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Precision Engineering 31 (2007) 94–101

Design and analysis of experiments in CMM measurementuncertainty study

Chang-Xue Jack Feng a,∗, Anthony L. Saal b, James G. Salsbury c,Arnold R. Ness a, Gary C.S. Lin a

a Department of Industrial & Manufacturing Engineering & Technology, Bradley University, 1501 W. Bradley Ave., Peoria, IL 61625, USAb Defensive Systems Division, Northrop Grumman Corporation, Rolling Meadows, IL 60008, USA

c Mitutoyo America Corporation, 945 Corporate Boulevard, Aurora, IL 60502-9176, USA

Received 18 February 2004; received in revised form 21 July 2005; accepted 23 March 2006Available online 5 June 2006

bstract

In applying a coordinate measuring machine to measure a mechanical object, many factors affect the measurement uncertainty. Although aumber of studies have been reported in evaluating measurement uncertainty, few have applied the factorial design of experiments (DOE) to

xamine the measurement uncertainty, as defined in the ISO Guide to the Expression of Uncertainty in Measurement (GUM). This research applieshe DOE approach to investigate the impact of the factors and their interactions on the uncertainty while following the fundamental rules of theUM. The measurement uncertainty of the location of a hole measured by a coordinate measuring machine is used to demonstrate our methodology.2006 Published by Elsevier Inc.

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eywords: Coordinate measuring machines; Design of experiments; Measurem

. Introduction

All measurement processes have some extent of uncertainty.hen reporting the measurement result, it is necessary to report

he uncertainty associated with the measurement. No perfecteasurement exits. Instead, the result of measurement is only

n approximation of the value of the quantity being reported.herefore, the measurement result is not complete without theccompaniment of a quantitative statement of its uncertainty.

Numerous studies in the field of coordinate measuring uncer-ainty have been conducted in the past. These studies mainlyoncentrated on the accuracy improvement by developing hard-are, software, and operating strategies. Wilhelm et al. [1]rovided an excellent review of the work in this field. For exam-le, Schwenke, Trapet, Waeldele, and associates have developedvirtual CMM to aid the evaluation of the CMM measurement

ncertainty [2–4,5]. Osawa et al. [6] has recently demonstratedhe use of its application in calibrating cylindrical workpieces.

eckenman and associates have presented measurement strate-

∗ Corresponding author. Tel.: +1 309 677 2986; fax: +1 309 677 2853.E-mail address: cfeng@bradley.edu (C.-X.J. Feng).

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ncertainty; Regression analysis

ies in reducing the CMM measurement uncertainty [7,8]). Thessues of acquisition and computational correction of the equip-

ent specific deviation behavior of a CMM have been examinedy Satrori and Zhang [9] and Zhang and Zhang [10].

In addition, the study of the error compensation issue of aMM has been reported in Zhang et al. [11], Balsamo et al.

12], Kreuci [13], Yee and Gavin [14], and Shen and Zhang15]. Gu and Chan [16] and Limaiem and Elmaraghy [17] havenvestigated inspection planning for CMM by means of optimumequencing and resource allocating.

The combined uncertainty of a measurement result is takeno represent the estimated standard deviation of the measure-

ent result [18]. The combined standard uncertainty is obtainedy combining individual standard uncertainties from Type And/or Type B methods of evaluation, using the usual methodor combining the standard deviations as expressed in Eq. (1).

2C =

N∑ (∂f

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∂x

∂f

∂xu(xi, xj) (1)

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his is often called the law of propagation of uncertainty orhe root sum of squares (RSS) method [18]. It simply says thathe combined uncertainty of each individual uncertainty source

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mdirrmcwphdistance towards the wall of the ring gage at a 45◦ angle wouldresult in a percent increase. Two master ring gages were used inthis experiment. Both ring gages were in pristine condition, asthey had never been used in production.

Table 1Factors and levels of the screening experiments

Factors Levels

Low High

(A) Speed (%) 25 100

C.-X.J. Feng et al. / Precisio

characterized by its variances u2C), multiplied by the square of a

uantity known as the sensitivity coefficient (denoted by ∂f/∂xi)hose magnitude describes the importance of the uncertainty

ource relative to the total measurement uncertainty. The term(xi,xj) is the covariance of xi and xj, and is a measure of theorrelation between these two uncertainty sources.

Once the relationship between the measurement uncertaintynd the measurement parameters are identified, empirical mod-ls could be developed to aid the selection of these parametersiven the complexity and the necessary measurement precision,hich would help either reduce the measurement cost or improve

he measurement productivity.Although a number of studies have been reported in evalu-

ting measurement uncertainty, few have applied the factorialesign of experiments to study the measurement uncertaintyased on the ISO Guide to the Expression of Uncertainty ineasurement, GUM [19]. This research applies the fractional

actorial experimentation to investigate the effect of the factorsnd their interactions on the measurement uncertainty, as definedy the GUM.

In the literature, several related studies have been reportedegarding measurement uncertainty, and its estimations. Thetudies of Feng and Pandey [20] and Feng and Wang [21,22]ere based on the mean absolute percent error (MAPE). A NIST

esearch group [23] used simulation techniques to estimate theeasurement uncertainty when measuring small circular fea-

ures and compared the results with experimental studies. Asointed out by Phillips et al. [23], most CMM measurementso not have a rigorous uncertainty budget. In fact, most of thencertainty in these cases is simply a guess from an experiencedperator. Often, these guesses would fail, and a better methodeeded to be in place for these situations. The problem with thetudy in Phillips et al. [23] is that they did not vary the factors inheir experiments, and therefore no impact from interactions ofeveral factors could be explored due to its simple experimentalesign lacking the presence of multiple factors. In the final stagef our research, Piratelli-Filho and Giacomo [24] reported theirMM uncertainty study with similar methodology for the length

ype of features of ball bar gages. We used a similar methodol-gy but added additional performance measures to study thencertainties of not only the location, but also the diameter of aole. Due to page limit, the latter part is not reported in this paper.eaders interested in the diameter uncertainty study are referred

o Saal [25]. Furthermore, we provided empirical models foreasurement uncertainty of the CMM under consideration.Furthermore, previous studies have contributed to the study

f one or quite a few factors; none of them has systematicallyxamined all five factors simultaneously given a touch triggerrobe. One parameter or another had been neglected, whethert was the factors themselves or the factor interactions, whichs another motivation behind this research. Additionally, nonef the previous studies in the literature had involved any dataining techniques, or the creation of predictive models, except

ur previous studies reported in Feng and Wang [21,22] basedn the MAPE measure but its focus was not to examine theocation uncertainty of the hole as did in Phillips et al. [23]. The

ethodology for predictive modeling part is not reported in this

((((

ineering 31 (2007) 94–101 95

aper due to page limit and is also available in Saal [25] andeng and Wang [26], Feng and Wang [21], and Feng et al. [27].

The research conducted by Tang and Sun [28] at the Cumminsngine Company dealt with the scanning probe in digitization,hile this research deals with the touch trigger probe. The factors

onsidered in Tang and Sun [28] included sample size, speed,tylus deflection, internal diameter (ID) versus outside diameterOD), and feature size. Tang and Sun [28] discovered that thecanning probe has a significant impact on the measurementncertainty.

The remainder of this paper is organized as follows. Sec-ions 2 and 3 cover the experimental study of the parametersn measurement uncertainty in the screening and confirma-ion experiments. In Section 4, we discuss the measurementncertainty study based on the standard deviation. Finally, someoncluding remarks will be presented in Section 5.

. Design and analysis of the screening experiment

The CMM used for the experimental studies is a MitutoyoV-507 located at Bradley University. This older style machineas specifications in accordance to the VDI/VDE 2617 guide-ine [29]. The linear measuring accuracy parallel to the machinexes is U1 = 1.5 + 4L/1000 �m (L is the measured length in mm).he volumetric measuring accuracy is U3 = 2 + 6L/1000 �m. Ifurrent CMM standards were applied, the machine specificationould be MPEE = 2 + 6L/1000 �m in accordance to ISO 10360-:2001 [30]. These specifications apply when the CMM isocated in a temperature controlled environment of 20 ± 0.5 ◦C,hich is not the case for this machine. In addition, the CMM is

quipped with a Renishaw TP2 touch trigger probe.To investigate the effect of the five parameters on measure-

ent uncertainty as shown in Table 1, a fractional factorialesign 25−1 was employed with six replicates. In Table 1, speeds the percentage of the machine’s full capabilities. The probeatio is the ratio between the diameters of the probe and theing gage. The measurement points are the number of pointseasured to determine the location and diameter of the cir-

le. A variety of measurement points were studied to determinehether additional points were necessary. Finally, the startingosition of the probe is defined with respect to the center of theole. At dead center, there is 0% offset, while narrowing the

B) Stylus length (mm) 31 51C) Probe ratio ( :1) 15 38D) Measurement points 5 33E) Starting position (%offset) 20 80

9 n Engineering 31 (2007) 94–101

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The sequential experimentation approach was employed toonduct the experimental study. It follows that a portion ofhe budget is spent on the screening experiment in order toetermine which factors are important in affecting the mea-urement uncertainty. Then only those factors that are impor-ant will be further investigated with more levels if moreudget or time is available. Depending on the results of thecreening experiment, a confirmation experiment will then beesigned and performed. See Emanuel and Palanisamy [31] orontgomery [32] for a discussion of sequential experiment-

tion.A totally randomized run order was attempted for the 96

creening experiments. After reviewing the results of the initialcreening results, a decision was made to run the experiments atix replicates back to back, to maintain repeatability, before mov-ng onto the next experiment. This is because it was extremelyard if not impossible to maintain the same uncertainty once anyactors are changed. Therefore, we decided to replicate exper-ment six times given the same combination of factors, whilelassic texts usually suggest the use of 2 or 3. Replication andandomization are among the three essential principles for DOE.he third principle is blocking, which was used in Feng andandey [20]. For example, one would divide the experimentsonducted during noontime of the day and those during midnights two different blocks due to the big difference in temperaturen the summer if the CMM is at the shop floor instead of at a con-rolled atmosphere. For a good introduction about DOE, refer tohe following excellent texts: Box et al. [33], Montgomery [32],nd Wu and Hamada [34]. The data from the 96 experiments arevailable in Saal [25]. Fig. 1 shows the coordinate system of theMM under study.

Before investigating the results obtained from the screeningxperiment, we examined the several options of the data analysis.ive aspects were investigated from the screening experimentsnd they were x-location, y-location, S-radius, diameter, andhe standard deviations of each. In an effort to avoid ignoringnything that could prove beneficial in the long run, each was

nvestigated. To clarify, the S-radius is the radius used in theetermination of true position tolerance. In fact, it is the radiusrom the origin that the actual center point can be simply cal-ulated based on the locations of x and y using the following

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Fig. 2. Regression analysis of the screen

Fig. 1. Coordinates of the Mitutoyo RV507 CMM.

quation:

i =√

x2i + y2

i (2)

Due to page limit, only representative figures are presentedn this paper. For example, results of analysis of variancesANOVA) for the y-location data are presented in Fig. 2. Minitab35] was used to conduct the ANOVA. Other widely used statis-ics packages can serve the same purpose, such as SPSS fromPSS based in Chicago, Statistica from StatSoft based in Tulsa,klahoma, and SAS based in Cary, North Carolina. According

o the P values found in the last column in Fig. 2, speed, probeatio, and starting offset were the factors that show a significantmpact on the directional measurement uncertainty, since their Palues are not great than 0.05 corresponding to a 95% confidencenterval. Fig. 3 shows the normal probability plot of residualsor the regression equation given in Fig. 2. It shows that theormality assumption of the random errors from the regressionodel appears to be satisfactory. Combining with the adjusted2 value of 90.7% implies that the regression model appears

o have a satisfactory goodness of fit. For a good introduction

n applying regression analysis for empirical modeling, refer toontgomery et al. [36] and Draper and Smith [37]. Figs. 4 and 5

re the main effects plots and ANOVA results for the S-radius,espectively.

ing experiment for the y-location.

C.-X.J. Feng et al. / Precision Engineering 31 (2007) 94–101 97

Fig. 3. Normal probability plot of the residuals for the y-location.

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Table 2Factors and levels of the confirmation experiment

Factors Levels

Low Medium High

(A) Speed (%) 50 62.5 75(B) Stylus length (mm) 31 51(C) Probe ratio ( :1) 9 22((

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Fig. 4. Main effects plot for S-radius.

Although the result of each analysis varies in regards of whatere found to be statistically significant, each of the individ-al main effects were statistically significant in one kind ofnalysis or another with regard to location. As a two-factor inter-ction, all are proven to be of significance as well. Based on thebove results, we determined that no profound basis led to thelimination of any of the factors prior to continuing on for theonfirmation experiment.

. Design and analysis of the confirmation experiment

In an effort to explore any nonlinear effects, three levels werehosen for a portion of the factors in the confirmation experi-

toat

Fig. 5. Regression analysis of the scree

D) Measurement points 12 19 26E) Starting position (%offset) 0 40 60

ent. The fractional factorial experimentation was 25−1 for aotal of 16 factor combinations, while four additional experi-

ents were added to increase three of the factors to a three levelxperiment. Although the factors are the same as in the screen-ng experiment, the levels differ in the confirmation experiments.able 2 shows factors and levels of the confirmation experiment.or the same reason, six replicates were selected to examine theariation within each level. Having six replicates led to a totalf 120 confirmation experiments. The detailed design of exper-ments and experimental data are available in Saal [25].

An analysis of variance was performed to determine whichndividual factors and factor interactions were of significance.

backward elimination approach was taken to eliminate thoseactors which did not have a P value smaller than 0.05. Datarom location measurements were examined first in the x- and-locations as well as the S-radius. Representative results wille provided next.

For each type of analysis, a normal probability plot of resid-als was generated, and all appeared to be satisfactory. Theain effects plots were generated to represent the results of

he regression analysis and shows only the factors that weretatistically significant at the 95% confidence interval. In addi-ion, the interaction plots were also generated based on theNOVA. For example, Fig. 6 shows the interaction plots for

he x-location. The following observations can be made basedn Fig. 6. Fig. 6(a) implies that a shorter stylus length (31 mms opposed to 51 mm) with the highest speed (75.0 mm/s) ledo the smallest uncertainty (see the lower left point). Fig. 6(b)

ning experiment for the S-radius.

98 C.-X.J. Feng et al. / Precision Engineering 31 (2007) 94–101

Fig. 6. Interaction plots from confirmation experiments for x-location: (a) speedand stylus length interaction plot, (b) stylus length and probe ratio interactionp

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lot, and (c) stylus length and start offset interaction plot.

mplies that a shorter stylus length (31 mm) with a larger ratio ofhe probe diameter to the gage ring diameter led to the smallestncertainty (see the right lower point). The ratio of the probeiameter to the gage ring diameter will be called the probe ratioas used in Table 1) later in the paper. This observation meanshat the larger the probe size the better for a given gage ringiameter. The upper left points in Fig. 6(b) mean that a smallerrobe ratio would lead to the largest uncertainty regardless thetylus length.

Finally, Fig. 6(c) implies that a shorter stylus length with theargest start offset position led to the smallest uncertainty (see

he lower right point). This appears to be unusual, but with the

easurement uncertainty smaller than the CMM specificationsn a controlled environment, and the other factors surroundinghese experiments that will be discussed later in Section 4, this

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Fig. 7. Main effect plot for x-location.

esult may not be unusual. Furthermore, all of these interactionlots suggest that the shorter the stylus length the better thencertainty, which appears to agree with our intuition. Noticehat the purpose of this research is to provide a methodologynstead of fingerprinting the uncertainty budget of the machinender consideration.

Based on the main effect plot in Fig. 7, we can concludehat speed makes very little difference with the exception ofhe midpoint of 62.5%. Another nonlinear effect was that ofhe pitch points. The best results came from the fewest points,nd the uncertainty become increasingly smaller as the numberf points increases. According to the observations made basedn the ANOVA and plot, a larger probe ratio and shorter sty-us length should be used to minimize the uncertainty in the-location.

Similar analyses were conducted for the uncertainty of y-ocation, S-radius, and diameter. For example, the y-locationnalysis supported the analysis in the x-location. A shorter stylusength and a larger probe ratio led to reduced uncertainty, andhe uncertainty becomes increasingly smaller as the number of

easurement points increases.The analysis for the S-radius is summarized next. An increase

n speed will reduce the overall uncertainty of the location of theole. Additionally, the uncertainty became smaller as the numberf pitch points increased. However, as one would expect, a lowermount of uncertainties is obtained with a shorter stylus and aarger probe ratio. We discovered from the ANOVA, main effectlots and interaction plots that the uncertainty of the S-radiusan be reduced if the speed and number of measurement pointsre increased as well as if the probe ratio and stylus length areeduced. One of the plots shows that the smaller probe ratioed to a smaller uncertainty no matter what the starting offset.t also shows that the uncertainty slightly reduces as the offsetncreases.

. Uncertainty study based on the standard deviation

In studying the uncertainty, it becomes increasingly importanto investigate the uncertainties of each measurement (exper-

ment) by examining the standard deviation of each set ofix observations (replicates) under the same input conditions.lthough the numbers are in fact small, we will first examine

he effect normal probability plots to determine if any of the

C.-X.J. Feng et al. / Precision Engineering 31 (2007) 94–101 99

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actors were of statistical significance. The effect probabilitylot was employed because only one standard deviation value isvailable for each set of experiments and variations of standardeviation would not be available. Therefore, standard ANOVAould not be applied in this case.

Only one representative plot is shown in Fig. 8. It showshe interaction of factors A and C is statistically significant inetermining the uncertainty of the diameter in terms the standardeviation. The interaction plot of these two factors is given inig. 9. It implies that a smaller probe ratio and a lower speed led

o the smallest uncertainty for the ring diameter in terms of thetandard deviation of diameter measurements. This appears toe in contradiction with the observations made to the x-location,-location, and S-radius as given in Sections 2 and 3. It shoulde in no surprise because different performance measures weresed.

If the position uncertainty is of major concern, then higherpeed with larger probe ratio should be used; otherwise, if theiameter of interest is of major concern, then a lower speedhould be used with a smaller probe ratio. This observationchoes the strength of our research methodology. For example,he study of Phillip et al. [23] offered a good start in using the

tandard deviation to measure the measurement uncertainty, butas able to give only descriptive results. This is because their

xperiments did not change any factors, and their analysis wasased on simple descriptive statistics and graphs. Therefore, no

Fig. 9. The interaction plots of speed and probe ratio for diameter.

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Fig. 10. Confirmation experiment locations plot.

nteractions of factors could be explored or no predictive processnowledge could be gained.

To better illustrate the actual experimental locations, a plotf the points is shown in Fig. 10. The locations shown are inicrometers and further illustrate the rather tight grouping for

he 120 experiments. The experimental results plotted in an areahat is less than 3.2 �m2 squared. In Fig. 10, the graph areaf the individual experiments were set up to represent a verylose approximation to the machines precision, and it is a betterisual aid. The results obtained from this research shows that theeadings are even more accurate than the claimed accuracy of theachine. In fact, we attempted to change the process parameters

s much as possible to get as much variation as we could, andith the exception of actually kicking and/or tampering with

he machine, we were not able to get large uncertainties to evenpproach the limits of the claimed accuracy.

. Conclusion

A methodology was proposed in applying the DOE approacho CMM measurement uncertainty study. More specifically,t follows the sequential experimental strategy to maximizehe information and knowledge we could gain given a limitedmount of budget and time. In the sequential experimentationtrategy, the screening experiment aims at identifying the statis-ically important factors affecting the measurement uncertainty.t is then followed by the confirmation experiment where thosemportant factors identified from screening experiment will beurther examined in more levels or details. Analysis of vari-nce instead of the traditional analysis of means (ANOME) issed to study the effect of each factor and factor interactions.eplicates, randomization and blocking are critical in design-

ng and conducting the measurement experiments. Based on thexperimental data, empirical model was developed by regres-

ion analysis for the purpose of CMM measurement uncertaintyrediction.

With regards to measurement uncertainty, our first consider-tion was that of the standard deviations as suggested by NIST

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n Taylor and Kuyatt [18] and ISO 15530-3 [38]. Looking at theractional factorial plots for the standard deviations, we see thatone of the factors are statistically significant with regards tohe location of a hole. There were no significant factors foundrom the screening experiment when looking at the diameter.owever, the confirmation experiment shows that the interactionf speed and probe ratio is statistically significant. The result-ng interaction plot shows that the uncertainty was reduced at alower speed when using a larger probe size, or smaller probeatio, while faster measurement speeds provides less uncertaintyith smaller probe size, or higher probe ratios.The algorithm used allows the CMM’s measurement uncer-

ainty to be below one micrometer. Several algorithms are avail-ble for users, but for the purpose of this experiment, the leastquares algorithm was used.

When comparing the statistically significant factors for theocation S-radius of both the screening experiment and the con-rmation experiment, we notice that they each had the same fouractors showing the same trends. Although we could not success-ully predict the values, we can certainly utilize these trends toid us in producing a robust process to minimize measurementncertainty. The four factors showed us that uncertainty is mini-ized when the speed is highest, stylus length is shortest, probe

atio is largest, and the number of pitch points is largest. Adher-ng to these results as if they were guidelines will add to the

inimization of the measurement uncertainty.

cknowledgements

Comments and suggestions from Professor A. Weckenmannnd the anonymous reviewers have helped improve the qualityf our presentation.

eferences

[1] Wilhelm RG, Hocken R, Schwenke H. Task specific uncertainty in coordi-nate measurement. Ann CIRP 2001;52(2):553–63.

[2] Schwenke H, Siebert BRL, Waldele F, Kunzmann H. Assessment of uncer-tainties in dimensional metrology by Monte Carlo simulation: proposal ofa modular and visual software. Ann CIRP 2000;49(1):395–8.

[3] Trapet, E, Franke, M, Haertig, F, Schwenke, H, Cox, M. Tracibility ofcoordinate measurements according to the method of the virtual measuringmachine: final project report MAT1-CT94-0076, PTB Report F-35, Parts1 and 2. Bundesallee, Germany; 1999.

[4] Schwenke H, Trapet E, Waeldele F. Pushing the limits of accuracy of coordi-nate measurements. In: Proceedings of the Fourth International Conferenceon Ultraprecision in Manufacturing Engineering. 1997. p. 331–5.

[5] Haertig F, Trapet E, Waeldele F, Wiegand U. Tracibility of coordinate mea-surements according to the virtual CMM concept. In: Proceedings of theFifth IMEKO TC-14. 1995. p. 245–54.

[6] Osawa S, Busch K, Franke M, Schwenke H. Multiple orientation tech-nique for calibration of cylindrical workpieces on CMMs. Precision Eng2005;29(1):56–64.

[7] Weckenmann A, Knauer M, Kunzmann H. The influence of measure-ment strategy on the uncertainty of CMM-measurements. CIRP Ann1998;47(1):451–4.

[8] Weckenmann A, Eitzert H, Garmer M, Weber H. Functionality-orientedevaluation and sampling strategy in coordinate metrology. Precision Eng1995;17(3):244–52.

[9] Satrori S, Zhang GX. Geometric error measurement and compensation ofmachines. Ann CRIP 1995;44(2):599–609.

[

[

ineering 31 (2007) 94–101

10] Zhang GX, Zhang YF. A method for machine geometric calibration using1-D ball array. Ann CIRP 1991;40(1):519–22.

11] Zhang G, Veale R, Charlton T, Borchardt B, Hocken R. Error compensationof coordinate measuring machines. Ann CIRP 1985;34(1):445–8.

12] Balsamo A, Di Ciommo M, Mugno R, Rebaglia BI, Ricci E, Grella R.Evaluation of CMM uncertainty through Monte Carlo simulation. AnnCIRP 1999;48(1):425–8.

13] Kreuci, JV. CMM measurement enhancement using probe compensationalgorithms. SME technical paper MS90-09, SME. Dearborn, MI 48121;1990.

14] Yee, KW, Gavin, RJ. Implementing fast part probing and error compensa-tion on machine tools. NIST Report 4447, National Institute of Standardsand Technology, Gaithersburg, MD 20899; 1990.

15] Shen Y-L, Zhang X. Pretravel compensation for horizontally orientedtouch trigger probes with straight styli. J Manuf Syst 1999;18(3):175–86.

16] Gu P, Chan K. Generative inspection process and probe path planning forcoordinate measuring machines. J Manuf Syst 1996;15(4):240–55.

17] Limaiem A, Elmaraghy HA. Integrated accessibility analysis and mea-surement operations sequencing for CMMs. J Manuf Syst 2000;19(2):83–93.

18] Taylor, BN, Kuyatt, CE. Guidelines for evaluating and expressing the uncer-tainty of NIST measurement results. Report TN 1297, National Institute ofStandards and Technology, Gaithersburg, MD; 1994.

19] Anon. Guide to the Expression of Uncertainty in Measurement (GUM).Geneva, Switzerland: International Organization for Standard (ISO); 1995.

20] Feng C-X, Pandey V. Experimental study of the effects of digitiz-ing parameters on digitizing uncertainty with a CMM. Int J Prod Res2002;40(3):683–97.

21] Feng C-X, Wang X. Subset selection in predictive modeling of CMM dig-itization uncertainty. J Manuf Syst 2002;21(6):419–39.

22] Feng C-X, Wang X. Digitization uncertainty modeling for reverse engi-neering applications: regression vs. neural networks. J Intel Manuf2002;13(3):189–200.

23] Phillips SD, Borchardt B, Estler WT, Buttreee J. The estimation of mea-surement uncertainty of small circular features measured by coordinatemeasuring machines. Precision Eng 1998;22(1):87–97.

24] Piratelli-Filho A, Giacomo BD. CMM uncertainty analysis with factorialdesign. Precision Eng 2003;27(July (3)):283–8.

25] Saal, T. Applying regression analysis to CMM measurement uncertaintystudy. MS project report (Advisor: Dr. Jack Feng), Bradley University,61625 Peoria, IL, USA: Department of Industrial & Manufacturing Engi-neering & Technology; May 2003.

26] Feng C-X, Wang X. Surface roughness predictive modeling: neural net-works vs. regression. IIE Trans 2003;35(1):11–27.

27] Feng C-X, Yu Z, Wang J. Validation and data splitting in predictive regres-sion modeling of honing surface roughness parameters. Int J Prod Res2005;43(8):1555–72.

28] Tang, S-Y, Sun, A. Analysis of CMM scanning measurement uncertaintyusing design of experiments. In: Proceedings of the 2001 Industrial Engi-neering Research Conference, paper no. 2045. Norcross, GA, USA: Insti-tute of Industrial Engineers; 2001 [published in the form of CD].

29] Anon. VDI/VDE 2617, Part 2.1. Accuracy of coordinate measuringmachines: characteristic parameters and their checking, Dusseldorf, Ger-many; 1986.

30] Anon. ISO 10360-2, Geometrical product specifications (GPS) – accep-tance and reverification test for coordinate measuring machines (CMMs)– Part 2: CMMs used for measuring size, Geneva, Switzerland; 2001.

31] Emanuel JT, Palanisamy M. Sequential experimentation using two-levelfractional factorials. Qual Eng 2000;13(3):335–46.

32] Montgomery DD. Des Anal Exp. 6th ed. New York: John Wiley & Sons;2005.

33] Box GEP, Stuant Hunter J, Hunter WG. Statistics for experimenters: design,

innovation, and discovery. 2nd ed. New York: Wiley; 2005.

34] Wu CFJ, Hamada M. Experiments: planning, analysis, and parameterdesign optimization. New York: Wiley; 2000.

35] Anon. Minitab reference manual, PC Version. PA: Minitab Inc., State Col-lege; 2000.

n Eng

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C.-X.J. Feng et al. / Precisio

36] Montgomery DD, Peck EA, Geoffrey Vining C. Introduction to linearregression analysis. 3rd ed. New York: Wiley; 2001.

37] Draper NR, Smith H. Applied regression analysis. 3rd ed. New York: Wiley;1998.

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ineering 31 (2007) 94–101 101

38] Anon. Geometrical product specifications – coordinate measuringmachines: technique for determining the uncertainty of measurement –Part 3. Use of calibrated workpieces or standards. Geneva, Switzerland:ISO; 2004 [15530-3].