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.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Price excludes VAT (USA)
Tax calculation will be finalised during checkout.
Leone FC, Nelson LS, Nottingham RB (1961) The folded normal distribution. Technometrics 3(4):543–550
Johnson NL (1962) The folded normal distribution: accuracy of the estimation by maximum likelihood. Technometrics 4(2):249–256
Nelson LS (1980) The folded normal distribution. J Qual Technol 12(4):236–238
Elandt RC (1961) The folded normal distribution: two methods of estimating parameters from moments. Technometrics 3(4):551–562
Kane VE (1986) Process capability indices. J Qual Technol 18(1):41–52
Pearn WL, Kotz S, Johnson NL (1992) Distributional and inferential properties of process capability indices. J Qual Technol 24(4):216–231
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):985–1000
Pearn WL, Chen KS (1998) New generalization of process capability index Cpk. J Appl Stat 25(6):801–810
About this article
Cite this article
Lin, P. Application of the generalized folded-normal distribution to the process capability measures. Int J Adv Manuf Technol 26, 825–830 (2005). https://doi.org/10.1007/s00170-003-2043-x