study of intraclass correlation coefficient method in a measurement system
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Study of Intraclass Correlation Coefficient Method in a Measurement System. E ng . Juan Ignacio Ruiz Guerrero, M.C. Manuel Darío Hernández Ripalda , Ph.D . Salvador Echeverría-Villagómez, M.C. Moises Tapia- Esquivias . Introduction. COMPARISON METHOD. Problems. VARIATION SOURCE. - PowerPoint PPT PresentationTRANSCRIPT
Study of Intraclass Correlation Coefficient Method in a Measurement System
Eng. Juan Ignacio Ruiz Guerrero, M.C. Manuel Darío Hernández Ripalda, Ph.D. Salvador Echeverría-Villagómez,M.C. Moises Tapia-Esquivias.
AIAG INTRACLASS CORRELATION COEFICIENT (ICC)number of distinct
categories (NDC) (AIAG, 2010)
Donal J. Wheeler, 2010
Simulations
To study measurement from similar
data GR&R
Confidence
intervals
To compare the
different results
Introduction
2
COMPARISON METHOD
Measurement System Analysis (MSA)
Repeatability
Reproducibility
Equipmet,part,method,operato
r
Anova (K. Burdick, M. Borror, & C. Montgomer
y, 2005)
Problems
3
VARIATION SOURCE
Fig. 1Repeatability
(Reyes)
Fig. 2 Reproducibility (Reyes)
Gage R & R is a system that is combined with variation of repeatability and reproducibility. Otherwise, GRR equals the sum variation in the system and change between systems (11).
Ec. 1 Gage reproducibility & repeatability (Wheeler, 2011)
Gage R&R
4
The correlation coefficient is defined as the proportion of the variation in the measurements of the product that can be attributed to the product stream, and is the complement of the ratio of the variation in the measurements of the product that can be attributed to the system measurement (3).
Ec.2 Intraclass correlation coefficient (7).
2. Theoretical Framework
2.1 Intraclass correlation coefficient
5
(NDC). This is defined as the number of non-overlapping confidence intervals of 97% for the true value of the property as they cross the variation of the expected product.
NDC can be distinguished reliably from the measurement system. NDC value is truncated to give an integer. The AIAG rule is that the NDC must be at least 5 for the measurement system may be acceptable. . The formula proposed by AIAG used, for example, in MINITAB can be written as (8):
Ec. 3 Number of distinct categories, (9).
2.2 Number of distinct categories
6
7
Overall Variation
Part-to-Part Variation Measurement System Variation
Variation due to Gage Variation due to Operators
RepeatabilityReproducibility
OperatorsOperator by Part
2.3.1 Measurement variation in tree
2.3 Anova
Based on the above values are calculated from the variation in the following manner using the equation of the number of distinct categories:
1 2 21 12.5 51 50 10
Table 1. Values of the variation in part.
3. Method description
3.1 Data Generation Process
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R&R del sistema de medición
%ContribuciónFuente CompVar (de CompVar)R&R del sistema de medición total 0.85656 46.85 Repetibilidad 0.75259 41.17 Reproducibilidad 0.10397 5.69 operadores 0.10397 5.69Parte a parte 0.97157 53.15= ICC*Variación total 1.82813 100.00
* The value of ICC, is obtained by the ratio of part to part on the total
variation.
Number of distinct categories = 1
Software like Minitab to perform the GR&R study by the ANOVA method simultaneously estimates the NDC and ICC, this can be read respectively in the window session of the program, such as "Number of Categories Different" and "Percentage of Contribution" part to part
3.2 Gage R&R in Measurement System
10
12
0.87 0.88 0.89 0.9 0.91 0.92 0.930123456789
10Frequency from ICC of
rejection
Frecuencia de CCI
1 2 3 4 505
10152025
Frequency from NDC of rejection
Frecuencia de Catego-rias
Thirty cases were generated in each of the categories with a DIST.NORM INV (PROBABILITY (), MEAN0, STD); using Excel, subsequently were entered into Minitab to perform the GR&R.
4. Development
Values of NDC must be greater than 5Values of ICC must be greater than 0.80
130.9840.9850.9860.9870.9880.989 0.99
012345678
Frequency from ICC in acceptance
Frecuencia de los CCI
10 11 12 1302468
1012141618
Frequency from NDC in acceptance
Frecuencia de Categorias
1 2 3 40
10203040
Frequency from NDC in the limit
Fre-cuencia de Cat-egorias
0.9 0.91 0.92 0.93 0.94 0.9502468
101214161820
Frequency from ICC in the limit
Frecuencia de CCI
To generate confidence intervals [3] for each of the categories, Minitab is uses in order to perform sampling using the values obtained in columns the number of categories and values obtained from the ICC. These 30 columns of data are placed into Minitab.
REJECTION
LIMIT
ACCEPTANCE LCL UCL LCL UCL LCL UCL
NDC 3.66666 4 3.7 4 11.05 12.03
ICC 0.89881 0.90927 0.90178 0.92905 0.986352 0.9874
According to the confidence intervals of the average obtained is observed that the values by ndc have greater uncertainty for the 3 categories, but the major difference is generated in the category of acceptance.
4.1 Confidence intervals
5. Results
14
Table 3. Confidence intervals for the mean for all categories.
15
Confidence intervals for the mean for all categories.
Concluding Remarks The current AIAG Measurement System punishes or penalizes too the measurement systems, a correct system could be rejected. This affects the Auto Industry who are governed by the AIAG methodology which involves the revision of the standard in automotive industry operates.Summary of results In this research we studied measurement methods, measurement GR&R of AIAG and intraclass correlation coefficient as proposed by Wheeler, which shows differences and similarities of the methods, they are different in their standard to qualify, as AIAG penalizes more rigor measurement systems while Wheeler method tends to rate measurement systems really acceptable. Conclusions By comparing the method AIAG and Wheeler method, one can conclude that the method estimates AIAG results with high values. The GR&R method attenuates actually AIAG variation measuring system instead of the production process. From this study, the method of Wheeler is recommended on the AIAG method, as the measurements obtained from AIAG are inflated, they overestimate the components of measurement error in a study coinciding with (10).
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1. AIAG. Analisis de los sistemas de medición. s.l. : AIAG, 2010.2. K. Burdick, Richard, M. Borror, Connie y C. Montgomery, Douglas. Desing and Analysis of Gage R&R Studies. Philadelphia, Pennsylvania. : Board, 2005.3. Wheeler, Donald J. The Intraclass Correlation Coefficient. Quality digest. [En línea] 02 de 12 de 2010. [Citado el: 19 de 03 de 2012.] http://www.qualitydigest.com/inside/twitter-ed/intraclass-correlation-coefficient.html.4. Montgomery, Douglas C. y Runger, George C. Probabilidad y estadística aplicadas a la Ingeniería. México, D.F. : Mc GRAW HILL INTERAMERICANA EDITORES,S.A de C.V., 2005.5. Mosquera Saravia, Cristián Rodrigo. Comparación entre los Métodos de evaluación de incertidumbre y estudios de repetibilidad y reproducibilidad para la evaluación de las mediciones. Comparación entre los Métodos de evaluación de incertidumbre y estudios de repetibilidad y reproducibilidad para la evaluación de las mediciones. [En línea] 03 de 2007. [Citado el: 1 de 03 de 2012.] http://biblioteca.usac.edu.gt/tesis/08/08_0105_MT.pdf.6. Romeo Olea, Daniel. Metodología para la implementación de la planeación avanzada de la calidad del producto en la industria metal mecánica. Instituto Politecnico Nacional, Escuela superior de ingeniería mecánica y eléctrica, Unidad profesional Azcapotzalco. [En línea] 28 de 04 de 2008. [Citado el: 20 de 10 de 2012.] http://itzamna.bnct.ipn.mx:8080/dspace/bitstream/123456789/187/1/TESIS%20APQP%20DANIEL%20RO.pdf.
References
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7. Wheeler, Donald. J. A Better Way to Do R&R Studies. qualitydigest. [En línea] 01 de 02 de 2011. [Citado el: 25 de 04 de 2012.] http://www.qualitydigest.com/inside/twitter-ed/better-way-do-rr-studies.html.8. Woodall, William H. y Borror, Connie M. Some Relationships between Gage R&RCriteria. Quality and Reliability Engineering International. [En línea] 19 de 06 de 2007. [Citado el: 1 de 11 de 2012.] http://www.iem.yuntech.edu.tw/home/lab/qre/Courses/2/AQM-2/files/962%E9%AB%98%E5%93%81%E7%AE%A1ppt%E8%AC%9B%E7%BE%A9/Gage_RR_criteria.pdf.9. Minitab. Versión (16.1.1). [Software de computo]. Pensilvania, Pensilvania, EEUU : Minitab Inc., 2010.10. Pandiripalli, Bhavani. Repeatability y Reproducibility studies: A comparison of techniques. Wichita State University, College of Engineering, Dept. of Industrial and Manufacturing Engineering. [En línea] 2010. [Citado el: 5 de 01 de 2013.] http://soar.wichita.edu/bitstream/handle/10057/3736/t10107_Pandiripalli.pdf?sequence=1.11. Fernández & Exiga, Sistemas y Análisis de medición (MSA). Gestiopolis. [En línea] 2006. [Citado el: 20 de 10 de 2012].http://www.gestiopolis1.com/recursos7/Docs/ger/medicion-del-desempeno-y-rendimiento.htm.
References
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Thanks for your attention
2013 Year of statistics
Eng. Juan Ignacio Ruiz-Guerrero, [email protected]. Manuel Darío Hernández-Ripalda, [email protected]. Salvador Echeverría-Villagómez, [email protected]. Moises Tapia-Esquivias, [email protected]