statistical methods for evaluating the effect of operators on energy efficiency of mining machines

Statistical methods for evaluating the effect ofoperators on energy efficiency of miningmachines

Maryam Abdi Oskouei*1 and Kwame Awuah-Offei2

Research has recognised operators skill as important factors affecting performance and energy

efficiency of mining equipment. Modern monitoring tools generate large, highly variable, and,

often, skewed energy efficiency data sets. Well-conceived statistical tests should be used to

assess the effect of operators on energy efficiency in such situations. However, in many cases in

the mining literature, the choice of statistical tests to evaluate operator effects has not been

systematic and rigorous and, often, the underlying assumptions of these tests have not been

examined before their use. This work provides a systematic method, synthesised from the

statistical literature, to rigorously evaluate the effect of operators on energy efficiency of mining

equipment. Mine engineers and managers can use this method to evaluate whether differences

exist in energy efficiency of their operators given sample data and focus on operator training, if

they find cause to improve operator performance.

Keywords: Energy efficiency, Mining equipment, Operators effect, Mining equipment performance, Statistical tests

IntroductionUS Department of Energy (DOE) energy bandwidthanalysis shows that the US mining industry consumesabout 365bn kW h year21 (1246tn Btu year21) and thereis a potential to reduce the annual energy consumption to169bn kW h (579tn Btu), which is about 46% of currentannual energy consumption. Digging equipment such ashydraulic shovels, cable shovels, draglines, continuousmining machines, and long-wall mining machines con-sume about 23bn kW h (79tn Btu) annually and, using apractical minimum (the so-called 2/3 rule), about 44% ofthis can be saved (U.S. Department of Energy (DOE),2007). The high potential for energy savings in miningoperations, particularly digging operations, has moti-vated mining companies to identify opportunities forimproving performance and energy efficiency.

Different indicators, such as energy efficiency andspecific energy, are used to describe the performance ofdigging equipment and operators. Generally, energyefficiency of an equipment or operation is defined as theratio of useful work done (energy output) to the inputenergy (Zhu and Yin, 2008). In cases where either energyoutput or input cannot be measured easily, proxyparameters are used in their place. Table 1 shows severalexamples of this approach in the literature (Muro et al.,2002; Awuah-Offei et al., 2011; Acaroglu et al., 2008; Iaiand Gertsch, 2013).

Specific energy (energy required to produce unitvolume/mass of rock/soil) is widely used in excavation,tunnel boring, and soil cutting to measure efficiency ofexcavation, boring, or cutting processes (Muro et al.,2002; Acaroglu et al., 2008). For instance, Muro et al.(2002) in designing an experiment to estimate the steadystate cutting performance, for varying cutting depth fora disc cutter bit, used specific energy as the measure ofperformance. Acaroglu et al. (2008) also used specificenergy of a disc cutter for predicting the performance oftunnel boring machines (TBMs). Specific energy has alsobeen used in drilling (Teale, 1965; Dupriest andKoederitz, 2005), shovel excavation (Awuah-Offeiet al., 2005; Karpuz et al., 1992), and ripping (Iai andGertsch, 2013). Specific energy is the inverse of energyefficiency, where material produced (payload) is used asa proxy for energy output. Hence, higher specific energy(or lower energy efficiency) is undesirable.

Operating conditions, mine planning and design,equipment characteristics and operators practice arefactors that can affect the performance of diggingequipment (Lumley, 2005; Bogunovic and Kecojevic,2011; Awuah-Offei et al., 2011; Hettinger and Lumley,1999; Kizil, 2010) (Fig. 1). In a given mine, maximisingenergy efficiency by changing the operating condition isdifficult (e.g. changing blasting practices to changefragmentation) and sometimes impossible (e.g. climaticconditions). Also optimising the equipment mechanismcan be costly. Mine planning and design is a viableway to maximise equipment efficiency. However, it is notalways possible to achieve this objective. Of allthese factors, operators practice and performance is,

2Missouri University of Science and Technology, USA.

*Corresponding author, email [email protected]

1University of Iowa, USA

2014 Institute of Materials, Minerals and MiningPublished by Maney on behalf of the InstituteReceived 6 January 2014; accepted 31 May 2014DOI 10.1179/1743286314Y.0000000067 Mining Technology 2014 VOL 000 NO 000 1

probably, the most inexpensive factor to change.Training operators to improve their performance is arelatively cheap and valid approach in many cases.Before embarking on this type of improvement, it iscritical to first establish that operators actually have aneffect on energy efficiency (i.e. different operators havedifferent energy efficiency numbers). This is not trivial inthe presence of high data variability and asymmetry.

Often, large data on the indicator of performance (inthis case, energy efficiency) can be acquired frommachinemonitoring systems. As these data are highly variableand, often, skewed, care must be taken not to drawconclusions on the effect of operators on energy efficiencyjust from comparing the sample means or performingstatistical tests without considering the limitations of suchtests. Such analysis can result in drawing incorrectconclusion and making poor decisions. Statistical analy-sis of data collected from monitoring systems is acommon and valid tool that can be used to study theeffect of operators on equipment performance. Manyauthors have assessed and compared operators perfor-mance using different criteria and statistical methods toidentify best strategies to improve the efficiency ofoperations (Patnayak et al., 2007; Komljenovic et al.,2010; Awuah-Offei et al., 2011).

Patnayak et al. (2007) used one-way analysis ofvariance (ANOVA) and Tamhanes T2 pairwise test tocompare the average hoist and crowd motor power offour teams of operators to assess the effect of operatorsskills on shovel performance. They did not check thenormality of the data and the equality of variances (thetwo conditions for ANOVA test) prior to conducting theANOVA test. Komljenovic et al. (2010) presented anoperator performance indicator (OPI) that specificallyevaluates dragline productivity and energy consump-tion. OPI was defined as the dragline production dividedby the dragline energy consumption in a given period oftime. By assuming that the OPIs follow the t-distribu-tion (when number of operators are less than 30)different confidence intervals were used to create aclassification system to evaluate operators performancebased on OPI (Komljenovic et al., 2010). This isessentially the t-test, which requires the data to benormal and equal variances both assumptions werenot verified. Awuah-Offei et al. (2011) used t-tests tostudy the differences in the fuel consumption and totalcycle time of operators. Similar to Komljenovic (2010),they did not test for normality and equality of variancebetween operators.

The suggested methods in these works are limited tocertain conditions because of assumptions made of thenature of the data (e.g. Komljenovic et al. (2010)

assuming OPI follows a t-distribution). The authorscould not find any work that provides general guidanceon how to quantitatively evaluate (test) the effect ofoperators on energy efficiency of mining equipment.Data collected from digging equipment tend to havehigh variability. Making accurate inferences on whetherdifferent operators have significantly different energyefficiencies using the digging equipment in the presenceof high variability and data skewness can be challenging.In this work, a process to evaluate the effect of operatorson energy efficiency of mining equipment is formulated.This process suggests the best statistical test forcomparing the operators considering the properties ofthe data set.

Proposed approachAny statistics based approach to study the effect ofoperators on energy efficiency relies on adequate andreliable data. Such data are available, these days, fromequipment monitoring systems, provided care is taken todocument who is running the machine at any time and theoperating conditions. However, the data are often highlyvariable and skewed. Any approach to study the effect ofoperator practice on the energy efficiency of diggingequipment should be able to handle the high variability inthe measured data of the performance metric. Forexample, a simple comparison of the sample means ofthe metric is invalid because it does not address whetherthe difference in means of the metric for the operators isby chance (due to the sample) or is significant.The metric could be any of the examples described in

the previous section, which includes t kW21 h21 fordraglines, tons/gal for truck and shovel systems, andspecific energy for drilling and TBM operations. Theanalytical approach should be a function of thecharacteristics of the observed data. The specific measureof energy efficiency is of little consequence. The approachpresented in this section can be applied to any miningmachine so long as adequate and reliable data can beacquired for a suitable metric for energy efficiency.The t-test and ANOVA are the two most common

tests for comparing the means of different samples. Thet-test is a pairwise test to compare the means of two setswith the null hypothesis of equality of means betweenthem. This test is easy to conduct but can cause type 1error (Zhou et al., 1997). Type 1 error occurs when atrue null hypothesis is rejected (Sheskin, 2004). In thecase of comparing operators performance, type 1 erroroccurs when two operators have equal performancemetric but the test concludes that operators performanceare significantly different. As the t-test is based onpairwise comparison, when there are more than twooperators for comparison, multiple pairwise tests arenecessary. In each run of the t-test at significant level ofa, there is (a6100)% chance of type 1 error. For nOpoperators, the probability of type 1 error is given byequation (1). The chance of type I error increases byincreasing number of operators

Chance of type I error~1{ 1{a nOp

2

(1)

The ANOVA test can replace t-test in cases wherethere are more than two operators to reduce the chance

1 Factors that affect the performance of digging equip-

ment

Abdi Oskouei and Awuah-Offei Evaluating energy efficiency of mining machines

2 Mining Technology 2014 VOL 000 NO 000

of type 1 error. ANOVA is a parametric analysis, whichtests the hypothesis of equality of means between two ormore sets. The null hypothesis is that the mean values ofthe data sets are the same against the alternatehypothesis that at least two sets have different means.For example, ANOVA can help infer whether alloperators at a mine have essentially the same meanenergy efficiency (null hypothesis) or at least two of theoperators have different mean energy efficiencies (alter-nate hypothesis).

Each statistical test has specific assumptions andviolating these assumptions can lead into misapplicationof the test (Herberich et al., 2010; Ankara and Yerel,2010). It is critical to choose a statistical test that iscompatible with the nature of the data set. Preliminarydata analysis can help to better understand the data andcheck for the assumptions of the tests. The beststatistical test should be chosen based on the result ofpreliminary data analysis. The importance of prelimin-ary data analysis and checking the assumptions beforeperforming the test has been overlooked when compar-ing the performance of mining equipment (Patnayaket al., 2007; Komljenovic et al., 2010).

In the case of comparing the means between groupsusing ANOVA or t-test, preliminary data analysisincludes estimating summary statistics, testing fornormality, and testing for equality of variances.Figure 2 shows the suggested approach in this work,which can be used as a guideline to choose the optimalstatistical test that is compatible with the data.

Both ANOVA and t-test require three assumptions.First, the observations should be independent. Thisassumption seems reasonable as we assume thatperformance of one operator does not affect theperformance of other operators. However, the mineengineer should ensure this assumption is true throughgood data collection practices and experimental design.Second, the observations should follow a normaldistribution. Graphical methods and quantitative meth-ods can be used to test for normality of the data. Graphssuch as histograms and quantilequantile (QQ) plots,can be used to compare an empirical distribution and atheoretical normal distribution. Quantitative methodslook at skewness and kurtosis of data and also the resultof statistical tests of normality (such as goodness-of-fittests) to check the normality of the data (Park, 2008).

The ShapiroWilk (SW) (Shapiro and Wilk, 1965),KolmogorovSmirnov (KS), AndersonDarling (AD)

(Anderson and Darling, 1952), and Cramervol Mises(CM) (Anderson, 1961) tests are some of the commontests that are used to test for normality of a data set. SWtest is the most powerful test; however, it is limited tosample sizes greater than or equal to 7 and less than orequal to 2000 (Shapiro et al., 1968; Stephens, 1974). Fordata collected from digging equipment monitoringsystems, even for short periods of observation, thesample sizes are likely to exceed the range of support ofthe SW test. KS, AD, and CM tests are recommendedfor larger (.2000 samples) data sets. These tests arebased on the empirical cumulative distribution (Park,2008; Schlotzhauer, 2009). When the KS test is rejectedit can be concluded that the data do not follow thenormal distribution with the sample mean and samplevariance; however it can be normal at other values of themean and variance. AD and CM tests also share thisweakness (Stephens, 1974; Drezner et al., 2010). Giventhe weakness of these statistical tests, it is helpful toconsider the results of both quantitative and graphicalmethods when testing for the normality. It is probablethat the data violate the assumption of normality. Oneapproach to handle the violation of the normalityassumption is to transform the data (typically using anatural log transformation).

The third assumption requires equal variances ofthe samples. Several statistical tests, including F-test,Bartletts test and Levenes test, examine the differencesin variation among two or more samples. The F-test andthe related Bartletts test are too sensitive to normalityof the data (Schultz, 1983). Levenes test (Levene, 1960;Van Valen, 1978), which is an alternative to the F-test, isrobust even when the data are not normally distributed(Levene, 1960; Van Valen, 1978). Hence, the authorssuggest the Levenes test to analyze the equality ofvariances in this work.

Welch ANOVA and Welch t-test, in which the thirdassumption (equality of variances) is relaxed (Welch,1947), can be used to address the problem caused byviolating the third assumption. Welchs test is apractical, simple and accurate test. It is based onStudents distribution with degree of freedom dependingon both sample size and sample variance. In some cases,Welchs test is recommended as a replacement of t-testeven when the variances are equal (Rodgers andNicewander, 1988; Krishnamoorthy et al., 2007).

To reduce the chance of misusing statistical tests, non-parametric tests can be used alongside parametric tests.Non-parametric tests have fewer assumptions comparedto parametric tests. However, they are less powerful indetecting differences (Schlotzhauer, 2009). The KruskalWallis test, which is a non-parametric equivalent testfor the ANOVA, can be used instead of ANOVA(WilcoxonMannWhitney a replacement for the t-test)(Cody, 2011). The null hypothesis of this test is that allsets (more than two sets) have identical cumulativedistribution function and the alternative hypothesis isthat at least two of the sets differ only with respect tolocation (median). In this test, the assumption ofnormality is relaxed. When performed on log-trans-formed data the results may be invalid in the case ofextremely skewed data (McElduff et al., 2010).

To sum up, it is critical to check the assumptions ofstatistical tests before using them. The proposedapproach (Fig. 3) presents a systematic means to study

2 Process for choosing the best statistical test


Mining Technology 2014 VOL 000 NO 000 3

the effect of operators on energy efficiency. The t-testand ANOVA are the two common tests for comparingthe means of two or more than two data sets,respectively. Data should follow a normal distributionfor valid results of ANOVA and t-test. Quantitative andgraphical methods can be used to test for normality.Non-parametric tests, such as KruskalWallis andWilcoxonMannWhitney, can replace ANOVA and t-test when the data are not normal. Equal variancebetween groups is another assumption of the ANOVAand t-test. Welch ANOVA and Welch t-tests are notsensitive to equality of variances and can be used inplace of ANOVA and t-test when the assumption ofhomogeneity (equality of variances) is violated. Figure 3describes the suggested algorithm of choosing thestatistical test compatible with the data set, for bothcases of two and more than two operators. The result ofvalid statistical tests can be used to investigate the effectof operator practice on the performance of diggingequipment.

Case studyData collected from a Bucyrus-Erie 1570w dragline withbucket capacity of 85 yd3 are used here to illustrate thesuggested method. The main duty of the dragline in thismine is to remove the overburden above the coalseam(s). During the 1-month data collection period,the material type remained, essentially, constant as thedragline was operating in one pit. During the period, 13operators worked on this dragline. Five of theseoperators, with sufficient working hours, were selectedfor this analysis (Abdi Oskouei and Awuah-Offei, 2014).Accuweigh (Tyler, TX, USA) monitoring system on thisdragline was modified (the programmable logic con-trollers were reprogrammed) to record energy consump-tion of drag, hoist, and swing motors. In this study,dragline energy efficiency is introduced as an indicatorof an operators performance. Energy efficiency ofdragline can be determined using the following equation

g~P

Et(2)

where g is the energy efficiency, P is the weight ofmaterial moved by the dragline (payload), and Et is thetotal energy consumed by drag, hoist, and swing motorsduring the cycle.

The energy efficiency of the five operators underreview was calculated for each productive cycle usingequation (3). Table 2 shows the summary of operatorperformance (after removing outliers) during the datacollection period

g(i)~P(i)

Et(i)~

P(i)

Es(i)zEd(i)zEh(i)(3)

where g(i) is the energy efficiency for cycle i; P(i) is thepayload for cycle i; Es(i) is the swing energy for cycle i;Ed(i) is the drag energy for cycle i; and Eh(i) is the hoistenergy for cycle i.

Figure 4 shows the boxplots of the energy efficiency ofthe five operators. Obviously, the data are highlyvariable. As with the mean energy efficiency data(Table 2), one can rank the operators in decreasingorder of median energy efficiency as E, A, C, D and B.Although, the mean and median energy efficiencies varyfrom operator to operator, it is difficult to concludefrom summary statistics and plots (e.g. Figure 4) alonewhether this variation is significant or not (i.e. becauseof sampling). This requires further analysis, which is thescope of this paper.

NormalityPreliminary data analysis includes testing for normalityand testing the equality of variance as described in themethodology section. KS, CM, and AD tests werecarried out at significant level of 0?05 to examine thenormality of data. Table 3 shows the results of thesetests. The results of these tests show that the nullhypothesis in all these tests (data follow normal

3 Algorithm of choosing the best statistical test



distribution) is rejected and energy efficiency of none ofthe operators follows the normal distribution (all p-values are less than 0?005). Log transformation iscommonly used to reduce the skewness of the data(Zhou et al., 1997). Even after log transformation, theresults (Table 4) of the statistical tests indicate that thetransformed data are not normal.Given the weakness of these statistical tests, it is

important to also use graphical methods to gain a betterunderstanding of the nature of the data. Figure 5 showshistograms of energy efficiency for the five operators. Itcan be seen that the data have right skewness and non-normal. Figure 5 shows that the transformed data arecloser to the normal distribution. QQ plots were alsoused to study the effect of log transformation of thedata. These plots compare ordered values of a variablewith quantiles of a normal distribution. The closer thedata are to the normal distribution, the closer the pointswill be to the linear pattern passing through the originwith the unit origin (Johnson and Wichern, 2007).Figure 6 displays these QQ plots of the original dataand the log-transformed data. The comparison betweenthe QQ plots and histograms indicates that logtransformation made the data more normal.

Equality of varianceThe results of the statistical tests show that neither theoriginal data nor the log-transformed data follownormal distribution. These statistical tests cannot alwaysbe trusted. Graphical methods were utilised to confirmthe results of the statistical tests. Histograms and QQ

plots indicate that the assumption of log-transformeddata following normal distribution may be valid.

Levenes test was performed to examine the equalityof variances between the log-transformed data from thedifferent operators. A p-value of 0?0008 was estimated,which indicates that, at a significance level of 0?05, thenull hypothesis of equal variances was rejected. Theresult of the Levenes test showed that the thirdassumption will be violated by this data set.Performing the Levenes test on the original data alsoindicated that the variances between energy efficiency ofoperators are significantly different (p-value,0?0001).

Evaluating operator effectsThis case study compared the energy efficiency of fiveoperators. Considering that t-tests can handle pairwisecomparisons, 10 runs would be needed to compare allfive operators. Therefore, the chance of committing type1 error was 40% (equation (1)). It was concluded that theresults of the t-test cannot be trusted because of the highrisk of committing type 1 error. Also, the assumption ofhomogeneity (equality of variances) between energyefficiency of operators (original and log-transformeddata) is violated in this case. The final conclusion wasdrawn based on the result of the Welch ANOVA andKruskalWallis test. The Welch ANOVA is valid if oneassumes the log-transformed data to be normal and willhandle the fact that the variances are unequal. The non-parametric KruskalWallis test does not require the datato be normal nor have equal variances. It is important tonote that these two tests, which are probably the most

4 Energy efciency of operators

Table 1 Examples of proxy use in mining energy efciency literature

Reference Metric Energy output (proxy) Energy input (proxy)

Acaroglu et al. (2008) Specific energy of disc cutter (kW h m23) Energy used by disc cutter (kW h) Volume of rockexcavated (m3)

Muro et al. (2002) Specific cutting energy of disccutter (kN cm cm23)

Excavation power (kN cm s21) Volume of rock excavatedper second (cm3 s21)

Awuah-Offei et al. (2011) Energy per unit loading rate ofcable shovel (kJ s kg21)

Dynamic energy (kJ) multipliedby digging time (s)

Payload (kg)

Iai and Gertsch (2013) Specific energy of ripper (J m23) Blading or ripping resistance in agiven extraction distance (J)

Width of a wide blademultiply by excavationdepth multiplied by totalexcavation distance (m3)



optimal in a lot of mining situations have never beenused in the mining literature to review the effect ofoperators on energy efficiency or performance. Thesystematic approach suggested in this work will leadmine engineers to the most appropriate test and, hence,reliable conclusions.

The results of the Welch ANOVA test at significancelevel of 0?05 showed that energy efficiency is significantlydifferent between operators (p,0?0001). The KruskalWallis test also confirmed the results of Welch ANOVAtest and indicated that energy efficiency of operators is

significantly different between operators (Table 5). Themine can, therefore, conclude with confidence thatoperator practices affect energy efficiency. The reasonsfor this are explored elsewhere (Abdi Oskouei, 2013).However, the causes of such effects have been welldocumented in the literature (see Knights et al., 2013 forexample).

This example illustrates many of the challenges andpit falls in analysing the effect of operators on energyefficiency of mining equipment. The data are highlyvariable (coefficient of variation more than 25%) and

Table 3 Result of statistical test on energy efciency of operators

Opr A Opr B Opr C Opr D Opr E

Statistic p-Value Statistic p-Value Statistic p-Value Statistic p-Value Statistic p-Value

KS 0.07166 ,0.010 0.06621 ,0.010 0.07527 ,0.010 0.07718 ,0.010 0.0426 ,0.010CM 6.02058 ,0.005 6.34709 ,0.005 7.68707 ,0.005 7.18008 ,0.005 1.2886 ,0.005AD 35.9658 ,0.005 37.9851 ,0.005 45.2889 ,0.005 45.5553 ,0.005 7.7490 ,0.005

KS: KolmogorovSmirnov; CM: Cramervol Mises; AD: AndersonDarling.

Table 2 Summary of operators performance during the data collection after removing outliers

Opr No. of cycles Time/h Material weight/t Energy consumption/kW h Production/t h21 Energy efficiency/t kW21 h21

A 3897 56.91 496 177 44 850 8719 11.063B 3611 54.62 450 217 43 894 8243 10.257C 3350 49.60 427 226 39 827 8613 10.727D 3058 45.64 383 552 36 879 8404 10.400E 2211 32.77 277 554 23 395 8469 11.864

Table 4 Result of statistical test on transformed energy efciency of operators

Opr A Opr B Opr C Opr D Opr E

Statistic p-Value Statistic p-Value Statistic p-Value Statistic p-Value Statistic p-Value

KS 0.04082 ,0.010 0.02514 ,0.010 0.03724 ,0.010 0.02766 ,0.010 0.03113 ,0.010CM 1.97118 ,0.005 0.75778 ,0.005 1.56015 ,0.005 0.79087 ,0.005 0.66522 ,0.005AD 11.7729 ,0.005 4.53897 ,0.005 9.07657 ,0.005 5.66382 ,0.005 5.03061 ,0.005

KS: KolmogorovSmirnov; CM: Cramervol Mises; AD: AndersonDarling.

5 Histogram of energy efciency and log-transformed energy efciency



skewed (non-normal), even after removing outliers. Asimple t-test will have a significant (40%) risk of type 1error. This risk will increase to 98% (equation (1)), if all13 operators at the mine were included in the analysis. Inany case, the use of a t-test cannot be justified in thiscase because the data violate the assumption of equalvariances. The data are not normal but approachesnormal upon log transformation, although the evidenceis inconclusive. Depending on whether one assumesnormality of the transformed data or not, the WelchANOVA and KruskalWallis tests, respectively, areoptimal based on the process presented in Fig. 3. Bothtests result in the same inference: the mean energyefficiency differs among operators (they have an effecton energy efficiency).

ConclusionThis research proposes a two stage process to evaluate theeffect of operators on performance of digging equipmentin mines. The first stage involves evaluating the validity ofthree basic assumptions independence, normality, andequality of variances. It is assumed that performance ofone operator is independent of the others. Graphical andquantitative tests are suggested for testing the normalityof data. Levenes test is suggested for analysing equalityof variances due to low sensitivity to the normality of thedata set. The second stage of the suggested processinvolves tests for equality of means. Depending on thenumber of pairs of operators to be compared, this workrecommends two different processes for determining theappropriate tests. Both parametric and non-parametrictests are considered, based on the stage one analysis (testfor independence, normality, and equality of variances).The goal is to draw the right inference about the effect ofoperators on energy efficiency, given the data propertiesand to reduce type 1 errors.

The proposed method is illustrated with a case studyof a dragline operation. In the case study, 1-monthsdata were collected for 13 operated, with five operatinglong enough to be included in the analysis. Based on themean and median of the energy efficiencies of productivecycles, the operators can be ranked as follows: E, A, C,D and B with operator E being the most energy efficient.However, to establish with confidence whether thevariation in energy efficiencies is independent ofsampling randomness, the proposed approach wasapplied to these operators. Preliminary data analysisshows that the data were non-normal. The analysis wasinconclusive with respect to whether log transformationmakes the data normal or not. The results of analysis,based on the proposed approach, suggest that thevariances of energy efficiencies for the five operatorsare not equal. The Welch ANOVA and KruskalWallistests were found to be optimal depending on whetherone concludes that the log-transformed data are normalor not. Both tests confirm, in this case, that the means ofthe energy efficiencies are significantly (p,0?0001)different. The authors conclude then that, at this mine,the energy efficiency of dragline operations differs fromoperator to operator. Mine engineers and managementcan, therefore, proceed with continuing operator train-ing efforts to improve energy efficiency and reduceenergy consumption.

Acknowledgement

The authors are grateful for the financial support providedby the Energy Research & Development Center atMissouri University of Science and Technology. Theyare also grateful for the support of Arch Coal, Inc. (St.Louis, MO, USA) and Drive & Controls Services, Inc.(Tyler, TX, USA) who helped in the data acquisition.Finally, they are grateful for the reviewers whose

6 Quantilequantile (QQ) plot of energy efciency and log-transformed energy efciency

Table 5 Result of Welch ANOVA and KruskalWallis test

Test Degree of freedom Statistics p-Value

Welch ANOVA 4 F value 154.63 ,0.0001KruskalWallis test 4 x2 614.38 ,0.0001



comments improved the quality of this paper by making itmore relevant to industry.

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