Robust 2^k factorial design with Weibull error distributions

References

• Bartlett , M. S. 1953 . Approximate confidence intervals . Biometrika , 40 : 12 – 19 .
   Web of Science ®Google Scholar
• Bhattacharrya , G. K. 1985 . The asymptotics of maximum likelihood and related estimators based on type II censored data . Journal of the American Statistical Association , 80 : 398 – 404 .
   Google Scholar
• Box , G. E. P. 1953 . Nonnormality and tests on variances . Biometrika , 40 : 318 – 335 .
   Web of Science ®Google Scholar
• Box , G. E. P. and Tiao , G. C. 1964 . A note on criterion robustness and inference robustness . Biometrika , 51 : 169 – 173 .
   Web of Science ®Google Scholar
• Box , G. E. P. 1978 . Statistics for Experimenters: An Introduction to Design, Data Analysis, and Model Building , New York : Wiley .
   Google Scholar
• Cohen , A. C. and Whitten , B. J. 1988 . Parameter Estimation in Reliability and Life Span Models , New York : Marcel Dekker .
   Google Scholar
• Elveback , L. R. 1970 . Health, normality and the ghost of Gauss . Journal of the American Medical Association , 211 : 69 – 75 .
   PubMed Web of Science ®Google Scholar
• Fisher , R. A. 1935 . The Design of Experiments , Edinburgh : Oliver & Boyd .
   Google Scholar
• Geary , R. C. 1947 . Testing for normality . Biometrika , 34 : 209 – 242 .
   PubMed Web of Science ®Google Scholar
• Hallinan , A. Jr. 1993 . A review of the Weibull distribution . Journal of Quality Technology , 25 ( 2 ) : 85 – 93 .
   Web of Science ®Google Scholar
• Hinkelmann , K. and Kempthorne , O. 1994 . Design and Analysis of Experiments, Volume 1 , New York : Wiley .
   Google Scholar
• Huber , P. J. 1981 . Robust Statistics , New York : Wiley .
   Google Scholar
• Islam , M. Q. 2001 . Nonnormal regression I. Skew distributions . Communications in Statistics-Theory and Methods , 30 ( 6 ) : 993 – 1020 .
   Web of Science ®Google Scholar
• Kendall , M. G. and Stuart , A. 1979 . The Advanced Theory of Statistics , London : Charles Griffin .
   Google Scholar
• Meeker , W. Q. and Escobar , L. A. 1998 . Statistical Methods for Reliability Data , New York : Wiley .
   Google Scholar
• Montgomery , D. C. 1984 . Design and Analysis of Experiments , New York : Wiley .
   Google Scholar
• Montgomery , D. C. 1997 . Introduction to Statistical Quality Control , New York : Wiley .
   Google Scholar
• Nelson , W. 1990 . Accelerated Testing , New York : Wiley .
   Google Scholar
• Pearson , E. S. 1932 . The analysis of variance in cases of nonnormal variation . Biometrika , 23 : 114 – 133 .
   Web of Science ®Google Scholar
• Puthenpura , S. and Sinha , N. K. 1986 . Modified maximum likelihood method for the robust estimation of system parameters from very noisy data . Automatica , 22 : 231 – 235 .
   Web of Science ®Google Scholar
• Smith , R. L. 1985 . Maximum likelihood estimation in a class of nonregular cases . Biometrika , 72 : 67 – 90 .
   Web of Science ®Google Scholar
• Şenoğlu , B. 2000 . “ Experimental design under nonnormality: skew distributions ” . Ankara, , Turkey : Department of Statistics, METU . PhD Dissertation, unpublished
   Google Scholar
• Şenoğlu , B. and Tiku , M. L. 2001 . Analysis of variance in experimental design with nonnormal error distributions . Communications in Statistics-Theory and Methods , 30 : 1335 – 1352 .
   Web of Science ®Google Scholar
• Şenoğlu , B. and Tiku , M. L. 2002 . Linear contrasts in experimental design with non-identical error distributions . Biometrical Journal , 44 ( 3 ) : 359 – 374 .
   Google Scholar
• Tan , W. Y. and Tiku , M. L. 1999 . Sampling Distributions In Terms of Laguerre Polynomials with Applications , New Delhi : New Age International; formerly, Wiley Eastern .
   Google Scholar
• Tiku , M. L. 1967 . Estimating the mean and standard deviation from censored normal samples . Biometrika , 54 : 155 – 165 .
   PubMed Web of Science ®Google Scholar
• Tiku , M. L. and Vaughan , D. C. 1997 . Logistic and nonlogistic density functions in binary regression with nonstochastic covariates . Biometrical Journal , 39 : 883 – 898 .
   Web of Science ®Google Scholar
• Tiku , M. L. 1986 . Robust Inference , New York : Marcel Dekker .
   Google Scholar
• Vaughan , D. C. 1992 . On the Tiku–Suresh method of estimation . Communications in Statistics-Theory and Methods , 21 : 451 – 469 .
   Web of Science ®Google Scholar
• Vaughan , D. C. and Tiku , M. L. 2000 . Estimation and hypothesis testing for a non-normal bivariate distribution and applications . Journal of Mathematical and Computer Modelling , 32 : 53 – 67 .
   Web of Science ®Google Scholar
• Vaughan , D. C. 2002 . The generalized secant hyperbolic distribution and its properties . Communications in Statistics-Theory and Methods , 31 : 219 – 238 .
   Web of Science ®Google Scholar
• Yates , F. 1937 . “ Design and analysis of factorial experiments ” . London : Imperial Bureau of Soil Sciences . Tech. Comm. No. 35
   Google Scholar