%0 Journal Article
%T An alternative expression for the constant c4[n] with desirable properties
%J Scientia Iranica
%I Sharif University of Technology
%Z 1026-3098
%A Munoz, J. F.
%A Moya-Fernandez, P. J.
%A Alvarez, E.
%A Blanco-Encomienda, F. J.
%D 2022
%\ 12/01/2022
%V 29
%N 6
%P 3388-3393
%! An alternative expression for the constant c4[n] with desirable properties
%K Bias
%K standard deviation
%K gamma function
%K Control chart
%K Process capability index
%R 10.24200/sci.2020.52702.2846
%X The constant c4[n] is commonly used in the construction of control charts and the estimation of process capability indices, where n denotes the sample size. Assuming the Normal distribution the unbiased estimator of the population standard deviation is obtained by dividing the sample standard deviation by the constant c4[n]. An alternative expression for c4[n] is proposed, and the mathematical induction technique is used to prove its validity. Some desirable properties are described. First, the suggested expression provides the exact value of c4[n]. Second, it is not a recursive formula in the sense it does not depend on the previous sample size. Finally, the value of c4[n] can be directly computed for large sample sizes. Such properties suggest that the proposed expression may be a convenient solution in computer programming, and it has direct applications in statistical quality control.
%U https://scientiairanica.sharif.edu/article_22092_15321f2f76194a8ea5887b246ff5484a.pdf