Comparison of Robust Estimators of Standard Deviation in Normal Distributions Within the Context of Quality Control

References

• Davis , R. B. , Woodall , W. H. ( 1988 ). Performance of the control chart trend rule under linear shift . J. Qual. Technol. 20 : 260 – 262 .
   Web of Science ®Google Scholar
• Blyth , C. R. ( 1972 ). Some paradoxes in choice from among random alternatives . J. Amer. Statist. Assoc. 67 : 366 – 373 .
   Web of Science ®Google Scholar
• Bryce , G. R. , Gaudard , M. A. , Joiner , B. L. ( 1997 ). Estimating the standard deviation for individual control charts . Qual. Eng. 10 : 331 – 341 .
   Google Scholar
• Duncan , A. J. ( 1955 ). The use of ranges in comparing variabilities . Industr. Qual. Contr. 11 : 18 – 22 .
   Google Scholar
• Fountain , R. L. , Keating , J. P. ( 1994 ). The Pitman comparison of unbiased linear estimators . Statist. Probab. Lett. 19 : 131 – 136 .
   Web of Science ®Google Scholar
• Fountain , R. L. , Keating , J. P. , Maynard , H. B. ( 1996 ). The simultaneous comparison of estimators . Mathemat. Meth. Statist. 5 : 187 – 198 .
   Google Scholar
• Huber , P. J. (1964). Robust estimation of a location parameter. Ann. Mathemat. Statist. 35:73–101.
   Google Scholar
• Keating , J. P. , Mason , R. L. , Sen , P. K. ( 1993 ). Pitman's Measure of Closeness: A Comparison of Statistical Estimators . Philadelphia : Society for Industrial and Applied Mathematics .
   Google Scholar
• Khattree , R. ( 1992 ). Comparing estimators for population variance using Pitman nearness . Amer. Statistician 46 : 214 – 217 .
   Web of Science ®Google Scholar
• Luko , S. ( 1996 ). Concerning the estimators and in estimating variability in a normal universe . Qual. Eng. 8 : 481 – 487 .
   Google Scholar
• Nayak , T. ( 1994 ). Pitman nearness comparison of some estimators of population variance . Amer. Statistician 48 : 99 – 102 .
   Google Scholar
• Nelson , L. ( 1975 ). Use of the range to estimate variability . J. Qual. Technol. 7 : 46 – 48 .
   Google Scholar
• Ott , E. ( 1975 ). Process Quality Control . New York : McGraw-Hill .
   Google Scholar
• Patnaik , P. B. ( 1950 ). The use of mean range as an estimator of variance in statistical tests . Biometrika 37 : 78 – 87 .
   PubMed Web of Science ®Google Scholar
• Pitman , E. J. ( 1937 ). The “closest” estimates of statistical parameters . Proc. Cambridge Philosoph. Soc. 33 : 212 – 222 .
   Google Scholar
• Podolski , G. ( 1989 ). Standard deviation: root mean square versus range conversion . Qual. Eng. 2 : 155 – 161 .
   Google Scholar
• Prescott , P. ( 1971 ). Use of a simple range-type estimator of σ in tests of hypotheses . Biometrika 58 : 333 – 340 .
   Web of Science ®Google Scholar
• Rao , C. R. ( 1981 ). Some comments on the minimum mean square error as a criterion in estimation . In: Statistics and Related Topics . Amsterdam : North Holland , pp. 123 – 143 .
   Google Scholar
• Rhiel , G. S. ( 1986 ). The effect of non-normality on the use of the range in estimating the population standard deviation . J. Statist. Comput. Simul. 24 : 71 – 82 .
   Web of Science ®Google Scholar
• Rocke , D. M. ( 1989 ). Robust control charts . Technometrics 31 : 173 – 184 .
   Web of Science ®Google Scholar
• Shewhart , W. A. ( 1931 ). Economic Control of Manufactured Product . New York : D. Van Nostrand .
   Google Scholar
• Tatum , L. G. ( 1997 ). Robust estimation of the process standard deviation for control charts . Technometrics 39 : 127 – 141 .
   Web of Science ®Google Scholar
• Tippett , L. H. C. ( 1925 ). On the extreme individuals and the range of samples taken from a normal population . Biometrika 17 : 364 – 387 .
   Web of Science ®Google Scholar
• Western Electric Company ( 1956 ). Statistical Quality Control Handbook . Chicago : American Telephone and Telegraph Company .
   Google Scholar
• Woodall , W. H. ( 2000 ). Controversies and contradictions in statistical process control . J. Qual. Technol. 32 : 341 – 350 .
   Web of Science ®Google Scholar
• Woodall , W. H. , Montgomery , D. ( 2000 ). Using ranges to estimate variability . Qual. Eng. 13 : 211 – 217 .
   Google Scholar
• †Passed away while working on project.
   Google Scholar