References

  • Bai, D. S. and Choi, I. S. (1997), “Process Capability Indices for Skewed Populations,” Manuscript.

  • Bissell, A. F. (1990), “How Reliable Is Your Capability Index?” Applied Statistics, 39, No. 3, 331–340.

  • Blom, G. (1958), Statistical Estimates and Transformed Beta Variables, New York: John Wiley & Sons.

  • Bowman, K. O. and Shenton, L. R. (1983), “Johnson’s System of Distributions,” in S. Kotz, N. L. Johnson, and C. B. Read, eds., Encyclopedia of Statistical Sciences, volume 4, 303–314, New York: John Wiley & Sons.

  • Boyles, R. A. (1991), “The Taguchi Capability Index,” Journal of Quality Technology, 23, 107–126.

  • Boyles, R. A. (1992), Cpm for Asymmetrical Tolerances, Technical report, Precision Castparts Corp., Portland, OR.

  • Boyles, R. A. (1994), “Process Capability with Asymmetric Tolerances,” Communication and Statistics, Part B—Simulation and Computation, 23, 615–643.

  • Chambers, J. M., Cleveland, W. S., Kleiner, B., and Tukey, P. A. (1983), Graphical Methods for Data Analysis, Belmont, CA: Wadsworth International Group.

  • Chen, H. F. and Kotz, S. (1996), “An Asymptotic Distribution of Wright’s Process Capability Index Sensitive to Skewness,” Journal of Statistical Computation and Simulation, 55, 147–158.

  • Chen, K. S. (1998), “Incapability Index with Asymmetric Tolerances,” Statistica Sinica, 8, 253–262.

  • Chou, Y., Owen, D. B., and Borrego, S. A. (1990), “Lower Confidence Limits on Process Capability Indices,” Journal of Quality Technology, 22, 223–229. Corrigenda, 24, 251.

  • Cohen, A. C. (1951), “Estimating Parameters of Logarithmic-Normal Distributions by Maximum Likelihood,” Journal of the American Statistical Association, 46, 206–212.

  • Croux, C. and Rousseeuw, P. J. (1992), “Time-Efficient Algorithms for Two Highly Robust Estimators of Scale,” Computational Statistics, 1, 411–428.

  • D’Agostino, R. B. and Stephens, M. (1986), Goodness-of-Fit Techniques, New York: Marcel Dekker.

  • Dixon, W. J. and Tukey, J. W. (1968), “Approximate Behavior of the Distribution of Winsorized t (Trimming/Winsorization 2),” Technometrics, 10, 83–98.

  • Ekvall, D. N. and Juran, J. M. (1974), “Manufacturing Planning,” Quality Control Handbook, Third Edition.

  • Elandt, R. C. (1961), “The Folded Normal Distribution: Two Methods of Estimating Parameters from Moments,” Technometrics, 3, 551–562.

  • Fowlkes, E. B. (1987), A Folio of Distributions: A Collection of Theoretical Quantile-Quantile Plots, New York: Marcel Dekker.

  • Gnanadesikan, R. (1997), Statistical Data Analysis of Multivariate Observations, New York: John Wiley & Sons.

  • Gupta, A. K. and Kotz, S. (1997), “A New Process Capability Index,” Metrika, 45, 213–224.

  • Hahn, G. J. (1969), “Factors for Calculating Two-Sided Prediction Intervals for Samples from a Normal Distribution,” Journal of the American Statistical Association, 64, 878–898.

  • Hahn, G. J. (1970a), “Additional Factors for Calculating Prediction Intervals for Samples from a Normal Distribution,” Journal of the American Statistical Association, 65, 1668–1676.

  • Hahn, G. J. (1970b), “Statistical Intervals for a Normal Population, Part I. Tables, Examples and Applications,” Journal of Quality Technology, 2, 115–125.

  • Hahn, G. J. (1970c), “Statistical Intervals for a Normal Population, Part II. Formulas, Assumptions, Some Derivations,” Journal of Quality Technology, 2, 115–125.

  • Hahn, G. J. and Meeker, W. Q. (1991), Statistical Intervals: A Guide for Practitioners, New York: John Wiley & Sons.

  • Johnson, N. L., Kotz, S., and Balakrishnan, N. (1994), Continuous Univariate Distributions, volume 1, Second Edition, New York: John Wiley & Sons.

  • Johnson, N. L., Kotz, S., and Balakrishnan, N. (1995), Continuous Univariate Distributions, volume 2, Second Edition, New York: John Wiley & Sons.

  • Johnson, N. L., Kotz, S., and Pearn, W. L. (1994), “Flexible Process Capability Indices,” Pakistan Journal of Statistics, 10, 23–31.

  • Kane, V. E. (1986), “Process Capability Indices,” Journal of Quality Technology, 1, 41–52.

  • Kotz, S. and Johnson, N. L. (1993), Process Capability Indices, London: Chapman & Hall.

  • Kotz, S. and Lovelace, C. R. (1998), Process Capability Indices in Theory and Practice, London: Arnold Publishers.

  • Kushler, R. H. and Hurley, P. (1992), “Confidence Bounds for Capability Indices,” Journal of Quality Technology, 24, 188–195.

  • Lehmann, E. L. (1998), Nonparametrics: Statistical Methods Based on Ranks, San Francisco: Holden-Day.

  • Luceño, A. (1996), “A Process Capability Index with Reliable Confidence Intervals,” Communications in Statistics—Simulation, 25, 235–245.

  • Marcucci, M. O. and Beazley, C. F. (1988), “Capability Indices: Process Performance Measures,” Transactions of ASQC Congress.

  • Montgomery, D. C. (1996), Introduction to Statistical Quality Control, Third Edition, New York: John Wiley & Sons.

  • Odeh, R. E. and Owen, D. B. (1980), Tables for Normal Tolerance Limits, Sampling Plans, and Screening, New York: Marcel Dekker.

  • Owen, D. B. and Hua, T. A. (1977), “Tables of Confidence Limits on the Tail Area of the Normal Distribution,” Communication and Statistics, Part B—Simulation and Computation, 6, 285–311.

  • Pearn, W. L., Kotz, S., and Johnson, N. L. (1992), “Distributional and Inferential Properties of Process Capability Indices,” Journal of Quality Technology, 24, 216–231.

  • Rodriguez, R. N. (1992), “Recent Developments in Process Capability Analysis,” Journal of Quality Technology, 24, 176–187.

  • Rodriguez, R. N. and Bynum, R. A. (1992), Examples of Short Run Process Control Methods with the SHEWHART Procedure in SAS/QC Software, Unpublished manuscript available from the authors.

  • Rousseeuw, P. J. and Croux, C. (1993), “Alternatives to the Median Absolute Deviation,” Journal of the American Statistical Association, 88, 1273–1283.

  • Royston, J. P. (1992), “Approximating the Shapiro-Wilks’ W Test for Nonnormality,” Statistics and Computing, 2, 117–119.

  • Shapiro, S. S. and Wilk, M. B. (1965), “An Analysis of Variance Test for Normality (Complete Samples),” Biometrika, 52, 591–611.

  • Silverman, B. W. (1986), Density Estimation for Statistics and Data Analysis, New York: Chapman & Hall.

  • Slifker, J. F. and Shapiro, S. S. (1980), “The Johnson System: Selection and Parameter Estimation,” Technometrics, 22, 239–246.

  • Terrell, G. R. and Scott, D. W. (1985), “Oversmoothed Nonparametric Density Estimates,” Journal of the American Statistical Association, 80, 209–214.

  • Tukey, J. W. (1977), Exploratory Data Analysis, Reading, MA: Addison-Wesley.

  • Tukey, J. W. and McLaughlin, D. H. (1963), “Less Vulnerable Confidence and Significance Procedures for Location Based on a Single Sample: Trimming/Winsorization 1,” Sankhy$\bar{a}$, Series A, 25, 331–352.

  • Vännmann, K. (1995), “A Unified Approach to Capability Indices,” Statistica Sinica, 5, 805–820.

  • Vännmann, K. (1997), “A General Class of Capability Indices in the Case of Asymmetric Tolerances,” Communications in Statistics—Theory and Methods, 26, 2049–2072.

  • Velleman, P. F. and Hoaglin, D. C. (1981), Applications, Basics, and Computing of Exploratory Data Analysis, Boston, MA: Duxbury Press.

  • Wadsworth, H. M., Stephens, K. S., and Godfrey, A. B. (1986), Modern Methods for Quality Control and Improvement, New York: John Wiley & Sons.

  • Wainer, H. (1974), “The Suspended Rootogram and Other Visual Displays: An Empirical Validation,” The American Statistician, 28, 143–145.

  • Wilk, M. B. and Gnanadesikan, R. (1968), “Probability Plotting Methods for the Analysis of Data,” Biometrika, 49, 525–545.

  • Wright, P. A. (1995), “A Process Capability Index Sensitive to Skewness,” Journal of Statistical Computation and Simulation, 52, 195–203.

  • Zhang, N. F., Stenback, G. A., and Wardrop, D. M. (1990), “Interval Estimation of Process Capability Index Cpk,” Comm. in Stat. Theory and Methods, 19, 4455–4470.