Özet
In this thesis study, using the ANOVA, Maximum Likelihood Estimation (ML), Restricted Maximum Likelihood Estimation (REML) and Minimum Norm Quadratic Estimation (MINQUE) methods, how to apply these estimates to the Measurement Systems Analysis (MSA) is discussed. In this respect, a general definition of the MSA is made in the first section. In the second section, the estimation methods of variance components in the MSA are mentioned and the theoretical basis for one way variance analysis is given. Besides, the advantages and disadvantages of these methods are discussed. In the third section, various numerical examples related to the MSA are analyzed and the methods are compared by estimating the variance components by different methods.
Künye
[1] Pan, J., Evaluating the Gage Repeatability and Reproducibility for Different Industries, Quality & Quantity (2006) 40: 499–518, 2006.
[2] Montgomery, D. C., Runger, G. C., Gage Capability Analysis and Designed Experiment, Part II: Experimental Design Models and Variance Component Estimation, Quality Engineering, 6, 2, 289-305.1993.
[3] Joiner, B. L., Gaudard, M. A., Variation Management and W. Edwards Deming. Quality Progress, 23, 12, 1990.
[4] MacKay, R. J., Steiner, S. H, Strategies for Variability Reduction. Quality Engineering, 10, 1, 125-136, 1997.
[5] McGhee, J. W., Introductory Statistics, St. Paul, MN: West, 1985.
[6] Automotive Industry Action Group (AIAG), Measurement Systems Analysis Reference Manual, third ed., Chrysler, Ford, General Motors Supplier Quality Requirements Task Force, 2002.
[7] Grubbs, F.E., Errors of Measurement, Precision, Accuracy and the Statistical Comparison of Measuring Instruments. Technimetrics, 15, 53–66, 1973.
[8] Tsai, P., Variable Gage Repeatability and Reproducibility Study Using the Analysis of Variance Method. Quality Engineering, 1, 1, 107-115, 1989.
[9] Montgomery, D. C., Runger, G. C., Gage Capability Analysis and Designed Experiments. Part I: Basic Methods, Qual. Eng., 6, 115-135, 1993.
[10] Montgomery, D.C., Statistical Quality Control: A Modern Introduction, sixth ed., Wiley, New York, 2009.
[11] Searle, S.R., Casella, G., McCulloch, C.E., Variance Components, Wiley, New York. 1992.
[12] Crump, L., The Estimation of Components of Variance in Multiple Classifications. Ph. D. Dissertation, Iowa State University, Ames, IA. 1947.
[13] Crump, L., The Present Status of Variance Components Analysis, Biometrics,7,1-16, 1951.
[14] Herbach, Leon H., Properties of Model II- Type Analysis of Variance Tests, Ann. Math. Stat., Vol.30 (1959), pp.939-959, 1959.
[15] Hartley, H.O., Rao, J.N.K., Maximum Likelihood Estimation for the Mixed Analysis of Variance Model. Biometrika 54, 93-108. 1967.
[16] Anderson, R.L., Bancroft, T.A. Statistical Theory in Research. McGraw-Hill, New York, 358-366. 1952.
[17] Patterson, H. D., Thompson, R., Recovery of Inter-Block Information When Block Sizes Are Unequal. Biometrika, 58(3):545–554, 1971.
[18] Rao, C. R., Estimation of Heteroscedastic Variances in Linear Models, J. Amer. Statist. Assoc., 65, 16, 1-172, 1970.
[19] Rao, C. R., Estimation of Variance and Covariance Components MINQUE Theory, J. Multi. Anal., 3, 257-275, 1971.
[20] Rao, C. R., Minimum Variance Quadratic Unbiased Estimation of Variance Components, J. Multi. Anal., 4,445-456, 1971.
[21] Milliken, G. A., Johnson, D. E., Analysis of Messy Data. Volume I: Designed Experiments, Van Nostrand Reinhold, New York, 1984.
[22] Bhakhri, R., Belokar, R.M., Quality Improvement Using Gage Repeatability & Reproducibility : A Case Study, International Research Journal of Engineering and Technology (IRJET), Volume04, 2017.
[23] Yurdigül, E. Y., Dengeli Veri Kümelerinde Varyans Bileşenlerinin Kestirimi, Yüksek Lisans Tezi. Atatürk Üniversitesi. Fen Bilimleri Ensitüsü, Zootekni Anabilim Dalı, 2013.
[24] Ünalan, A., Çankaya, S., Jersey Sığırlarında Süt Verimine Ait Varyans Unsurlarının Farklı Yöntemlerle Tahmini, Anadolu Tarım Bilim Dergisi, 27(1):41-47, 2011.
[25] Kayaalp, G.T., Bek, Y., Varyans Unsurları Tahmin Yöntemlerinin Karşılaştırmalı Olarak İncelenmesi, Çukurova Üniversitesi Ziraat Fakültesi Dergisi, 2: 127-142. 1994.
[26]
Karabayır, A., Atatürk Üniversitesi Tarım İşletmesinde Yetiştirilen Esmer Sığırların Süt Verim Özellikleri için Farklı Metod ve Modeller ile Varyans Unsurları ve Kalıtım Derecesi Tahminleri, Yüksek Lisans Tezi. Atatürk Üniv. Fen Bil. Enst., Zootekni Anabilim Dalı. 1996.
[27] Esenbuğa, N., Dayıoğlu, H., İvesi ve Morkaraman Koyunlarında Döl Verimi ile Kuzuların Büyüme ve Gelişme Özellikleri için Farklı Metotlarla Varyans Bileşenlerinin Tahmini. Turkish Journal of Veterinary and Animal Sciences, 26:161–169. 2002.
[28] Başkan, Şanslı., İstatistiksel Kalite Kontrolü, Ege Üniversitesi Fen Fakültesi Yayınları, No:159, 68-273 ss., İzmir. 1997.
[29] Özdemir, T., İstatistiksel Kalite Kontrol. A. Ü. F. F. Döner Sermaye İşletmesi Yayınları. Ankara. 2000.
[30] Patır, S., İstatistiksel Proses Kontrol Teknikleri ve Kontrol Grafiklerinin Malatyadaki Bir Tekstil (iplik dokuma) İşletmesinde Bobin Sarım Kontrolüne Uygulanması. Sosyal ve Ekonomik Araştırmalar Dergisi.12 (18), 231-249. 2009.
[31] Türkiye İstatistik Kurumu (TÜİK). İstatistiksel Kalite Kontrol, Sorularla resmi istatistikler dizisi, 2011, ww.tuik.gov.tr/Kitap.do?metod=KitapDetay&KT_ID=18&KITAP_ID=245
[32] Bircan, H., Özcan, S., Excel Uygulamalı Kalite Kontrol, Yargı Yayınevi, Sivas, 2003.
[33] Duetler, T., Grubbs-Type Estimators for Reproducibility Variances in an Interlaboratory Test Study. Journal of Qualıty Technology, vol 23, no 4, 324-335, 1991.
[34] Harville, D.A., Maximum Likelihood Approaches to Variance Component Estimation and to Related Problems, J. Amer. Stat. Ass. 72:320-338. 1977.
[35] Poduri S.R.S. Rao, Variance Components Estimation Mixed Models, Methodologies and Applications, Chapman&Hall/CRC.1997.
[36] Rao, J. N. K., Subrahmaniam, K., Combining independent estimators and estimation in Linear regression with unequal variances, Biometrics, 27,971-990. 1971.
[37] Mollaoğulları, A., Varyans Bileşenleri için Minimum Karesel Tahmin Yöntemleri, Yüksek Lisans Tezi. Çanakkale Onsekiz Mart Üniversitesi. Fen Bilimleri Enstitüsü, Matematik Anabilim Dalı, 2011.
[38] Houf, R. E., Berman, D. B., Statistical Analysis of Power Modüle Thermal Test Equipment Performance, IEEE Transactions on Components, Hybrids and Manufacturing Techonology, 4:516–520.1988.
[39] Refaie, A., Bata, N., Evaluating Measurement and Process Capabilities by Gage Repeatability & Reproducibility with Four Quality Measures, Measurement, 43,842–851, 2010.
[40] Inman, J.,Ter, J.L., Lenth, R.V., Niemi, L., Two Case Studies Involving an Optical Emission Spectrometer, Journal of Qualify Technology, Vol. 24, No. 1, January, 1992.
[41] Louka, G.A., Besseris, G.J., Gage Repeatability & Reproducibility for an Optical Micrometer Industrial Type Machine”. International Journal for Quality Research. Vol.4, No.4, 2010.