Concept of the One-Sided Variance with Applications

  • Park, Hyo-Il (Department of Statistics, Chongju University)
  • Received : 2012.07.04
  • Accepted : 2012.08.28
  • Published : 2012.09.30


In this study, we propose definitions for the one-sided variance for asymmetric distribution. We consider to apply the one-sided variance to the construction to define modified $C_{pk}$, which is a definition for the process capability index for the asymmetric process distribution. Then we consider to obtain the consistent estimation for the one-sided variance and to apply to the various industrial fields.


  1. Bickel, P. J. and Doksum, K. A. (1977). Mathematical Statistics-Basic Ideas and Selected Topics, Holden-Day, San Francisco, California.
  2. Bond, S. A. and Satchell, S. E. (2002). Statistical properties of sample semi-variance, Applied Mathematical Finance, 9, 219-239.
  3. Chung, K. L. (1974). A Course in Probability Theory, 2nd Ed. Academic Press, New York.
  4. Park, H. I. (2011). A modified definition on the process capability index $C_{pk}$ based on median, Communications in Korean Statistical Society, 18, 527-535, 286-297.
  5. Park, S. H. and Park, Y. H. (2005). Statistical Quality Control, 3rd Ed., Min-Young Press, Seoul, Korea.