Abstract
When performing process quality control in a situation in which measures are made of several possibly related variables, it is desirable to use methods giving more powerful control that capitalize on the relations between the variables rather than to use methods of individual control of variables. Although the seperate controls on the individual variables are more easily interpretable the existency of correlation between variables reduces the sensitivity of control.
Initially, Hotelling (1947) proposed a multivariate control chart based on T2 under the multivariate normality assumption of random variables. Based on Hotelling's T2, Jackson (1959), Schall and Chandra (1987), Murphy (1987), Hawkins (1991), Mason, Tracy and Young (1995) developed some interesting approaches to answer which variable or set of variables cause the signal of out of control. In this study some of these approaches are presented and an assessment of these are performed. Jackson (1959), Schall ve Chandra (1987), Murphy (1987), Hawkins (1991), Mason, Tracy ve Young (1995).
References
- HAWKİNS D. M., (1991), Multivariate quality control based on regression-adjusted variables, Techonometrics, 33, 61-75.
- HAWKİNS D. M., ve BRADU (1990), Application of the Moore-Penrose invers of a data matrix in multiple regression, Linear algebra and its applications, 127, 403-426.
- HAWKİNS D. M., and WİXLEY R.A.J. (1986), A note on the transformation of Chi-squared variables to normality, The American Statistician, 40, 296-298.
- HOTELLING H., (1947), Multivariate Quality Control, Techniques of Statistical Analysis, (Ed. C. Eisenhart, M.W. Hastay, and W.A. Wallis, McGraw-Hill, New York, s. 84-111.
- JACKSON J.E., (1959), Quality control methods for several related variables, Technometrics, 1, 359-377.
- MASON R. L., TRACY N. D. and YOUNG J. C., (1995), Decomposition of T2 for Multivariate control chart interpretation, Journal of Quality Technology, 27, 99-108.
- TRACY, N. D., YOUNG J.C., ve MASON R., (1995), A bivariate control chart for paired measurements, Journal of Quality Technology, 27, 4, 370-376.
- MONTGOMERY, DOUGLAS C., (1991), Introduction to Statistical Quality Control, 322-332.
- MURPY, B. J., (1987), Selecting out of control variables with the T2 multivariate quality control procedure, The Statistician, 36, 571-583.
- RAVEH A., (1985), On the use of the inverse of the correlation Matrix in multivariate data analysis, The American Statistician, 39, 39-42.
- RENCHER A.C., (1993), The contribution of individual variables to hotelling T2, Wilks’ A, and R2 . Biometrics, 49, 479-489.
- SCHALL, S. and CHANDRA J., (1987), Multivariate quality control using principal components, Int. J. of Prod. Res., 25, 571-588.
- WEİSBERG, S., (1985), Applied Linear Regression (2nd ed.), Newyork, John Wiley.
Abstract
Değişkenler arası anlamlı korelasyonun sözkonusu olduğu durumlarda kalite kontrol sürecini gerçekleştirmede değişkenlerin bireysel olarak ele alındığı durumlardan daha güçlü kontrolleri verecek istatistiksel yöntemlerin kullanılması gerekir. Bireysel değişkenleri dikkate alan ayrı ayrı kontrol grafiklerinin kullanımı daha kolay yorumlanabilir olmasına rağmen kalite değişkenleri arası korelasyonun varlığı duyarlılığı azaltır.
İlk olarak, Hotelling (1947) kalite tesadüfi değişkenlerinin dağılımının çok değişkenli normal dağılım olduğu varsayımı altında T2 istatistiğine dayalı çok değişkenli kontrol grafiği önermiştir. Jackson (1959), Schall ve Chandra (1987), Murphy (1987), Hawkins (1991), Mason, Tracy ve Young (1995), Hotelling’in T2’ sini baz alarak bu kontrol dışı durumun hangi değişken veya değişkenlerden kaynaklandığına dair yaklaşımlar önermişlerdir. Bu çalışmada çok değişkenli kalite kontrol konusunda ileri sürülen yöntemlerin bir değerlendirilmesi yapılmaktadır.
References
- HAWKİNS D. M., (1991), Multivariate quality control based on regression-adjusted variables, Techonometrics, 33, 61-75.
- HAWKİNS D. M., ve BRADU (1990), Application of the Moore-Penrose invers of a data matrix in multiple regression, Linear algebra and its applications, 127, 403-426.
- HAWKİNS D. M., and WİXLEY R.A.J. (1986), A note on the transformation of Chi-squared variables to normality, The American Statistician, 40, 296-298.
- HOTELLING H., (1947), Multivariate Quality Control, Techniques of Statistical Analysis, (Ed. C. Eisenhart, M.W. Hastay, and W.A. Wallis, McGraw-Hill, New York, s. 84-111.
- JACKSON J.E., (1959), Quality control methods for several related variables, Technometrics, 1, 359-377.
- MASON R. L., TRACY N. D. and YOUNG J. C., (1995), Decomposition of T2 for Multivariate control chart interpretation, Journal of Quality Technology, 27, 99-108.
- TRACY, N. D., YOUNG J.C., ve MASON R., (1995), A bivariate control chart for paired measurements, Journal of Quality Technology, 27, 4, 370-376.
- MONTGOMERY, DOUGLAS C., (1991), Introduction to Statistical Quality Control, 322-332.
- MURPY, B. J., (1987), Selecting out of control variables with the T2 multivariate quality control procedure, The Statistician, 36, 571-583.
- RAVEH A., (1985), On the use of the inverse of the correlation Matrix in multivariate data analysis, The American Statistician, 39, 39-42.
- RENCHER A.C., (1993), The contribution of individual variables to hotelling T2, Wilks’ A, and R2 . Biometrics, 49, 479-489.
- SCHALL, S. and CHANDRA J., (1987), Multivariate quality control using principal components, Int. J. of Prod. Res., 25, 571-588.
- WEİSBERG, S., (1985), Applied Linear Regression (2nd ed.), Newyork, John Wiley.
Details
| Primary Language | Turkish |
|---|---|
| Subjects | Statistical Analysis, Statistical Quality Control |
| Journal Section | Research Articles |
| Authors | |
| Publication Date | April 15, 2002 |
| Published in Issue | Year 2002 Volume: 1 Issue: 1 |
