 4

(1161 1321] 10 (0255 0278] 18


Discussion












Acknowledgements


References















About the Authors







(0 0238] 1 (0 0129] 1 (0 0015] 1(0238 0476] 2 (0129 0258] 2 (0015 0030] 2(0476 0714] 3 (0258 0387] 3 (0030 0045] 3(0714 0894] 4

(1161 1321] 10 (0255 0278] 18


Discussion












Acknowledgements


References















About the Authors






Acknowledgements


References















About the Authors



the design of a sustainability assessment standard using life cycle information

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