Skip to main content
SpringerLink
Log in

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

  • Research Article
  • Published:
Journal of Pharmaceutical Innovation Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. Xu J, Bai L. Sampling distribution of the coefficient of variation when the population takes normal distribution N(0, σ2). Adv Mater Res. 2011;291–294:3300–4.

    Article  Google Scholar 

  2. Subrahmanya Nairy K, Aruna Rao K. Tests of coefficients of variation of normal population. Comm Stat Simul Comput. 2003;32(3):641–61.

    Article  Google Scholar 

  3. Food and Drug Administration. Guidance for industry: powder blends and finished dosage units—stratified in-process dosage unit sampling and assessment. In: Gad SC, editor. Pharmaceutical Manufacturing Handbook: Regulations and Quality. Hoboken: Wiley; 2003

  4. Pernenkil L, Cooney CL. A review on the continuous blending of powders. Chem Eng Sci. 2006;61(2):720–42.

    Article  CAS  Google Scholar 

  5. McKay AT. Distribution of the coefficient of variation and the extended “t” distribution. J R Stat Soc. 1932;95(4):695–8.

    Article  Google Scholar 

  6. Hendricks WA, Robey KW. The sampling distribution of the coefficient of variation. Ann Math Stat. 1936;7(3):129–32.

    Article  Google Scholar 

  7. Hürlimann W. A uniform approximation to the sampling distribution of the coefficient of variation. Stat Probab Lett. 1995;24(3):263–8.

    Article  Google Scholar 

  8. Banik S, Kibria BMG. Estimating the population coefficient of variation by confidence intervals. Commun Stat Simul Comput. 2011;40(8):1236–61.

    Article  Google Scholar 

  9. Almonte C, Kibria BMG. On some classical, bootstrap and transformation confidence intervals for estimating the mean of an asymmetrical population. Model Assist Stat Appl. 2009;4(2):91–104.

    Google Scholar 

  10. Zhou XH, Dinh P. Nonparametric confidence intervals for the one- and two-sample problems. Biostatistics. 2005;6(2):187–200.

    Article  PubMed  Google Scholar 

  11. Andersson PG. Alternative confidence intervals for the total of a skewed biological population. Ecology. 2004;85(11):3166–71.

    Article  Google Scholar 

  12. Mahmoudvand R, Hassani H. Two new confidence intervals for the coefficient of variation in a normal distribution. J Appl Stat. 2009;36(4):429–42.

    Article  Google Scholar 

Download references

Acknowledgments

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.

Author information

Authors and Affiliations

  1. Department of Chemical and Biochemical Engineering, Rutgers, The State University of New Jersey, 98 Brett Road, Piscataway, NJ, 08854, USA

    Yijie Gao, Marianthi G. Ierapetritou & Fernando J. Muzzio

Authors
  1. Yijie Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Marianthi G. Ierapetritou
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Fernando J. Muzzio
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fernando J. Muzzio.

Appendix

Appendix

Table 3 Chi-on-Mu-square critical values at different significance level and degree of freedom
Full size table

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gao, Y., Ierapetritou, M.G. & Muzzio, F.J. Determination of the Confidence Interval of the Relative Standard Deviation Using Convolution. J Pharm Innov 8, 72–82 (2013). https://doi.org/10.1007/s12247-012-9144-8

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12247-012-9144-8

Keywords

Search

Navigation