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

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.