Journal of Pharmaceutical Innovation

, Volume 8, Issue 2, pp 72–82 | Cite as

Determination of the Confidence Interval of the Relative Standard Deviation Using Convolution

  • Yijie Gao
  • Marianthi G. Ierapetritou
  • Fernando J. MuzzioEmail author
Research Article


Coefficient of variation is a widely used measure of dispersion and is important in comparing variables with different units or average values. In pharmaceutical industry, it is termed as the relative standard deviation (RSD) and is used widely to describe blend concentration variability, finished dose variability, dissolution q point variability, etc. Although theoretical formula and simulation methods for the estimation of the RSD confidence interval have been developed in previous literature, they are not well known, and they are either too complex to apply easily or require intensive computation. As a result, the statistical reliability of RSD estimates are rarely evaluated, which increases process risk as well as consumer risk. In this paper, we introduce a novel convolution numerical method for the quick and straightforward estimation of RSD confidence intervals. A standard statistical distribution group is developed, denoted as the Chi-on-Mu-square distribution, which is similar to the widely used Chi-square distribution. Results indicate the Chi-square distribution itself can be a good approximation in the RSD confidence interval calculation, especially when small RSD is expected or large number of samples is involved. The effect of deviations from the normal distribution populations is also discussed.


Coefficient of variation Confidence interval Relative standard deviation Quality by design 



This work is supported by the National Science Foundation Engineering Research Center on Structured Organic Particulate Systems, through grant NSF-ECC 0540855 and by grant NSF-0504497.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Yijie Gao
    • 1
  • Marianthi G. Ierapetritou
    • 1
  • Fernando J. Muzzio
    • 1
    Email author
  1. 1.Department of Chemical and Biochemical EngineeringRutgers, The State University of New JerseyPiscatawayUSA

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