evaluating environmental performance using statistical process control techniques

Stochastics and Statistics

Evaluating environmental performance using statistical processcontrol techniques

Charles J. Corbett a,*, Jeh-Nan Pan b

a The Anderson School at UCLA, 110 Westwood Plaza, P.O. Box 951481, Los Angeles, CA 90095-1481, USAb Department of Statistics, National Cheng-Kung University, Tainan 70101, Taiwan, ROC

Received 28 August 2000; accepted 27 March 2001

Abstract

This paper builds on recent work on measuring and evaluating environmental performance of a process using

statistical process control (SPC) techniques. We propose the CUSUM chart as a tool to monitor emissions data so that

abnormal changes can be detected in a timely manner, and we propose using process capability indices to evaluate

environmental performance in terms of the risk of non-compliance situations arising. In doing so, the paper fills an

important gap in the ISO 14000 and TQEM literatures, which have focused more on environmental management

systems and qualitative aspects rather than on quantitative tools. We explore how process capability indices have the

potential to be useful as a risk management tool for practitioners and to help regulators execute and prioritize their

enforcement efforts. Together, this should help in setting up useful guidelines for evaluating actual environmental

performance against the firm’s environmental objectives and targets and regulatory requirements, as well as encour-

aging further development and application of SPC techniques to the field of environmental quality management and

data analysis. � 2002 Elsevier Science B.V. All rights reserved.

Keywords: Environment; Quality control; Quality management; Environmental performance evaluation; SPC; CUSUM chart; Process

capability indices

1. Introduction

The potential for operations research and op-erations management to make important contri-butions to environmental management practicehas been increasingly recognized by academics and

practitioners alike, as witnessed (among others) byrecent or forthcoming special issues in journalssuch as European Journal of Operational Research(volume 102, 1997, and a focused section on re-verse logistics is forthcoming), Computers & In-dustrial Engineering (Gupta and Flapper, 1999),Journal of Electronics Manufacturing (Gupta,1999), and Production and Operations Manage-ment. Several reviews also testify to this effect; see,for instance, Bloemhof-Ruwaard et al. (1995) andReVelle (2000) for applications of OR to envi-ronmental management, and Angell and Klassen

European Journal of Operational Research 139 (2002) 68–83www.elsevier.com/locate/dsw

*Corresponding author. Tel.: +1-310-825-1651; fax: +1-310-

206-3337.

E-mail address: [email protected] (C.J.

Corbett).

0377-2217/02/$ - see front matter � 2002 Elsevier Science B.V. All rights reserved.

PII: S0377-2217 (01 )00155-2

(1999) for links between operations managementand environment. One area in which OR has clearpotential has been largely neglected, though: theapplication of statistical process control (SPC)tools to environmental process control and man-agement. The potential has been noted before (forinstance, in Corbett and Van Wassenhove, 1993,1995), and Madu (1996) offers a deeper discussionof how a broad range of quality control methods,including control charts, can be applied to envi-ronmental management. The current paper buildson this by discussing environmental applicationsof SPC in greater detail. In particular, processcapability indices are very promising and have (toour knowledge) not been discussed in this contextbefore.

In many countries, the costs of pollution haverisen dramatically during the past decades. Somemajor accidents such as Bhopal and the ExxonValdez have been well publicized, with their totalcosts running into several billions of dollars. Smallaccidents, though they may only affect the localcommunity, clearly also carry a cost to the firm,especially if they occur too frequently. And evenrelatively small emissions in excess of local regu-lations can be very costly to firms through taxesand penalties. Exceeding the amount of SO2 orNOx emissions permitted, or releasing higher con-centrations of heavy metals into the local river, canlead to substantial fines, civil and criminal lawsuits,and even partial or full shutdown of the offendingprocess. Striking the right balance between tightcontrol of these processes while still maintainingefficiency is precisely the purpose of SPC.

Two key approaches to environmental im-provement commonly found in the literature areenvironmental management systems standardssuch as ISO 14000 (see e.g. Marcus and Willig,1997) or EMAS (which requires more public dis-closure of environmental performance data), andthe Total Quality Environmental Management(TQEM) philosophy. ISO 14000, largely analo-gous to the widespread ISO 9000 series of qualitymanagement systems standards, was introduced inFall 1996, and by the year 2000 over 13,000companies worldwide had already sought ISO14000 certification. Early evidence suggests thatthere is significant overlap between ISO 9000 and

ISO 14000, not just in how the standards are de-signed but also in drivers of diffusion (Corbett andKirsch, 2001). Environmental Performance Eval-uation is a key aspect of ISO 14000; indeed, clause4.5.1 (Monitoring and Measurement) of ISO14000 requires that a firm implement ‘‘documentedprocedures to monitor and measure on a regularbasis the key characteristics of its operations andactivities that have significant impacts’’ (Kuhre,1998). With the increasingly widespread adoptionof ISO 14000 and of environmental managementsystems more generally, many firms now havemuch more detailed data on environmental per-formance of their processes than ever before, butoften do not know how to use such data to helpcontrol their processes.

The observation underlying ‘‘Total QualityEnvironmental Management’’ (TQEM) is thatmany of the concepts used in Total QualityManagement (TQM) should also help manageenvironmental impacts, as explained in more detailin Madu (1996) and Angell and Klassen (1999).TQM can be viewed as a holistic approach toquality management, including continuous im-provement, proper training and empowerment ofworkers, appropriate incentives, quality manage-ment systems, and extensive use of SQC tech-niques to support all this. TQEM carries the samephilosophy into the environmental realm. How-ever, most discussions of this analogy so far havefocused on the ‘‘softer’’ aspects of TQM. While allthese are undeniably important, the quantitativetools associated with statistical process controlmethods are a key ingredient of TQM, but onethat has hardly been explored in the TQEM liter-ature. A valuable exception is Madu (1996), whodoes explain how control charts can be used forenvironmental monitoring.

The current paper builds on that by showinghow process capability indices can be useful forquantitatively evaluating environmental perfor-mance of a process with respect to prevailing reg-ulation. This is an important risk managementtool for practitioners, as it helps identify whichprocesses are at risk of provoking complianceproblems, but also for regulators, as it containsuseful information for enforcement. It is commonfor customers to ask suppliers to share their SPC

C.J. Corbett, J.-N. Pan / European Journal of Operational Research 139 (2002) 68–83 69

charts and to reduce acceptance sampling whenthese SPC charts show that the suppliers’ processesare in control; similarly, regulators could ask forenvironmental SPC charts and decide on that basiswhich firms need more or less frequent inspections.

Especially with all the new and detailed envi-ronmental performance data now being gatheredas a result of the trend towards adopting envi-ronmental management systems and ISO 14000,applying quantitative methods as SPC is becomingfar easier than before. However, there are someimportant differences between the quality man-agement and environmental management contexts,which have not been highlighted to date; we dis-cuss the implications of these differences here.

In Section 2 we review some pertinent literatureon environmental management and statisticalprocess control. Section 3 discusses how to per-form measurement, monitoring and evaluation ofenvironmental performance in the context of anexample based on nitrate contamination data.Section 4 explains in detail the stepwise procedurefor combining quality control charts and processcapability analyses respectively for evaluating therisk of a process discharge. Section 5 offers adeeper discussion of process capability analysis inthe contexts of environmental risk assessment andenvironmental regulation and enforcementThroughout, but especially in Section 6, we discusshow the environmental context differs from astandard application to quality control and howexisting SPC techniques need to be modified ac-cordingly. In Section 7 we discuss our findings andoffer suggestions for future work.

2. Review of pertinent literature and theory

The pertinent literature for our purposes can begrouped into two categories: monitoring environ-mental performance, and quality control chartsand related methods.

2.1. Monitoring environmental performance

Many initiatives exist worldwide to monitorair and water quality of entire regions; we only

review a small representative sample here. TheWHO (World Health Organization) air qualitymonitoring project began operation in 1973 andis part of the Global Environmental MonitoringSystem. Sulfur dioxide ðSO2Þ and suspendedparticle matter (SPM) data were selected for in-clusion in the project as indicators of industrialpollution (Koning et al., 1982). Information onthese pollutants was routinely collected from in-dustrial, commercial and residential stations fromone urban area in each of the 14 participatingcountries. From 1976 to 1982, the network hasbeen extended into developing countries, to atotal of 65 cities in over 40 countries. Degraeveand Koopman (1998) apply mathematical pro-gramming to determine a mix of policy measuresto help achieve air quality standards in theEuropean Union.

Others have looked at environmental monitor-ing at a local rather than regional level. Crockett(1997) reports on water and wastewater qualitymonitoring at McMurdo research station in Ant-arctica. Results of the effluent monitoring effortsshow that concentrations of metals, particularlycopper, are considerably higher than before. Atthe individual facility level, Friend (1998) suggestsa set of metrics that may impact both profitabilityand environmental quality, capture and quantifyeco-efficiency costs and benefits, and help manag-ers understand and focus on tangible, yet difficult-to-quantify benefits such as innovation, etc. Inorder to do this, he developed eco-efficiency met-rics for cost structure and input measures includ-ing the consumption of energy, water, materialsand labor; the output measures include solidwaste, air emissions, effluents, packaging andthroughput, etc. Miakisz and Miedema (1998) re-port that 33 electric utility companies in the USand Canada participated in a unique environ-mental benchmarking program (EBP). The EBPprovides each participant with ideas on how toimprove its performance measures in eight differ-ent categories, such as heat rates, combustionturbines, energy savings, air emissions, and otherresiduals.

Pollution prevention technologies have gener-ally been advocated as holding potential to movemanufacturing operations toward sustainable de-

70 C.J. Corbett, J.-N. Pan / European Journal of Operational Research 139 (2002) 68–83

velopment and improved environmental perfor-mance (Lewis, 1988). For various reasons, firms inEurope have historically been more proactive inpollution prevention than firms in the US whotend to rely more on end-of-pipe measures (Gra-edel and Allenby, 1995, p. 80). However, the Pol-lution Prevention Act passed in the US in 1990explicitly states that ‘‘source reduction is moredesirable than waste management and pollution,yet opportunities for source reduction are oftennot realized’’ (Freeman, 1995, pp. 28–29). Mea-sures of performance have grown more varied overthe past two decades, as different stakeholders seekto assess a broad range of environmental impacts.Since 1987, all US manufacturing plants are nowrequired by the Environmental Protection Agencyto publicly report all toxic pollutants released, inthe so-called Toxic Releases Inventory. Carreraand Iannuzzi (1998) pointed out that many com-panies do not track or measure environmentalcosts and therefore do not know their true envi-ronmental costs. Applying SQC methods as ad-vocated here can help firms measure and interprettheir environmental impacts and associated costsmuch more meaningfully.

2.2. Quality control and environmental management

The term ‘‘Total Quality Environmental Man-agement’’ (TQEM) has come into vogue in recentyears, as witnessed by the large number of articleson the subject and even journals bearing that name(Total Quality Environmental Management andEnvironmental Quality Management). The under-lying philosophy of TQEM is that the principles ofTQM apply to environmental improvement too(Angell and Klassen, 1999). Though the potentialof applying quality control tools to environmentalmanagement has been pointed out before (Corbettand Van Wassenhove, 1993, 1995; Madu, 1996),the current paper goes beyond those works byhighlighting the potential of process capabilityindices as a tool for environmental performanceevaluation, and by offering a more detailed dis-cussion of the differences between the qualitycontrol and environmental management contextsand the consequences for carrying SPC tools de-

veloped for the former arena over into the latterarena. The extensive review by Angell and Klassen(1999) supports our belief that these questionshave not yet been explored.

ReVelle (2000) states that operational researchhas been usefully applied to a wide variety of en-vironmental problem areas including water re-source management, water quality management,solid waste operation and design, cost allocationfor environmental facilities, and air quality man-agement. Despite almost four decades of such ac-tivity, challenging operational problems remain inall of these areas. A similar argument can be madeabout the application of modern statistical processcontrol charts and related methods to the field ofenvironmental quality management since thesetechniques still remain unfamiliar to most envi-ronmental personnel. Although control chartshave gained considerable acceptance for sometypes of quality checks familiar to environmentalchemists (Juran and Gryna, 1993), they are lessfrequently applied in environmental monitoring.One reason for this lack of use is that most refer-ences emphasize control charts for mean and range(X and R charts) which are not usually applicablesince environmental samples are not commonlyrun in replicate.

Woodall and Montgomery (1999) provide anoverview of current research on control chartingmethods for process monitoring and improvement.They offer a historical perspective along with ideasfor future research. Woodall (1997) presents acomprehensive bibliography on control chartingmethods using attribute data, for example, p, np, cand u charts, which might be applicable for mon-itoring qualitative environmental indicators. Per-formance of control charts is commonly evaluatedbased on their average run length (ARL), the av-erage number of samples required to detect an out-of-control point. Exponentially weighted movingaverage (EWMA) control charts are developed formonitoring the rate of occurrences of rare eventsbased on the interval times of these events. Gan(1998) provides a simple procedure for determin-ing the parameters of a one-sided or two-sidedEWMA chart. Cumulative sum (CUSUM) charts,first proposed by Page (1954) and studied since bymany authors, have proven to be very effective in


detecting small process shifts. Both Gan (1998)and Pan and Lin (1999) found the CUSUM chartto be optimal for detecting shifts in the processmean, while the EWMA chart is found to beslightly less sensitive due to subjective selection ofthe smoothing constants.

Each control chart method has its advantagesand disadvantages. Some authors (Montgomery,1980, 1996; Woodall and Montgomery, 1999) useeconomic criteria to determine optimal chart pa-rameters. Montgomery (1980) presents a compre-hensive review and survey on these economicdecision models. Ho and Case (1994) also providea brief literature review on economic design ofcontrol charts. These economic control charts havenot yet been widely applied in practice, primarilydue to the difficulty of arriving at reliable estimatesfor the cost parameters involved. However, in thecase of emissions monitoring, the cost of an out-of-compliance situation is often defined preciselyby the prevailing legislation, in the form of pen-alties and taxes for excess emissions. Further ex-ploration of economic control charts forenvironmental process control is a promising areafor future research; for the moment, we start withexploring how to modify conventional controlcharts and process capability analyses for envi-ronmental purposes.

3. Measurement, monitoring and evaluation of

environmental performance

Here, we first outline the general problem ofenvironmental process control and evaluation. Westart with some issues related to measurement,then monitoring using modified control charts,and performance evaluation using process capa-bility indices.

3.1. Measurement

Accurate measurement is naturally a prerequi-site for meaningful process control, and measure-ment of environmental performance indicators iseven more challenging than it is for traditionalquality control purposes. Contamination is a

common source of error in all types of environ-mental measurements. Most approaches presentnumerous opportunities for sample contaminationfrom a variety of sources (Lewis, 1988). This sec-tion addresses the problem of assessing and con-trolling sample contamination. A similar approachmay also be applied to other types of environ-mental problem, such as air and water qualitymonitoring, as long as the key quality character-istics and their specification limits are clearly de-fined. Lewis (1988) indicates that equipment andapparatus, sampling in the field, sample contain-ers, ambient, glassware, and reagents, etc., arecommon sources of contamination. The mostcommonly used analytical tools for assessing andcontrolling sample contamination are blanks. Ac-cording to Lewis (1988), there are three types oflaboratory blanks: system, solvent and reagentblanks for assessing and controlling many types oflaboratory contamination. There are also threetypes of field blanks: matched-matrix, samplingmedia, and equipment blanks, which are used toprovide information about contaminants that maybe introduced during the sample collection, stor-age, and transport. Regardless of the types ofblank used for the application, one should mini-mize the potential risk for inadvertently introduc-ing contamination during the preparation of theblank or at any other point where the actualsamples are not exposed to a similar opportunityfor contamination. When properly used, blanksare very effective tools for assessing and control-ling sample contamination and in adjusting mea-surement results to compensate for the effect ofcontamination (Lewis, 1988). Whether blank dataare used primarily for ongoing process control orfor retrospective assessment, Shewhart charts(mean and range or mean and standard deviation,i.e. X–R or X–S) and other types of control chartsprovide the most effective tools for monitoring andinterpreting the blank results.

3.2. Monitoring

Process control using control charts typicallyinvolves two phases (Gan, 1998; Montgomery,1996). A process being ‘‘in control’’ implies that


the process is stable and the probability distribu-tion does not vary significantly over time. A con-trol chart would be a test of the hypothesis that theprobability distribution of observation x is sta-tionary, i.e. the mean of the distribution is con-stant. In general, the population mean will beunknown. The first period of the data analysis,also called the base period, is used for estimatingthe population mean as well as for establishing thetentative or trial upper control limit (UCL) andlower control limit (LCL). Any out-of-controlpoints for which assignable causes can be foundshould be removed or eliminated before the trialcontrol limits are calculated. Depending on how,when and where the measurements are taken, onemay need to look beyond the boundaries of theprocess itself for assignable causes, further thanone would normally do in the context of qualitycontrol.

These estimated values are used for the subse-quent period, known as the monitoring period. Theestimated population mean obtained during thebase period continues to be used during this period.Any rejection of the hypothesis that the processmean remains unchanged would be called ‘‘processout of control’’ or ‘‘lack of control’’, indicating thatthe process is unstable. Shewhart control charts arebased on the Central Limit Theorem, which meansthe sampling distribution will follow the normaldistribution, regardless of the shape of the under-lying population distribution when sample size n issufficiently large. If the population distribution issymmetric, then even with n ¼ 4 or 5, the samplingdistribution tends to approach the normal distri-bution. However, as most environmental data, suchas blanks for contamination, are not commonly runin replicate, the Shewhart control charts for meansand ranges are not usually applicable. In this case, aspecial type of control chart for individual mea-surements based on moving ranges of observations(the so-called IX–MR chart; Wadsworth et al.,1986, p. 192), is used for monitoring the blank re-sults. The moving range of a series of observationsxi ði ¼ 1; . . . ; nÞ is commonly defined as MRi ¼jxi � xi�1j for i ¼ 2; . . . ; n. Since the Central LimitTheorem cannot be applied to the distribution ofindividual measurements, a Lack of Fit test must beconducted on the blank measurements before set-

ting up the control limits. Once normality of themeasurements has been confirmed, the trial controllimits for the individual values are commonly es-tablished as follows (Wadsworth et al., 1986,p. 192):

UCL ¼ l̂l þ 3r̂r ¼ l̂l þ E2MR ¼ l̂l þ 2:66MR;

LCL ¼ l̂l � 3r̂r ¼ l̂l � E2MR ¼ l̂l � 2:66MR;

where l̂l represents the process mean, E2 is a con-stant which depends on the number of observa-tions used for the moving ranges (and E2 ¼ 2:66when consecutive pairs of observations are used),and MR ¼

Pni¼2 MRi=ðn� 1Þ represents the aver-

age of the moving ranges.

3.3. Evaluation

If the blank measurements are within the UCLand LCL and only a random pattern of variationoccurs, then this process is said to be in statisticalcontrol or stable. As long as the blank results arein control, then process performance can be pre-dicted by process capability analysis. Process ca-pability analysis compares the inherent variabilityof the process with the specification limits, in ourcase emission limits, so that the environmentalperformance potential can be detected undernormal, in-control conditions. The process capa-bility index, defined as Cp ¼ ðUSL� LSLÞ=ð6r̂rÞ,where r̂r is the estimated standard deviation of theprocess under statistical control, is the specifica-tion range divided by the process spread. It mea-sures potential capability, assuming that theprocess average is equal to the midpoint of thespecification range and that the process is incontrol (Juran and Gryna, 1993). Using 6r̂r as thedenominator is equivalent to defining the Cp indexto be equal to 1 whenever the specification limitsare three process standard deviations away fromthe mean. This has been found to be a usefulbenchmark for quality applications; for environ-mental control purposes, it is unknown whether adifferent range than 6r̂r might be more appropri-ate. More experience is needed with differentprocesses and regulatory environments in order to


determine suitable benchmarks for the environ-mental case.

In environmental contexts, however, one nor-mally only faces an upper specification limit(USL); there is of course no lower specificationlimit for minimum emission levels. In such a case,the Cp index is given by Cp ¼ ðUSL� l̂lÞ=ð3r̂rÞ.The Cpk index, on the other hand, reflects thecurrent process mean’s proximity to the USL orLSL. Cpk is estimated by

Cpk ¼ minfðUSL� l̂lÞ=ð3r̂rÞ; ðLSL� l̂lÞ=ð3r̂rÞg

(Juran and Gryna, 1993). When no Lower Speci-fication Limit exists, Cpk ¼ ðUSL� l̂lÞ=ð3r̂rÞ ¼ Cp.Montgomery (1996) shows several values of the Cpindices, along with the associated values of processfallout, expressed in non-conforming parts permillion (ppm). These potential process defectivesor fallouts were calculated based on a normaldistribution of the key quality characteristics. Forexample, Cp ¼ 1:0 indicates there will be 1350 ppmfor USL only and 2700 ppm for a two-sidedspecification; Cp ¼ 0:5 indicates 66,807 ppm andCp ¼ 1:3 indicates 48 ppm for one-sided specifi-cations, etc. The potential risk of process con-tamination can thereby be determined.

The Shewhart and IX–MR charts are most ef-fective for detecting contamination when measure-ment variability is small relative to the level ofcontamination to be detected. However, manymeasurements may be required to be able to detectsmall sustained shifts in the process mean. CUSUMcharts are better tools for detecting small shifts ofthe process mean compared to the other candidates,such as EWMA charts (Gan, 1998; Pan and Lin,1999). The traditional CUSUM chart directly in-corporates all the information in the sequence ofsample values by plotting the cumulative sums ofthe deviations of the sample values from a targetvalue (Hansen and Ghare, 1987; Montgomery,1996). To better understand the basic principles ofCUSUM charts, let xj denote the measurement ofthe jth sample blank and let l be the target for theprocess mean. TheCUSUMchart is then formed byplotting the cumulative sum up to and including theith sample, i.e. plotting the quantity Si ¼

Pij¼1

ðxj � lÞ against the sample blank number i. Nor-

mally, one uses a V block or mask to detect processshifts. If the process mean shifts upward or down-ward, out-of-control points will lie outside the up-per or lower arm of the mask. In the followingexample, we demonstrate the use of CUSUMchartsfor processmonitoring and apply process capabilityconcepts for assessing the potential risk ofcontamination.

4. An application of environmental control charts

In this section, we describe a step-by-step pro-cedure for applying environmental control chartsand performing process capability analysis; we il-lustrate the procedure using nitrate concentrationdata from Lewis (1988).

4.1. Step 1. Identify the key process indicators andmetrics

Clearly, identifying which process indicatorsneed to be monitored is a critical first step. Severalcriteria play a role in identifying these key processindicators:• Regulation: any emissions that are subject to

regulatory limits should be constantly moni-tored and controlled, to minimize the numberof non-compliances and hence penalties or othernegative consequences.

• Risk: any process variables that are indicators ofpotential accidents should also be selected, aspart of an effective risk management program.

• Public awareness: some types of emissions arenot subject to regulatory limits as such, or thelevel of emissions at the facility in questionmay be well within the limits specified, but ifemissions are tracked and publicly reported,firms may wish to monitor and control themanyway. For instance, the Toxic Releases Inven-tory (TRI) data on emissions of all facilitiesabove a certain size, collected by the EPA inthe US, are now available on the Internetthrough the Environmental Defense Fund’swebsite at www.scorecard.org.Practitioners who have gone through the process

of implementing an environmental management


system, especially along the lines of ISO 14001, of-ten find that this step, known as ‘‘identification ofaspects and impacts’’, is the most challenging. Formany firms, especially less-heavily regulated firms,it is the first time they attempt to systematicallyidentify all areas in which they have significant en-vironmental impact, and to measure that. Suchimpact assessments are often somewhat subjectivein nature; the SPC-based approach we advocatehere allows a far more quantitative and precisemeasurement.

4.2. Step 2. Collect the data using an appropriatedata sheet

After selecting the key process indicators to bemonitored and controlled, the nitrate concentra-tion level in our example, we usually need 20samples to develop the trial limits (see for instanceWadsworth et al., 1986, p. 191). The data, fromLewis (1988), are shown in Table 1. The first 20nitrate concentration blank results correspond tophase I (the base period); blank results 21–60represent the subsequent blank measurements forphase II (the monitoring period).

4.3. Step 3. Examine the distribution of the histor-ical data and perform an appropriate transforma-tion, then plot the data onto an IX–MR chart orother suitable charts

Since the original 20 historical data are signifi-cantly skewed, the raw data were transformed bytaking the natural logarithm of each value. Afterthis transformation, the data show significant im-provement in the normality test. The Kolmogorov–Smirnov test statistic for normality with Lilliefors

significance level is 0.13, less than the critical valueof 0.294 (for n ¼ 20 at 5% significance level). Inother words, we cannot reject the hypothesis ofnormally distributed disturbances, but given thatthe sample size is only 20, we cannot confidentlyaccept the normality hypothesis either. The Shap-iro–Wilks statistic is 0.902 with correspondingp-value of 0.0466, suggesting that we marginallyreject the hypothesis of normality at a 5% signifi-cance level but would accept it at any higher level.Fig. 1 shows the IX–MR charts for the transformednitrate concentration data. If the logarithm, inverseand square root transformations (themost commonones) fail, we might consider using the Johnsontransformation (Pan and Lin, 1999; Polansky et al.,1999) to transform non-normal data to normaldata.

4.4. Step 4. Establish the trial control limits for theIX–MR charts by eliminating the out-of-controlpoints

To develop trial limits for future monitoring,we must eliminate the out-of-control pointswhenever there exist special causes of variation(assignable causes) for these points, as they can-not be considered normal conditions for theprocess. We first eliminate the outliers for theMR chart and check the stability of the chart,then remove the outliers for the IX chart andcheck for the stability too. As one can see fromboth IX and MR charts shown in Fig. 1, obser-vation 11 is an outlier as it lies above the tenta-tive UCL. Fig. 2 shows that, after removing theoutlier, the IX–MR charts passed the stability testfor both the mean and variability. Therefore, thetrial control limits for the IX–MR charts can be

Table 1

Nitrate blank measurements data from Lewis (1988)

Phase I 0.033 0.049 0.002 0.002 0.008 0.002 0.014 0.016 0.009 0.009

1.631 0.063 0.042 0.022 0.093 0.022 0.002 0.002 0.031 0.004

Phase II 0.006 0.028 0.021 0.020 0.031 0.002 0.002 0.026 0.040 0.726

0.081 0.089 0.128 0.053 0.019 0.353 0.353 0.389 0.066 0.731

0.283 0.277 0.213 0.452 0.288 0.051 0.056 0.253 0.054 0.097

0.672 0.221 0.206 0.293 0.128 0.431 0.180 0.108 0.052 0.216


determined. The normality tests also improveafter eliminating the outlier.

4.5. Step 5. Perform the initial process capabilityanalysis for phase I (the base period) to justify thebaseline for assessing the environmental risk

Fig. 2 shows that the nitrate blank process is instatistical control, so a process capability analysiscan be performed to determine the Cp and Cpk in-dices. In the nitrate concentration example, only anUSL is given, with USL¼ 1%. Note that the USLfor the transformed data is USL ¼ lnð1Þ ¼ 0%. Thetop chart in Fig. 3 shows that the transformed ni-trate concentration data follow a normal distribu-tion and that Cp ¼ Cpk ¼ 1:141, which means the

process fallout is approximately 320 ppm. SinceCp ¼ Cpk > 1, we may conclude that the initialprocess capability with respect to contaminationrisk is quite low. The probability of rejection (i.e. anitrate concentration that is not in compliance withthe USL) is 0.032%.

4.6. Step 6. Use the CUSUM chart for detectingsmall sustained shifts of the process mean if necessary

The top chart in Fig. 4 shows the IX chart forphase II (the monitoring period). Note that thetrial limits are based on Step 4 (Section 4.4). Thelower chart in Fig. 4 indicates that the CUSUMchart can be applied for early detection of processchanges. The V block shows that the process mean

Fig. 1. IX–MR charts for nitrate blank measurements (phase I).

Note: The top chart contains the IX chart, the lower chart contains the MR chart for the nitrate concentration data (after logarithmic

transformation) during the trial period (phase I). The dotted lines indicate the tentative LCL and UCL.


shifts downward and we can detect such a trend atpoint 5. Compare this to the top chart in Fig. 4,where the IX–MR chart detected the change atpoint 11. This illustration is consistent with theearlier observation that CUSUM charts are moreeffective in detecting changes in process mean thantraditional IX–MR charts (Pan and Lin, 1999). Inreality, this will lead the decision maker to pro-actively respond to the out-of-control situationand correct the problems in a timely manner.

4.7. Step 7. Continue to monitor environmental datausing the trial limits and take corrective measuresfor out-of-control situations

Analysis of out-of-control situations needs tobe addressed in order to improve the stability andcapability of the process. Periodic review of thespecifications in relation to the process capabilityshould be conducted on a regular basis. The lower

chart in Fig. 3 shows that the process capabilityhas deteriorated during the monitoring period toCp ¼ Cpk ¼ 0:822 < 1, which indicates the poten-tial risk for unacceptable nitrate contaminationlevels has increased from approximately 320 ppmto approximately 8000 ppm. The probability ofrejection is 0.8%, which means the environmentalrisk is much higher than it was during the initialbaseline period. Corrective measures need to betaken to prevent future non-compliances.

5. Evaluating environmental performance using

process capability indices

The procedure proposed in the previous sectionuses cumulative sums of observations to allowoperators to detect process shifts earlier than theymight be able to with a traditional IX–MR chart.In addition, the information used to construct the

Fig. 2. Setting up trial control limits after removing out-of-control points.

Note: The top chart contains the IX chart, the lower chart contains the MR chart for the nitrate concentration data (after logarithmic

transformation) during the test period (phase I). The dotted lines indicate the LCL and UCL.


CUSUM chart is used to perform process capa-bility analyses, to determine the likelihood of theprocess entering an out-of-control state, or, in thiscase, an unacceptable emissions level.

5.1. Environmental risk assessment using processcapability indices

It is particularly the process capability analysisthat can help decision-makers assess whether the

process is capable of complying with existing en-vironmental legislation for a sufficiently largeproportion of time. We will illustrate how theprocess capability analysis can be used in con-junction with risk assessment tools used in aquality control context.

A well-known tool for risk assessment is failuremode and effect analysis (FMEA), as described infor instance Kolarik (1995). Sometimes a criticalityanalysis component is added to this, as for instancein the D1-9000 standards at Boeing. This involves

Fig. 3. Process capability analyses for nitrate concentration data.

Note: The top figure corresponds to phase 1, the trial period; the bottom figure corresponds to phase II, the monitoring period.


identifying each process step that may fail, thenassigning rankings for occurrence probability, se-verity, and detectability. The ‘‘occurrence ranking’’indicates how likely a failure is considered to be(where higher scores correspond to higher proba-bilities), and is related to the process capability in-

dices. The ‘‘severity ranking’’ indicates the potentialimpact of a failure (with higher scores correspond-ing to more serious impact). The ‘‘detectabilityranking’’ indicates how likely it is that a failure cango undetected until its full impact materializes; inthe traditional quality control setting, this is the

Fig. 4. Control charts for the nitrate blank measurements (phase II).

Note: The top figure shows the IX chart, the lower figure shows the CUSUM chart for the nitrate concentration data (after logarithmic

transformation), for the monitoring period (phase II).


probability of shipping products containing an un-detected defect. Higher scores again correspond tohigher probability of defects going undetected. Thethree rankings are then multiplied, and higher totalscores indicate higher risk.

As noted above, with a one-sided specificationlimit, aCp ¼ Cpk ¼ 0:5 would indicate 66,807 ppm;Cp ¼ Cpk ¼ 1:0 indicates 1350 ppm; and Cp ¼Cpk ¼ 1:3 indicates 48 ppm. During the failuremode and effect analysis for Cpk ¼ 0:5, the occur-rence ranking suggests a very high probability ofoccurrence. From the viewpoint of the personevaluating the process, a non-compliance is almostcertain to occur; the highest-ranking score is usuallyassigned in such a case. However, forCpk ¼ 1:3, theprobability of occurrence is remote; the lowestranking score is usually assigned in this case. Otherrisk assessment tools, such as severity and detect-ability ranking, can also be applied to an environ-mental FMEA.

Though clearly the latter case corresponds to aprocess that is far more tightly controlled, theanalysis does not tell us which capability level isrequired for any specific instance. Whether a Cp ¼Cpk ¼ 1:3 is sufficient (as in many manufacturingindustries) or a Cp ¼ Cpk ¼ 1:67 is needed (com-mon in the electronics industry) depends, as always,on the cost of Type I and Type II errors. Given thatthe processes for which the approach proposed inthis paper is most applicable will often be relativelyheavy continuous and semi-continuous industrialprocesses, the cost of stopping the process for a falsealarm might be very substantial. The cost of ex-ceeding the emissions limits can also vary widely,depending on the type of emission, the exact legis-lation and measurement methods, and other fac-tors. We are currently investigating economicdesign of CUSUM charts to incorporate these fac-tors, and are also engaged in applying these linksbetween risk assessment and process capabilityanalysis in a chemical plant.

5.2. Process capability indices and environmentalregulation

Another audience that could benefit fromprocess capability analysis is formed by the

regulatory community. Just as customers ofteninspect their suppliers’ quality by requiring themto submit their control charts and other SPCanalyses, regulators could assess a firm’s degreeof compliance by evaluating its process capabil-ity analysis. The regulator could use this inseveral ways. First, the process capability anal-ysis indicates how many non-compliance situa-tions one would expect over a given period oftime; the regulator can then compare that to thenumber of non-compliances actually found,whether during its own monitoring efforts oraudits, during third-party audits, or through thefirm’s self-reported environmental performance.Second, the process capability analysis can helpa regulator decide where to allocate scarcemonitoring and audit resources. Almost no en-vironmental regulatory agency in the world hassufficient resources to ensure permanent compli-ance of all facilities under their oversight, andprioritizing their monitoring and enforcementefforts is a major challenge. A firm that candemonstrate a high process capability levelwould require far less frequent audits than a firmwith a low capability level. Third, process ca-pability analyses are easier to compare acrossfirms than many other metrics are, such asnumber of non-compliances, total emissions, etc.This means that regulators can use process ca-pability analyses to benchmark environmentalperformance of comparable firms, and can betterassess when firms’ complaints about (proposed)regulations being too strict are justified or ex-aggerated. Each of these potential uses of pro-cess capability analyses naturally also applies tothird-party auditors, such as ISO 14001 auditors.

6. Differences between quality control and environ-mental management

We should emphasize that, although applyingSPC tools to environmental monitoring has sub-stantial potential, whether for air, water or otheremissions, it is by no means a direct and standardapplication. There are some important differencesbetween the quality control setting and the envi-


ronmental monitoring case that apply equally tothe air and water emissions cases.

First, in a majority of quality control situations,the specification limits are bilateral, i.e. deviationsfrom the mean in either direction are undesirable.This is true whether the process involved is apackaging filling line, a machining operation, orone of many other possibilities. For environmentalcontrol, however, specification limits are alwaysunilateral: emissions may not exceed a certainlimit, but there is (clearly) no lower limit. Thisproblem certainly has been studied in the SPCliterature (see for instance Ghosh et al., 1997 orPan and Wu, 1996), but nowhere near as exten-sively as the bilateral case.

Second, in traditional quality settings, thespecification limits generally apply per unit,where the units are the same as the measurementunits used in monitoring. On a machining op-eration, the aim is to avoid a single widget fromfalling outside the specification limits. In theenvironmental case, however, the specificationlimits depend on the prevailing legislation, andwill often concern cumulative or average emis-sions over longer periods, whether hourly, daily,or monthly. In that case, one could be moni-toring the process using daily emissions data,with no specification limits on daily emissionsthemselves, but only an upper limit on totalmonthly emissions. This complicates the designof the control chart and, to our knowledge, sucha situation has not yet been studied in the SPCliterature.

Third, most traditional SPC settings assumethat the underlying stochastic process is univar-iate and stationary, producing uncorrelated ob-servations. Data used in environmentalmonitoring, though, are more likely to be mul-tivariate and/or correlated, as several types ofemission are regulated and these are moreheavily influenced by other common ambientfactors: for instance, SO2 and NOx emissions aredriven in part by the product mix being pro-duced during that period, leading to significantcorrelation over time in emissions data andacross emission types. Some recent developmentsin the SPC literature have considered bothmultivariate and correlated observations (see for

instance Lu and Reynolds, 1999; Montgomeryand Mastrangelo, 1991; Woodall and Faltin,1993), but this is a largely open area and needsto be further explored.

7. Conclusions and future research

In this paper, we describe a detailed quantitativeprocedure for monitoring and evaluating environ-mental performance. We show how an appropriatemodification of existing statistical quality controltechniques, in particular the CUSUM chart andcorresponding process capability analysis, can bevery useful for environmental process managementand monitoring. We have discussed how this wouldwork, using an extended example based on nitratecontamination data. Drawing on existing theoryand based on the example, we suggest that CUSUMcharts are valuable for emissions monitoring, asthey tend to detect process shifts earlier than tra-ditional IX–MR charts. The process capabilityanalysis is particularly promising, as this gives de-cision-makers a concrete tool, to our knowledge forthe first time, to assess the likelihood that theirprocess will continue to comply with prevailinglegislation. We have examined how process capa-bility analysis is useful as a risk management toolfor practitioners but also how it can benefit regu-latory agencies.

Applying principles of statistical quality con-trol to environmental management opens upmany promising areas of research. First, oneneeds to continue to analyze and compare vari-ous types of charts, using emissions data ratherthan defect rates, to determine which design isappropriate for monitoring emissions. More ex-tensive comparisons of traditional IX–MR chartswith CUSUM and other charts should be per-formed. Second, we believe that emissions mon-itoring is a natural application of economiccontrol charts, for which extensive theory existsbut relatively little practical implementation.More theory and more practical guidelines oneconomic design of control charts, specifically foremissions monitoring, is called for. Third, betterunderstanding of the precise form of regulatoryrequirements is needed: the appropriate control


charts and process capability measures dependon whether emission rates may never exceed acertain limit or whether it is average emissionsper unit time that are restricted, etc. We hopethat this paper will provide the motivation forsome of this work.

Acknowledgements

We are grateful to the three anonymous re-viewers for their helpful comments. The secondauthor would like to gratefully acknowledge fi-nancial support from the AT&T Foundation forIndustrial Ecology and the University of Califor-nia Pacific Rim Research Program.

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