Comparison with reference method is one of the necessary requirements for the validation of non-standard methods. This comparison was made using the experiment planning technique with two-way ANOVA. In ANOVA, the results obtained using the EDXRF method, to be validated, were compared with the results obtained using the ASTM E572-13 standard test method. Fisher's tests (F -test) were used to comparative study between of the elements: molybdenum, niobium, copper, nickel, manganese, chromium and vanadium. All F -tests of the elements indicate that the null hypothesis (Ho) has not been rejected. As a result, there is no significant difference between the methods compared. Therefore, according to this study, it is concluded that the EDXRF method was approved in this method comparison requirement

Ferreira, Jane Zoppas

Krummenauer, Alex

Veit, Hugo Marcelo

Journal of Physics Conference Series

English

Lume 5.8

Journal of Physics: Conference SeriesPAPER • OPEN ACCESSComparative study between EDXRF and ASTME572 methods using two-way ANOVATo cite this article: A Krummenauer et al 2018 J. Phys.: Conf. Ser. 975 012004 View the article online for updates and enhancements.Related contentAdvanced Secure Optical ImageProcessing for Communications: Acomparative study of CFs, LBP, HOG,SIFT, SURF, and BRIEF for security andface recognitionA Al Falou-The comparative study for the isotropicand orthotropic circular platesC Popa and G Tomescu-Vaccination Strategies: a comparativestudy in an epidemic scenarioD. B. Prates, C. L. T. F. Jardim, L. A. F.Ferreira et al.-This content was downloaded from IP address 143.54.152.156 on 08/01/2019 at 11:471Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distributionof this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.Published under licence by IOP Publishing Ltd1234567890 ‘’“”9th Brazilian Congress on Metrology (Metrologia 2017) IOP PublishingIOP Conf. Series: Journal of Physics: Conf. Series 975 (2018) 012004  doi :10.1088/1742-6596/975/1/012004      Comparative study between EDXRF and ASTM E572 methods using two-way ANOVA A Krummenauer , H M Veit and J  Zoppas-Fer reira Programa de Pós-Graduação em Engenharia de Minas, Metalúrgica e de Materiais (PPGE3M), Universidade Federal do Rio Grande do Sul (UFRGS), Av. Bento Gonçalves, 9500, Porto Alegre, RS, Brazil. alex_krum@yahoo.com.br Abstract. Comparison with reference method is one of the necessary requirements for the validation of non-standard methods. This comparison was made using the experiment planning technique with two-way ANOVA. In ANOVA, the results obtained using the EDXRF method, to be validated, were compared with the results obtained using the ASTM E572-13 standard test method. Fisher's tests (F-test) were used to comparative study between of the elements: molybdenum, niobium, copper, nickel, manganese, chromium and vanadium. All F-tests of the elements indicate that the null hypothesis (Ho) has not been rejected. As a result, there is no significant difference between the methods compared. Therefore, according to this study, it is concluded that the EDXRF method was approved in this method comparison requirement. 1.  Introduction In Brazil, the laboratories of RBLE (Brazilian Network of Testing Laboratories), accredited by CGCRE/INMETRO, according to ABNT NBR ISO/IEC 17025:2005 standard [1] must comply, among other things, the following requirements: non-standard methods (item 5.4.4), and validation of methods (item 5.4.5), described in this standard. To assist in this task, INMETRO provides document DOQ-CGCRE-08 - Guidance for validation of analytical methods [2] which guides laboratories in the validation process of a non-standard method, i.e., that is not described in a national or international standard. The LACOR (Laboratory of Corrosion, Protection and Recycling of Materials), at  UFRGS, is accredited by CGCRE/INMETRO (RBLE 1139) and uses the Thermo Scientific Niton XL3t GOLDD+ portable EDXRF analyzer to perform metal determination tests in steel samples, by energy dispersive X-ray fluorescence spectrometry (EDXRF). However, the EDXRF method is a non-standard method and therefore it must be validated. One of the requirements for validation, as determined by item 8.2.6.3.4 of document DOQ-CGCRE-08 [2], is the comparison with a reference method. The purpose of this comparison is to evaluate the accuracy of method to be validated by analyzing samples with concentrations through the entire range in which the method should be validated. Samples were analyzed, with six measurements, by using the two methods separately [2]. There are several techniques that can be used to compare the results obtained by two test methods. In this sense, document DOQ-CGCRE-08 [2] suggests: hypothesis tests and planning of experiment. In this comparison, it was decided to use the two-way factorial experiment (two-way ANOVA) described in the experiment planning technique [3, 4, 5]. In order to obtain the results of the method to be validated, the NITON analyzer was used to analyze the samples 2Q15S1 [6], 2Q15S2 [6], 4Q15S1 21234567890 ‘’“”9th Brazilian Congress on Metrology (Metrologia 2017) IOP PublishingIOP Conf. Series: Journal of Physics: Conf. Series 975 (2018) 012004  doi :10.1088/1742-6596/975/1/012004      [7], and 4Q15S2 [7]. These samples were measured by ASTM E572-13 reference method [8], with the wavelength dispersive X-ray fluorescence spectrometry (WDXRF) method, in the Inter-Laboratory Analysis Programs (ILAP), performed by ASTM International [6, 7], in which LACOR laboratory participated. The term ED “energy dispersive” in EDXRF refers to the technique of detecting X-rays emitted, which is affected by a detector which generates an intensity spectrum as a function of energy [9]. While the term WD "wavelength dispersive" in WDXRF refers to the use of single crystal or synthetic multilayer Bragg diffraction to disperse characteristic X-rays [9]. Figure 1 shows a comparison between the detection techniques used in EDXRF and WDXRF.   Figure 1. Comparison between the detection techniques used in EDXRF and WDXRF [9, 10].   In this study, the results of the following chemical elements were analysed: molybdenum (Mo), niobium (Nb), copper (Cu), nickel (Ni), manganese (Mn), chromium (Cr), and vanadium (V). Comparison of the results for tungsten (W) and cobalt (Co) was also obtained, but with other methods, outside the scope of this paper. Therefore, these results are not mentioned in this article. 2.  Objective This study performs a comparative study between the non-standard EDXRF method and the ASTM E572 reference method (WDXRF), by using the two-way ANOVA. The objective is to validate the EDXRF method and maintain the accreditation by CGCRE/INMETRO of the metal determination testing by FRX. 3.  Mater ials and methods In this study, the four samples, used in interlaboratory comparisons [6, 7], were measured with six measurements, under repeatability conditions, by using the NITON analyzer along with the Mobile Test Stand accessory. NITON has been configured with: calibration curve (table 1), general metals analysis from the main menu, two filters – main range (20s) and low range (20s), disable Al, and autoswitch ON [10]. All measurements were taken by using the following procedure quoted in the NITON manual: 1 - preparation of the sample; 2 - clean with isopropyl alcohol and lint-free paper; 3 - perform a system check once every working day; 4 - warm up for ten minutes after start up [10].  31234567890 ‘’“”9th Brazilian Congress on Metrology (Metrologia 2017) IOP PublishingIOP Conf. Series: Journal of Physics: Conf. Series 975 (2018) 012004  doi :10.1088/1742-6596/975/1/012004      Results with six measurements (n = 6), in each sample, were compared with six randomly selected results from other laboratories that participated in interlaboratory comparisons [4, 5]. Two-way ANOVA was used for each chemical element: factor A – concentration – with four levels (a = 4) and factor B – method – with two levels (b = 2).  Table 1. Parameters of the calibration curve and coefficient of determination (R²). Chemical element Intercept (a) Slope (b) R2 Mo -0.0054 1.0219 0.9999 Nb 0.0033 0.8916 0.9999 Cu -0.0148 1.1157 0.9993 Ni 0.0021 1.0096 1.0000 Mn -0.0258 0.9803 0.9997 Cr -0.0932 0.9758 0.9995 V 0.0019 0.9116 0.9996 3.1.  Factorial experiment (two-way ANOVA) According to Ribeiro and ten Caten [3] and Montgomery [4, 5], the statistical model of two-way ANOVA is equation (1). 𝑦𝑦𝑖𝑖𝑖𝑖𝑖𝑖 = 𝜇𝜇 + 𝜏𝜏𝑖𝑖 + 𝛽𝛽𝑖𝑖 + (𝜏𝜏𝛽𝛽)𝑖𝑖𝑖𝑖 + 𝜀𝜀𝑖𝑖𝑖𝑖𝑖𝑖  (1) Where μ is the population mean; τi is the effect of the i-th level of “concentration”; βj is the effect of the j-th level of “method”; τβij is the effect of the “concentration·method” interaction; εijk is the random error, with i = 1, a;  j = 1, b and k = 1, n. Assumption: εijkThus, there are three hypothesis tests to be performed [3, 4, 5]:  → N(μ = 0, σ). • For the factor “concentration”: Ho: τi = 0 and  H1: τi• For the factor “method”: Ho: β ≠ 0 for some i, i = 1, a. j = 0 and H1: βj• For the factor “concentration·method”: Ho: τβ ≠ 0 for some j,  j = 1, b. ij = 0 and H1: τβijFor each hypothesis tests, it was computed F tabulated (Ftab) of the Fisher distribution (F- distribution) and compared with the F calculated (Fcalc). If Fcalc > Ftab then the null hypothesis is rejected and therefore the change in levels of the factor analyzed has a significant effect on the mean response [3, 4, 5].  ≠ 0 for some ij.  The value of Fcalc is obtained from equation (2) and Ftab is calculated by equation (3). 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 =𝑉𝑉𝐹𝐹𝑉𝑉𝑖𝑖𝐹𝐹𝑉𝑉𝐹𝐹𝑉𝑉 𝑏𝑏𝑉𝑉𝑏𝑏𝑏𝑏𝑉𝑉𝑉𝑉𝑉𝑉 𝑔𝑔𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑉𝑉𝐹𝐹𝑉𝑉𝑖𝑖𝐹𝐹𝑉𝑉𝐹𝐹𝑉𝑉 𝑏𝑏𝑖𝑖𝑏𝑏ℎ𝑖𝑖𝑉𝑉 𝑏𝑏ℎ𝑉𝑉 𝑔𝑔𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔=𝑀𝑀𝑀𝑀(𝑓𝑓𝐹𝐹𝐹𝐹𝑏𝑏𝑔𝑔𝑉𝑉)𝑀𝑀𝑀𝑀𝑀𝑀 (2) 𝐹𝐹𝑏𝑏𝐹𝐹𝑏𝑏 = 𝐹𝐹𝛼𝛼 ;𝐺𝐺𝐺𝐺 𝑉𝑉𝑔𝑔𝑛𝑛𝑉𝑉𝑉𝑉𝐹𝐹𝑏𝑏𝑔𝑔𝑉𝑉 ;𝐺𝐺𝐺𝐺 𝑑𝑑𝑉𝑉𝑉𝑉𝑔𝑔𝑛𝑛𝑖𝑖𝑉𝑉𝐹𝐹𝑏𝑏𝑔𝑔𝑉𝑉  (3) Where MQ(factor) is mean square or variance, MQR is mean square of error, α is significance level, GLnumerator is degrees of freedom of numerator and GLdenominator is degrees of freedom of denominator [3, 4, 5]. If Fcalc > Ftab, or p-value < 0.05 (α = 5 %), the effect studied is significant for a confidence level of 95 % [3, 4, 5]. According to Ribeiro and ten Caten [3] and Montgomery [4, 5], the formulas for calculations are described below. 𝑇𝑇𝑇𝑇 =(𝑇𝑇… )2𝐹𝐹𝑏𝑏𝑉𝑉 (4) 𝑆𝑆𝑀𝑀𝑆𝑆 = �(𝑇𝑇𝑖𝑖 . . )2𝑏𝑏𝑉𝑉− 𝑇𝑇𝑇𝑇𝐹𝐹𝑖𝑖=1 (5) 41234567890 ‘’“”9th Brazilian Congress on Metrology (Metrologia 2017) IOP PublishingIOP Conf. Series: Journal of Physics: Conf. Series 975 (2018) 012004  doi :10.1088/1742-6596/975/1/012004      𝑆𝑆𝑀𝑀𝑆𝑆 = ��𝑇𝑇.𝑖𝑖 . �2𝐹𝐹𝑉𝑉− 𝑇𝑇𝑇𝑇𝑏𝑏𝑖𝑖=1 (6) 𝑆𝑆𝑀𝑀𝑆𝑆𝑆𝑆 = ���𝑇𝑇𝑖𝑖𝑖𝑖 . �2𝑉𝑉𝑏𝑏𝑖𝑖=1𝐹𝐹𝑖𝑖=1− 𝑇𝑇𝑇𝑇 − 𝑆𝑆𝑀𝑀𝑆𝑆 − 𝑆𝑆𝑀𝑀𝑆𝑆 (7) 𝑆𝑆𝑀𝑀𝑀𝑀 = ���𝑦𝑦𝑖𝑖𝑖𝑖𝑖𝑖2𝑉𝑉𝑖𝑖=1𝑏𝑏𝑖𝑖=1𝐹𝐹𝑖𝑖=1−���𝑇𝑇𝑖𝑖𝑖𝑖 . �2𝑉𝑉𝑏𝑏𝑖𝑖=1𝐹𝐹𝑖𝑖=1 (8) 𝑆𝑆𝑀𝑀𝑇𝑇 = ���𝑦𝑦𝑖𝑖𝑖𝑖𝑖𝑖2𝑉𝑉𝑖𝑖=1𝑏𝑏𝑖𝑖=1𝐹𝐹𝑖𝑖=1− 𝑇𝑇𝑇𝑇 (9)  The verification of equation (9) can be done by equation (10). 𝑆𝑆𝑀𝑀𝑇𝑇 = 𝑆𝑆𝑀𝑀𝑆𝑆 + 𝑆𝑆𝑀𝑀𝑆𝑆 + 𝑆𝑆𝑀𝑀𝑆𝑆𝑆𝑆 + 𝑆𝑆𝑀𝑀𝑀𝑀 (10)  Where TC is the correction term, SQ(factor) is the sum of squares of each factor, MQ(factor) is the calculation of the mean square, equation (11), and GDL are the degrees of freedom of each factor. Table 2 presents these calculations. 𝑀𝑀𝑀𝑀(𝑓𝑓𝐹𝐹𝐹𝐹𝑏𝑏𝑔𝑔𝑉𝑉) =𝑆𝑆𝑀𝑀(𝑓𝑓𝐹𝐹𝐹𝐹𝑏𝑏𝑔𝑔𝑉𝑉)𝐺𝐺𝐺𝐺𝐺𝐺 (11)  Table 2. Calculations for two-way ANOVA. Factor Sum of squares GDL Mean square Fcalc Ftab A SQA (a - 1) MQA 𝑀𝑀𝑀𝑀𝑆𝑆 𝑀𝑀𝑀𝑀𝑀𝑀⁄  𝐹𝐹𝛼𝛼 ;𝐺𝐺𝐺𝐺𝑆𝑆;𝐺𝐺𝐺𝐺𝑇𝑇  B SQB (b - 1) MQB 𝑀𝑀𝑀𝑀𝑆𝑆 𝑀𝑀𝑀𝑀𝑀𝑀⁄  𝐹𝐹𝛼𝛼 ;𝐺𝐺𝐺𝐺𝑆𝑆;𝐺𝐺𝐺𝐺𝑇𝑇  AB SQAB (a - 1)*(b - 1) MQAB 𝑀𝑀𝑀𝑀𝑆𝑆𝑆𝑆 𝑀𝑀𝑀𝑀𝑀𝑀⁄  𝐹𝐹𝛼𝛼 ;𝐺𝐺𝐺𝐺𝑆𝑆𝑆𝑆 ;𝐺𝐺𝐺𝐺𝑇𝑇  Error SQR ab(n - 1) MQR   Total SQT abn - 1    4.  Results and discussion The six results obtained with NITON, in the four samples for Mo, and also the six sample means of these samples from laboratories that participated in ILAP of the ASTM [6, 7], method E572, are presented in table 3. Results of the other chemical elements were obtained by using the same methodology. By using the methods and calculations described in item 2 of this article, with the data from table 3, the following values were obtained for Mo: a = 4, b = 2, n = 6, TC = 53.129788, SQA = 45.504863, SQB = 0.000199, SQAB =0.000051, SQR = 0.003461 e SQT = 45.508574. Table 4 presents the values of two-way ANOVA calculations for Mo.   Table 3. Values obtained with NITON (EDXRF) and ASTM E572 (WDXRF) for Mo. Concentration Values measured with NITON (%) Sample means obtained with E572 (%)    0.051 % (2Q15S2) 0.049 0.050 0.050 0.051 0.052 0.049 0.058 0.055 0.050 0.054 0.052 0.051 0.102 % (2Q15S1) 0.102 0.101 0.104 0.105 0.101 0.104 0.110 0.108 0.106 0.107 0.110 0.109 2.003 % (4Q15S1) 2.020 2.003 2.002 2.008 2.008 2.011 2.020 2.008 2.003 2.007 2.020 2.001 2.058 % (4Q15S2) 2.044 2.043 2.052 2.046 2.011 2.035 2.046 2.056 2.076 2.035 2.033 2.024 51234567890 ‘’“”9th Brazilian Congress on Metrology (Metrologia 2017) IOP PublishingIOP Conf. Series: Journal of Physics: Conf. Series 975 (2018) 012004  doi :10.1088/1742-6596/975/1/012004      Table 4. ANOVA two-way calculations for Mo. Factor Sum of squares GDL Mean square Fcalc Ftab Concentration (A) 45.504863 3 15.168288 175298 2.8 Method (B) 0.000199 1 0.000199 2.3 4.1 Interaction (AB) 0.000051 3 0.000017 0.2 2.8 Error 0.003461 40 0.000087   Total 45.508574 47     As mentioned previously, the studied effect is significant for Fcalc > Ftab. Table 4 shows that the factor “concentration” was significant and the factor “method” and the interaction were not significant. This result shows that the concentrations had great variation between the samples, but this was expected, since each sample actually had a very different value of concentration of Mo in relation to the others. However, most importantly, the methods do not have significant differences and therefore for Mo the EDXRF method is approved in requirement 8.2.6.3.4 of document DOQ-CGCRE-08 [2], for a confidence level of 95 %. That was the purpose of this study. Figure 2 shows the analysis of the factor method using the F-distribution of Fisher.  Figure 3 shows the comparison between the means of measurements made for Mo, with the EDXRF method and the means obtained with the ASTM E572 method (WDXRF) and it can be observed that there is no difference between the values.     Figure 2. Analysis factor method using F-distribution of Fisher. Figure 3. Comparing the sample means of the measurements of EDXRF and ASTM E572.  As for the other elements that followed the same methodology of Mo, table 5 presents a summary of two-way ANOVA calculations of each of the chemical elements. Analyzing the data in table 5, it is concluded that all chemical elements that have been analyzed and compared with the E572 method [8] are approved for requirement 8.2.6.3.4 of document DOQ-CGCRE-08 [2], for a confidence level of 95 %. There was no significant difference between the methods because no Fcalc was greater than Ftab (see table 5).    61234567890 ‘’“”9th Brazilian Congress on Metrology (Metrologia 2017) IOP PublishingIOP Conf. Series: Journal of Physics: Conf. Series 975 (2018) 012004  doi :10.1088/1742-6596/975/1/012004      Table 5. Summary of two-way ANOVA calculations for the factor “method” of chemical elements. Chemical element Sum of squares GDL Mean square Fcalc Ftab Mo 0.000199 1 0.000199 2.3 4.1 Nb 0.000006 1 0.000006 4.0 4.1 Cu 0.000284 1 0.000284 4.0 4.1 Ni 0.001349 1 0.001349 1.0 4.1 Mn 0.000524 1 0.000524 1.0 4.1 Cr 0.003485 1 0.003485 1.0 4.1 V 0.000003 1 0.000003 0.2 4.1 5.  Conclusion The comparison of the EDXRF method with the ASTM E572 reference method (WDXRF), using the two-way ANOVA technique, resulted in the approval of the method for measuring Mo, Nb, Cu, Ni, Mn, Cr, and V, in the alloy steels analysis. However, it should be noted that this alone does not characterize the complete validation of the analytical method, since many other requirements have to be approved, as described, for example, in DOQ-CGCRE-08 [2], for final definitive approval of the EDXRF method. Acknowledgments The authors thank CAPES for the support with the masters scholarship program; UFRGS, PPGE3M and LACOR by technical and instrumental support; FINEP, for the resources obtained, through the SIBRATEC - Technological Services Provision Networks, for the acquisition, by LACOR, of the portable EDXRF analyzer. References [1] ABNT 2005 NBR ISO/IEC 17025:2005 General Requirements for the Competence of Testing and Calibration Laboratories (Rio de Janeiro: ABNT)  [2] INMETRO 2016 DOQ-CGCRE-008 Orientação sobre Validação de Métodos Analíticos (Rio de Janeiro: INMETRO) [3] Ribeiro J L D and ten Caten C S 2014 Projeto de Experimentos (Porto Alegre: UFRGS) [4] Montgomery D C 2009 Introduction to Statistical Quality (New York: Wiley & Sons) [5] Montgomery D C 1997 Design and Analysis of Experiments (New York: Wiley & Sons) [6] ASTM International 2015 Proficiency Test Program: Chemical Analysis of Stainless Steel Second Quarter 2015 (West Conshohocken: ASTM International) [7] ASTM International 2016 Proficiency Test Program: Chemical Analysis of Stainless Steel Fourth Quarter 2015 (West Conshohocken: ASTM International) [8] ASTM International 2016 E572-13 – Standard Test Method for Analysis of Stainless and Alloy Steels by Wavelength Dispersive X-Ray Fluorescence Spectrometry (West Conshohocken: ASTM International)  [9] Santos E S 2012 Determinação de Cobre, Ferro, Níquel e Zinco em Matrizes Etanólicas por Espectrometria de Fluorescência de Raios-X com Energia Dispersiva após Pré-Concentração em Papel Cromatográfico, Ph.D. dissertation (Salvador: UFBA) [10] Thermo Fisher Scientific 2010 Niton XL3 Analyzer User’s Guide Revision C 

Comparative study between EDXRF and ASTM E572 methods using two-way ANOVA

https://lume.ufrgs.br/bitstream/10183/250815/1/001086729.pdf

Comparative study between EDXRF and ASTM E572 methods using two-way ANOVA

Abstract

Similar works

Full text

Available Versions

Lume 5.8