Advertisement

Application of the generalized folded-normal distribution to the process capability measures

  • P.C. Lin
Original Article

Abstract

A generalized folded distribution arises when deviations are measured and the weighted magnitude is recorded, where the weight depends on the degree and the direction (sign) of the deviation. When the underlying distribution is normal, the resulting distribution is referred to as the generalized folded-normal distribution. In this paper, we derive explicit forms of the cumulative distribution function and the probability density function of the generalized folded-normal distribution, and calculate the expected value and the variance. An application of the generalized folded-normal distribution to the process capability measures is illustrated.

Keywords

Generalized folded-normal distribution Process capability index rth moment 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Leone FC, Nelson LS, Nottingham RB (1961) The folded normal distribution. Technometrics 3(4):543–550MathSciNetCrossRefGoogle Scholar
  2. 2.
    Johnson NL (1962) The folded normal distribution: accuracy of the estimation by maximum likelihood. Technometrics 4(2):249–256MathSciNetCrossRefGoogle Scholar
  3. 3.
    Nelson LS (1980) The folded normal distribution. J Qual Technol 12(4):236–238CrossRefGoogle Scholar
  4. 4.
    Elandt RC (1961) The folded normal distribution: two methods of estimating parameters from moments. Technometrics 3(4):551–562MathSciNetCrossRefGoogle Scholar
  5. 5.
    Kane VE (1986) Process capability indices. J Qual Technol 18(1):41–52CrossRefGoogle Scholar
  6. 6.
    Pearn WL, Kotz S, Johnson NL (1992) Distributional and inferential properties of process capability indices. J Qual Technol 24(4):216–231CrossRefGoogle Scholar
  7. 7.
    Pearn WL, Lin GH, Chen KS (1998) Distributional and inferential properties of the process accuracy and process precision indices. Commun Stat Theory Methods 27(4):985–1000CrossRefGoogle Scholar
  8. 8.
    Pearn WL, Chen KS (1998) New generalization of process capability index Cpk. J Appl Stat 25(6):801–810CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  1. 1.General Education CenterNational Chin-Yi Institute of TechnologyTaipingTaiwan

Personalised recommendations