www.elsevier.com/locate/wasman

Waste Management 27 (2007) 337–344

A methodology for solid waste characterization based ondiminishing marginal returns

Mukesh Sharma a, Edward McBean b,*

a Department of Civil Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, Indiab University of Guelph, School of Engineering, Guelph, Ont., Canada N1G2W1

Accepted 3 February 2006Available online 5 April 2006

Abstract

A methodology is developed for estimating the number of waste sorts for characterizing solid wastes into categories based on dimin-ishing minimum incremental information. Convergence in the square of the coefficient of variation with successive waste sorts is used toindicate cost-efficient termination of sampling at substantially reduced numbers of sorts in comparison with existing methodologies.These findings indicate that the numbers of waste sorts beyond that determined using the proposed methodology do not add substantialmarginal gains in information and/or reduction in the confidence interval of the estimate. The methodology is demonstrated using wastecomposition analyses from the Greater Vancouver Regional District where 22 waste sorts are examined. The proposed methodology issimple, and the number of waste sorts can be estimated with a hand-held calculator and utilized in the field.� 2006 Elsevier Ltd. All rights reserved.

1. Introduction

Knowledge of the percentages of solid waste within indi-vidual waste category types is important information forplanning solid waste management programs. Planning ele-ments that may require an understanding of the percentagesinclude (i) evaluation of the success, or lack thereof, ofongoing recycling programs, (ii) quantification of the degreeof success of bans to exclude specific materials (e.g., gyproc)from the refuse stream, (iii) characterization of the waste asfeedstock to an incinerator, and (iv) determination of quan-tities of organics in the waste stream which influence biogasproduction levels once the waste is landfilled. However, thenumber of waste sorts needed to answer (i)–(iv), to effi-ciently characterize percentages for individual categoriesof the waste, remains an important question.

To quantify the percentages of solid wastes in individualcategories, the Greater Vancouver Regional District(GVRD) authorized the completion of a number of waste

0956-053X/$ - see front matter � 2006 Elsevier Ltd. All rights reserved.

doi:10.1016/j.wasman.2006.02.007

* Corresponding author. Tel.: +1 519824 4120x53923; fax: +1 519 8360227.

E-mail address: emcbean@uoguelph.ca (E. McBean).

sorts (CRA and CAS, 1999). Waste sorts divided the wastesinto 9 primary categories and 31 secondary categories. Fromthis substantial database, the research described hereinassesses the information content from varying numbers ofwaste sorts, and develops a simple methodology for selectingefficient numbers of waste sorts to characterize solid wastes.

2. Literature review of current waste composition

methodological approaches

There are two general approaches taken to analyze solidwaste stream composition, the ‘material flows approach’and the ‘output method’ (McCauley-Bell et al., 1997).

The material flows approach considers the productionand expected lifecycles of products and, from these, esti-mates the waste stream percentages (by weight) withinthe various categories of waste. This approach considerswaste as the end result of a production lifecycle. An advan-tage of the material flows approach is the broad geograph-ical scope for which the solid waste stream can beestimated, but criticisms of this method include its focuson product categories, and not on waste stream categories.Another problem with the material flows method is that it

338 M. Sharma, E. McBean / Waste Management 27 (2007) 337–344

excludes some waste components because they do not orig-inate from a product sector (e.g., yard waste). The generalconsensus is that the material flows approach is more appli-cable for large geographical areas, e.g., a country-widebasis, rather than local studies (Reinhart and McCauley-Bell, 1996).

The ‘output method’ for estimating the composition ofthe solid waste stream generally occurs at a disposal siteand involves the sampling, sorting, and weighing of indi-vidual categories of the waste stream (Tchobanoglouset al., 1993). The output approach may be used to provideinformation regarding the condition of the waste compo-nents prior to separation or disposal (e.g., regarding thecleanliness, and hence value of cardboard for recycling pur-poses (CRA and CAS, 1999)). Following the sampling,sorting, and weighing procedures, statistical analyses areperformed on the data.

Advantages of the output method include its provisionof information unique to local planning for waste collec-tion, recycling, treatment, and disposal. A disadvantageof the output method is the cost associated with a wastecomposition study, which often limits the number of wastesorts. A review of cost data by Reinhart and McCauley-Bell (1996) reported results for 15–80 waste sorts, withcosts ranging from US$11,000 to US$26,000. As the stud-ies increased in size and complexity (to include moisturecontent analysis, for example), the cost ranged fromUS$63,000 to US$111,500 for 94–217 waste sorts. Themean cost per waste sort for all of the studies wasUS$488 ± 177 (Reinhart and McCauley-Bell, 1996). Expe-rience regarding costs for waste sorts undertaken for theGVRD study for 22 sorts was US$425 per sort.

Another disadvantage of the output method is the vul-nerability of the data to bias due to demographic issues, sea-sonality, and irregular events. Nevertheless, the ability totailor the output method to local needs (e.g., source typegeneration characteristics, and seasonal variability) makesit the preferred choice. Questions remain regarding wastesort designs to attain the accuracy (confidence) needed forproper disposal/incineration operation/recycling programinterpretation. This includes whether increases in the num-ber of sorts add to statistical significance (Klee, 1991).

All of the three following literature methods are basedon the ‘output’ method but the differences arise in termsof the recommended necessary number of waste sorts. Allare structured around estimates of the statistics and thenormal distribution, in selecting the confidence interval.As will be noted, none of the methods work for categorieswith low mean percentages or large variances, as the num-ber of waste sorts estimated as needed become infeasible.

2.1. Approach 1: ASTM methodology

The American Society for Testing and Materials(ASTM) has developed a standard test method for deter-mining the composition of unprocessed municipal solidwaste (ASTM, 1992). This method provides a script for

conducting a waste composition study, including a statisti-cally based method for estimating the number of sorts forwaste characterization. The number of sorts required toachieve the desired level of measurement precision is afunction of the categories under consideration, and thedesired confidence level. The calculations are an iterativeprocess, beginning with a suggested sample mean and stan-dard deviation for waste components based on historicalstatistics as an initiating point. Typically, a 90% confidenceinterval is selected (ASTM, 1992). One of the problemswith the ASTM method is that the table used for the meansand standard deviations was developed in 1972 using dataaggregated from one-week sampling periods at several dif-ferent solid waste facilities around the US (McCauley-Bellet al., 1997). Since waste composition is dynamic, changingfrom year to year, the passage of more than three decadesis of concern.

Another problem indicated in the literature with theASTM method is the appropriateness of the normal distri-bution for describing the probability density function forindividual waste categories. Klee (1993) has indicated thatthe data for individual waste categories are not normallydistributed. In fact, Klee (1993) indicated that the dataare generally positively skewed or J-shaped; however, fre-quently, the distribution of the estimate of a mean is nor-mally distributed as the number of samples increases(McBean and Rovers, 1998). It is noted that tests of nor-mality were checked for 10 data sorts from the waste sortdata presented below using the Anderson–Darling Testand the normality assumption held for P = 0.05. For asmall number of samples, the t-distribution may be pre-ferred to the normal distribution. This issue of using thet-distribution over the normal distribution is discussed laterin the text where it is noted that it becomes difficult to usethe t-distribution to determine sample size, as the t-valueitself is a function of sample size (N).

2.2. Approach 2: USEPA methodology: PROTOCOL – acomputerized solid waste quantity and composition

estimation system

PROTOCOL is a software for estimating the number ofwaste sorts required to characterize waste percentages inindividual categories (Klee, 1991, 1993). Currently, PRO-TOCOL uses waste composition data (mean and standarddeviation) generated in 1972 for the US as first estimates ofnecessary sample sizes. McCauley-Bell et al. (1997) recom-mends that the default waste composition data be replacedby more current information on waste characterization(e.g., Florida waste stream components).

2.3. Approach 3: CIWMB (California Integrated Waste

Management Board) Guidelines

CIWMB (1990) recommends the number of waste sorts,N, required for a statistically representative sampling bythe following equation (Klee and Caruth, 1970):

Table 1Waste categories and percentages within individual categories employed inGVRD study

Primarycategories

Secondary categories Meanquantity(%)

Standarddeviation(%)

CV

Metals 3.40 1.50 0.45Ferrous (foods) 0.87 0.64 0.73Ferrous (other) 1.50 1.49 0.98Nonferrous (beer) 0.06 0.08 1.20Nonferrous (soft drink) 0.15 0.11 0.75Nonferrous (food) 0.30 0.27 0.90Nonferrous (other) 0.30 0.29 0.97Other 0.22

Paper 32.29 10.57 0.32Fine, computer paper 5.00 6.06 1.22Newsprint 5.30 4.30 0.81Cardboard 5.10 3.12 0.61Other 16.90

Plastics 13.31 5.37 0.40Film 6.66 2.43 0.37PET 0.83 0.74 0.89HDPE 1.09 0.81 0.72PVC 0.11 0.11 1.01LDPE 0.12 0.15 1.24PP 0.29 0.19 0.67PS 1.10 0.63 0.59Other 3.11

Organics 37.40 11.11 0.30Yard & garden 5.61 5.90 1.05Food waste 18.77 12.20 0.65Wood – secondary waste 7.43 9.50 1.28Textiles 3.86 3.83 0.99Rubber 0.99 1.88 1.89Multiple materials/other 0.74

Glass 3.10 2.29 0.77Beverage 1.80 1.62 0.92Food 0.60 0.67 1.18Other 0.74

Inorganic 2.90 3.80 1.30Gypsum/drywall 0.10 0.31 3.12Rock/sand/concrete 1.60 2.70 1.70Other 1.2

Householdhazardouswaste (HHW)

5.94 3.03 0.51

Medical/biological 3.90 3.32 0.84HHW Containers 1.90 2.10 1.10Other 0.14

Statistics (mean and standard deviations) as determined from 22 wastesorts.

M. Sharma, E. McBean / Waste Management 27 (2007) 337–344 339

N ¼ ZSd

� �2

ð1Þ

where Z is the standard normal deviate, a function of sta-tistical significance; S the standard deviation; and d is thelevel of precision required.

As an indication of the number of waste sorts implied byEq. (1), for the recommended 90% confidence level, two-sided test, Z = 1.645 and S = 0.1632, transformed (arcsin)basis (as defined in CIWMB, 1990), and assuming thatpaper is the category with the largest mean at 30% andthe desired precision is 10%, then d = 0.03 (i.e., 0.1 · 0.3)and hence the number of waste sorts, N = 80, from Eq.(1). Given the sizable number of waste sorts estimated fromEq. (1), an alternative procedure to establish an efficientvalue of N has merit.

As follows from consideration of the three methods,there is significant need for an efficient procedure to esti-mate the number of waste sorts needed, which provides adefensible rationale for assigning the percentage wastecomposition in the individual categories. As a first step indemonstrating any such procedure, the need exists to havea dataset that can be used to assess the merits of an alter-native procedure.

3. Summary statistics for individual categories as a case

study demonstration

3.1. Sample size (quantity) selection

The waste categories employed in the GVRD assessmentare listed in Table 1, with mean quantity (in% weight),standard deviation (in% weight) and coefficient of variation(CV) (defined as the standard deviation divided by themean, as determined for N = 22 waste sorts). The samplingwas done as per the ASTM method (ASTM Designation:D 523 l-92). The communities from which the wastes werederived are moderately affluent with typical North Ameri-can urban population density (32.5 persons/ha; Ref.www.gvrd.bc.ca/growth). To obtain the waste samples forthe individual waste sorts, a portion of the load from eachtruck (randomly selected for sampling) was dumped on anasphalt surface. Successive representatives, but randomlocations, throughout the dumped load were selected, andthe waste sorts subsequently completed. By this procedure,the pre-measured tare weight of each container used in thewaste sort was subtracted and a tally of the waste loadskept until approximately 136 kg (net) sample was achieved.Thus, a sample of approximately 136 kg was collected in arandom manner for each waste sort.

4. Statistical analyses and number of waste sorts

To establish the percentages of the waste stream withinindividual categories of waste, including estimates of accu-racy of percentage characterizations, the question remainsas to how many waste sorts need to be completed to have

statistical confidence in assigning the percentage of thewaste in individual categories. Defining Xij as the wastepercentage in waste category i, for the jth waste sort, themean X i, for the ith category of wastes until Nth sampleis taken as

X i ¼XNi

j¼1

X ij

N i

� �ð2Þ

340 M. Sharma, E. McBean / Waste Management 27 (2007) 337–344

and the standard deviation, Si, is:

Si ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPNi

j¼1

ðX i � X ijÞ2

Ni � 1

vuuutð3Þ

The confidence limit on the estimate of the mean is then:

CIi ¼ X i ��tSiffiffiffiffiffiNip ð4Þ

where Ni is the number of waste sorts of the ith category andt is the t-statistic at the desired level of statistical signifi-cance. In Eq. (4), as Ni increases, t decreases. In part becauseNi is in the denominator, and is a square root function, thevalue of � tSiffiffiffi

Np

ibecomes relatively stable (i.e., change is typi-

cally <0.2 for each new sample) for Ni P 7 (typically). Thisunderstanding is key to identifying when the confidenceinterval, CI, is relatively insensitive to increases in N.

The CIi in Eq. (4) is relatively insensitive to the distri-bution of Xij. In turn, then, if we specify CIi for exampleto be 30% of the mean (i.e., collect enough sorts so thatwe have a characterization or confidence in the estimateof the mean), then the precision is � tSiffiffiffi

Np

i¼ B, where B is

some specified level such as proximity to the mean, e.g.,within 30% of the mean, then the number of samplesneeded is

Ni ¼tSi

B

� �2

ð5Þ

The investigators described in the preceding subsections(except that they have assumed the normal distributionrather than the t-distribution) have employed this equationin various forms.

It is useful to examine how CI changes from Eq. (4) forincreasing numbers of waste sorts. As an example, themean (from Eq. (2)) and the estimated 90% confidencelimits, assuming that the normal distribution applies

Numbe

11109876543210

25.00

20.00

15.00

10.00

5.00

0.00

Mea

n w

ith

90%

CI

Fig. 1. Mean and confidence interval of

(from Eq. (4)) with increasing numbers of waste sortsfor plastics as a primary category, are depicted inFig. 1. Note that the form of Fig. 1 (and the mean andstandard deviation at each value of N) is dependent uponthe order in which the waste sorts were obtained. This(order of sampling) may show initial instability in thetrend of CI but as N increases, there is stability in mean,standard deviation and CI (per Fig. 1).

As demonstrated in Fig. 1, as the number of waste sortsis increased, there is a decreasing range for the 90% confi-dence interval (CI) (the band width around the expectedvalue decreases (essentially), as illustrated in Fig. 1, andhence indicates greater certainty of the estimate of the truepercentage mean). Fig. 2 depicts the 90% CI-range (i.e.,upper 90% bound minus lower 90% bound) versus numbersof waste sorts used in the quantification of the CI, for theprimary categories of waste. The curves shown in Fig. 2indicate the following:

� For five of the primary categories (plastics, metals, glass,inorganics, and household hazardous) shown in Fig. 2,greater certainty (smaller range for the 90% CI of theestimate of the percentage mean within the five primarycategories) is demonstrated until approximately fivewaste sorts are employed. For N P 5 waste sorts, thereis a smaller range for all waste categories for the 90% CIwith increasing N but the rate of decrease of CI is small.In general, until five samples are taken, the one-side CIon the mean reduces by 2 units per sample whereas forN P 5, the reduction in CI is only about 0.1 units persample for this example application.� Two of the categories, namely paper and organics, dem-

onstrate substantial fluctuations in Fig. 2 in the 90% CI,indicating that there is significant variability in the per-centage of the waste sorts as paper and organics, fromsort to sort. For N P 11, the rate of decrease of the90% CI with increasing N is small.

r of Sorts

24232221201918171615141312

plastics vs. number of waste sorts.

60

Household HazardousInorganicsGlassMetalsOrganicsPlasticPaper

90%

Co

nfi

den

ce In

terv

al R

ang

e ab

ou

t M

ean

50

40

30

20

10

0

9 10 11 12 13 14 15 16 17 18 19 20 21 220 1 2 3 4 5 6 7 8

Number of Waste Sorts

Fig. 2. 90% confidence interval about mean vs. number of waste sorts.

M. Sharma, E. McBean / Waste Management 27 (2007) 337–344 341

Similar to that shown in Fig. 2, results from 90% CI forthe secondary categories of wastes (per Table 1) were deter-mined and plotted (not shown here); all plots for secondarycategories were similar to that shown in Fig. 2 (in pattern,demonstrating diminishing marginal returns following ini-tial instabilities).

Application of Eq. (5) to estimate the required numberof samples is not straightforward as the value of t is alsoa function of N, requiring an iterative procedure to findN. Generally, Eq. (5) is simplified by approximating thet-distribution by the normal distribution and sample stan-dard deviation is replaced by population standarddeviation.

From Eq. (5), and replacing ‘t’ with ‘Z’ and Si with ri

gives

Ni ¼Za=2

Biri

� �2

ð6Þ

where Z is the normal standard deviate (one-tailed) for theconfidence level desired (1 � a), ri is the population stan-dard deviation, and 2Bi is the interval for calculatingCIi ¼ X i � Bi. Based on Eq. (6), for 90% confidence leveland for Bi ¼ 0:3X i; and Bi ¼ 0:1X i;, Ni for each category(primary and secondary) was calculated for the GVRDdata set (see Table 2), where ri was taken as Si fromTable 1. The required number of waste sorts becomes verylarge (for both the 30% and 10% acceptable intervals), par-ticularly for the secondary categories having large CV (e.g.,LDPE in plastic category). These results indicate that ahuge sampling exercise/cost is necessary for the specifiedconfidence in the estimate of the mean percentage weightðX Þ and hence the need for an alternative procedure. As an-other example, from Reinhart and McCauley-Bell (1996)

where the PROTOCOL software for 90% confidence levelfor five waste components (using the Florida adjustedmeans and standard deviations) has been used, the neededminimum numbers of waste sorts are indicated in Table 3.

5. Methodology based on diminishing changes in confidence

limit

It should be recognized that even after the simplificationundertaken to obtain Eq. (6), the required number of sam-ples for some categories can be very large (Tables 2 and 3).However, through the research reported herein, a simplemethodology is presented that identifies when diminishingmarginal returns indicate that termination of sampling iswarranted.

An alternative approach based on Eq. (4) for determin-ing the number of waste sorts is proposed based on reach-ing the point where only small improvements in the CI areobtained. In this method, the required numbers of wastesorts are updated while waste sorting is taking place inthe field. Herein, to demonstrate the proposed approach,Eq. (6) has been rewritten for B ¼ 0:3X (although there isno restriction on the value of B adopted), with sample esti-mates of the standard deviation for the waste category i, Si,replacing ri and substituting Si

X i¼ CVi, and for Bi ¼ 0:3X i:

Ni ¼Za=2

0:3CVi

� �2

Ni ¼ KðCViÞ2ð7Þ

where K = 29.88 (for Za/2 = 1.64 (for 90% confidence)).Hence, while sampling in the field, as each waste sort is col-lected, a new CV is calculated and an update for N isdetermined.

Table 2Required number of waste sorts as per Eq. (6) for various waste categories(for 90% confidence limit on mean)

Number of waste sorts from (3)

I II III

CV N (30%) N (10%)

Primary categoriesMetals 0.45 6 54Paper 0.32 3 29Plastics 0.40 5 44Organics 0.30 3 24Glass 0.77 16 146Inorganic 1.30 51 456Household hazardous 0.51 8 70

Secondary categoryFerr (food) 0.726 16 142Ferr (other) 0.981 29 259Nonferr (beer) 1.2 44 392Nonferr (soft drink) 0.75 17 152Nonferr (food) 0.9 24 220Nonferr (other) 0.966 35 314Fine, computer paper 1.22 45 402Newsprint 0.809 20 176OCC 0.605 11 99Film 0.365 4 36PETE 0.89 24 213HDPE 0.724 17 148PVC 1.01 31 274LDPE 1.235 46 410PP 0.671 13 121PS 0.59 11 94Yard & garden 1.05 33 298Food waste 0.653 13 115Wood – secondary waste 1.279 49 440Textiles 0.99 29 264Rubber (including tires) 1.89 107 964Beverage 0.92 25 226Food 1.178 42 374Rock/sand/dirt/concrete 1.7 85 765Medical/biological 0.84 21 192HHW containers 1.1 37 334

342 M. Sharma, E. McBean / Waste Management 27 (2007) 337–344

The basis of this methodology is that if CV2i becomes

nearly stable in magnitude with additional sampling, thereis little information return for increasing Ni. A measure ofchange in information content between the jth and (j + 1)stwaste sort, then the change, DNi, is

DN i ¼ K½ðCVjþ1i Þ

2 � ðCVjiÞ

2� ð8ÞIf the absolute value of DNi is less than unity, it indicates

that additional waste sorts will not provide significant addi-tional information. This understanding can assist in evolv-

Table 3Number of waste sorts as per PROTOCOL software for CI of 90%

Subcategory number Category Number of waste sorts

1 Newsprint 952 Ferrous 1573 Plastic 234 Aluminum 475 Glass 87

(McCauley-Bell et al., 1997). For 90% confidence limit on the mean.

ing a convergence criterion for stopping the sampling. ForDNi = 0.99 (i.e., less than 1), Eq. (8) becomes the conver-gence criterion:

absolute½ðCVjþ1i Þ

2 � ðCVjiÞ

2� 6 0:033 ð9Þ

This stepwise procedure can be followed as it is simple,relies upon information specific to a site, and sampling canbe terminated once convergence in CV2

i as per Eq. (9) isachieved in two successive samplings. The entire exercisecan be carried out in the field with a handheld calculator.It is noted that this exercise goes on concurrently for allwaste categories under consideration.

Similarly, the convergence criterion in Eq. (9) can becalculated for alternative confidence intervals and accept-able range for the mean value. For example, for 90% con-fidence interval and for the estimated mean to be within50% of the true mean, the value of K is 10.75 and therequired convergence in CV2

i is 0.092 or less. Fig. 3 showsthe value of K as a function of fraction of the mean forobtaining the desired 90/95% confidence interval; the frac-tion on the X-axis when multiplied by the mean will beequal to B in Eq. (6).

To get past the initial instability, one should consider aminimum of 10 samples. The minimum number of samplesis based on experience. It must be recognized that the orderof sampling (which is random) influences the estimate ofthe required number of samples. For example, imagine justby chance that the first five samples showed very low vari-ability where, in fact, the variability is actually high; onemight incorrectly terminate the sampling since the CV iscalculated to be low. In response, we propose a minimumof 10 samples to eliminate the potential problem.

5.1. Demonstration of proposed confidence interval

methodology to GVRD waste sort data

To demonstrate the proposed methodology, the GVRDdata were employed. Fig. 4 presents the CV for the primaryand the secondary categories as a function of mean per-centage weight (%). Fig. 4 indicates the general trend thatthe CV decreases as the percentage of the waste in the ithcategory increases. The pattern in Fig. 4 is similar to thepattern reported by Steir et al. (1999).

For the seven primary categories, determination of Eq.(9) is illustrated in Fig. 5.

The following conclusions for these data can be drawnfrom Fig. 6.

(i) In some categories, after eight sorts (e.g., plastic andorganics; see Fig. 6), there is a convergence in CV2

and there is little additional information gained foradditional waste sorts.

(ii) For paper and household hazardous categories, theconvergence in CV2 for three successive sorts occursat approximately 15 sorts. For inorganics, methoddid not converge even after 22 sorts.

95% CI

90%CI

K-v

alu

e

Fraction of Mean

0.80.60.40.20

120

100

80

60

40

20

0

Fig. 3. Value of K as function of fraction of mean.

0

0.035

0.07

0.105

0.14

0.175

0.21

0.245

0.28

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Number of Samples

abs(

CO

V2 N

+1-C

OV

2 N)

Paper

Plastic

Organics

Metals

house hazardous

Fig. 5. Convergence in CV2 with number of samples.

Primary Category

Secondary Category

CV

Percent Weight

4035302520151050

2.00

1.80

1.60

1.40

1.20

1.00

0.80

0.60

0.40

0.20

0.00

Fig. 4. CV versus %weight of constituent in for primary and secondary categories.

M. Sharma, E. McBean / Waste Management 27 (2007) 337–344 343

Table 4Comparison of required number of sorts (primary and secondarycategories)

Primary categories CV (I) (II)

N (as conventionalapproach, as per (7))

N (as CIMethod, (9))a

Metals 0.45 7 10 (8)Paper 0.32 7 15Plastics 0.40 7 10 (7)Organics 0.30 7 10 (7)Glass 0.77 16 15Inorganic 1.30 51 >22Household hazardous 0.51 8 15Plastic HDPE 0.74 17 17Plastic PVC 1.01 31 18Plastic LDPE 1.23 46 21Plastic PP 0.67 14 17Organic (textile) 0.99 29 19Metal (nonferrous) 0.90 24 16Metal nonferrous (food) 0.90 24 15Metal nonferrous (others) 1.08 32 19

a N constrained as 10, number in parenthesis is unconstrained number.

344 M. Sharma, E. McBean / Waste Management 27 (2007) 337–344

(iii) At a minimum, 10 sorts (even if the method suggestsless than 10 sorts) should be taken to get past initialinstabilities and to ensure that there is no ill-represen-tation of the category due to fewer number of sorts.

For Za/2 = 1.64 (for 90% confidence) and ±0.3 of themean as an acceptable interval on mean (i.e., B in Eq. (5)),the numbers of sorts required are estimated by (I) the con-ventional method, and (II) the proposed method, Eq. (9).

The conventional approach (I, Table 4) and the pro-posed method (II, Table 4) for four categories give similaranswers. However, when the CV is large (column 2, Table4), the conventional procedure generally gives very highestimates of the number of sorts. For example, for PVC,N = 31 as per Eq. (3), and N = 18 as per the normal distri-bution method where convergence was achieved in CV2.The proposed method indicates that there is minimal infor-mation for the numbers of waste sorts beyond 15; the con-fidence interval is not changing appreciably and hence littleis being learned with increases in the number of waste sorts.As soon as convergence in CV2 is identified, there is littlevalue in continuing to sample.

6. Conclusions

The proposed method has been developed to determinethe required number of waste sorts for a waste categorywhile sampling in the field. The information on requirednumbers of waste sorts evolves during the sampling, thusthe proposed approaches are specific to a site. Specifically,

the proposed methodology indicates termination in thesampling when any further addition of waste sorts doesnot add to substantial marginal gain in information.

The convergence in square of CV (coefficient of varia-tion) is a useful indicator when further waste sorts provideminimal improvement. The proposed methodology pro-vides a defensible basis to decrease the number of wastesorts needed over the existing methodologies. This findingoccurs even under the situations when variability in meanis high unlike the existing methods, which may stipulate alarge number of waste sorts. Thus, the proposed methodol-ogy makes the sampling cost-effective without sacrificingsubstantially on confidence in waste characterization.

Acknowledgement

Support from the Erskine Fellowship Award at theUniversity of Canterbury, New Zealand, for providingthe opportunity to prepare this paper is gratefullyacknowledged.

References

ASTM, 1992. Standard Test Method for Determination of theComposition of Unprocessed Municipal Solid Waste. D523 1-92,September.

CIWMB, 1990. General Guidelines for Sampling When Performing aQuantitative Field Analysis for a Solid Waste Generation StudyAppendix (CIWMB – November 1990) (Chapter 9, Appendix 1).

CRA and CAS, 1999. Waste Composition Study for the BurnabyIncinerator. Report to the Greater Vancouver Regional District, May.

Klee, A.J., 1993. New approaches to estimation of solid waste quantityand composition. ASCE Journal of Environmental Engineering 119(2), 248–261.

Klee, A.J., 1991. PROTOCOL, A Computerized Solid Waste Quantityand Composition Estimation System, EPA/600/2-91/005A RREL.Cincinnati, OH, February.

Klee, A.J., Caruth, D., 1970. Sample weights in solid waste compositionstudies. ASCE Journal of the Sanitary Engineering Division 96 (4), 27–34.

McBean, E., Rovers, F., 1998. Statistical Procedures for Analysis ofEnvironmental Monitoring Data and Risk Assessment. Prentice-HallPublishing Co., Englewood Cliffs, New Jersey.

McCauley-Bell, P., Reinhart, D.R., Steir, H., Ryan, B.O., 1997. Municipalsolid waste composition studies. ASCE Journal of Practice Periodial ofHazardous, Toxic, and Radioactive Waste Management 1 (4), 158–163.

Reinhart, D.R., McCauley-Bell, P., 1996. Methodology for ConductingComposition Study for Discarded Solid Waste. University of CentralFlorida, Florida Center for Solid and Hazardous Waste Management,Report #96-1.

Steir, H., Reinhard, D.R., McCauley-Bell, P.R., 1999. An evaluation ofmunicipal solid waste composition bias sources. Journal of Air andWaste Management Association 49, 1096–1102.

Tchobanoglous, G., Theisen, H., Vigil, S., 1993. Integrated Solid WasteManagement. McGraw-Hill Inc., New York.