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Estimating the Number of Aberrant Laboratories*

Published online by Cambridge University Press:  27 July 2009

Ingram Olkin ,
Irwin Guttman  and
Robert Philips
Ingram Olkin
Affiliation:
Department of Statistics, Stanford University, Stanford, California 94305
Irwin Guttman
Affiliation:
Department of Statistics, University of Buffalo, Buffalo, NY 14214-3000
Robert Philips
Affiliation:
Department of Statistics, University of Toronto, Toronto, Ontario M5S 1A1, Canada
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Abstract

It has long been observed that independent laboratories differ in reporting the results of repeated experiments. The problem is to detect those laboratories that might be considered aberrant. Previous analyses have been based on an analysis of variance framework or on subset selection for the detection of aberrant laboratories. The present procedure is also based on an ANOVA model but uses a Bayesian estimate of the number of aberrant laboratories. Subsequent to the determination of the aberrant laboratories, a linear model is used to separate sampling and laboratory effects.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 9 , Issue 1 , January 1995 , pp. 133 - 150
Copyright
Copyright © Cambridge University Press 1995

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References

1.Belapoldi, R.A., Paule, R., Schaffer, R., & Mandel, J. (1979). A reference method for the determination of chloride. National Bureau of Standards Special Publication, pp. 260–267.Google Scholar
2.Bennett, C.A. & Franklin, W.L. (1954). Statistical analysis in chemistry and the chemical industry. New York: John Wiley and Sons.Google Scholar
3.Box, G.E.P. & Tiao, G.C. (1968). A Bayesian approach to some outlier problems. Biometrika 55: 119–129.CrossRefGoogle ScholarPubMed
4.Daniel, C. (1960). Locating outliers in factorial experiments. Technometrics 2: 149–156.CrossRefGoogle Scholar
5.Draper, N.R.D. & Smith, H. (1981). Applied regression analysis, 2nd ed.New York: John Wiley and Sons.Google Scholar
6.Elder, R.S. (1987). An evaluation of the laboratory ranking test. Journal of Quality Technology 19: 197–203.CrossRefGoogle Scholar
7.Grubbs, F.E. (1948). On estimating precision of measuring instruments and product variability. Journal of the American Statistical Association 43: 243–264.CrossRefGoogle Scholar
8.Jaech, J.L. (1964). A program to estimate measurement error in nondestructive evaluation of reactor fuel element quality. Technometrics 6: 293–300.CrossRefGoogle Scholar
9.Jaech, J.L. (1979). Estimating within-laboratory variability from interlaboratory test data. Journal of Quality Technology xx: xxx.Google Scholar
10.Jordan, D.C. & de Alvare, L.R. (1979). Maximum likelihood estimation evaluation of a material with unequal number of replicates. Analytical Chemistry 51: 1079–1080.CrossRefGoogle Scholar
11.Kramer, K.H. (1967). Use of mean deviation in the analysis of interlaboratory tests. Technometrics 9: 149–153.CrossRefGoogle Scholar
12.Mandel, J. (1958). Intra- and interlaboratory testing. Paper presented at the Gordon Conference on Statistics in Chemistry and Chemical Engineering, New Hampton, NH, 07 21–25.Google Scholar
13.Mandel, J. (1959). The measuring process. Technometrics 1: 251–267.CrossRefGoogle Scholar
14.Mandel, J. (1976). Models, transformations of scale, and weighting. Journal of Quality Technology 8: 86–97.CrossRefGoogle Scholar
15.Mandel, J. (1978). Accuracy and precision: Evaluation and interpretation of analytical results. In Kolthoff, I.M. & Elving, P.J. (eds.), Treatise on analytical chemistry. New York: Wiley, pp. 244–299.Google Scholar
16.Mandel, J. (1978). Planning, design and analysis of interlaboratory studies. American Society for Testing and Materials Standardization News 6(12): 11–13.Google Scholar
17.Mandel, J. & Paule, R.C. (1970). Interlaboratory evaluation of a material with unequal numbers of replicates. Analytical Chemistry 42: 1194–1197.CrossRefGoogle Scholar
18.Olkin, I. & Sobel, M. (1987). A model for interlaboratory differences. In Gupta, A.K. (ed.), Advances in multivariate statistical analysis. Dortrect: D. Reidel Publishing Co., pp. 303–314.CrossRefGoogle Scholar
19.Rocke, D.M. (1983). Robust statistical analysis of interlaboratory studies. Biometrika 70: 421–431.CrossRefGoogle Scholar
20.Youden, W.J. (1959a). Evaluation of chemical analyses on two rocks. Technometrics 1: 409–417.CrossRefGoogle Scholar
21.Youden, W.J. (1959b). Graphical diagnosis of interlaboratory test results. Industrial Quality Control 15: 24–28.Google Scholar
22.Youden, W.J. (1963). Ranking laboratories by round-robin tests. Materials Research and Standards 3: 9–13.Google Scholar
23.Youden, W.J. & Steiner, E.H. (1975). Statistical manual of the Association of Official Analytical Chemists. Arlington, VA: Association of Official Analytical Chemists.Google Scholar