@article {
author = {Munoz, J. F. and Moya-Fernandez, P. J. and Alvarez, E. and Blanco-Encomienda, F. J.},
title = {An alternative expression for the constant c4[n] with desirable properties},
journal = {Scientia Iranica},
volume = {29},
number = {6},
pages = {3388-3393},
year = {2022},
publisher = {Sharif University of Technology},
issn = {1026-3098},
eissn = {2345-3605},
doi = {10.24200/sci.2020.52702.2846},
abstract = {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.},
keywords = {Bias,standard deviation,gamma function,Control chart,Process capability index},
url = {https://scientiairanica.sharif.edu/article_22092.html},
eprint = {https://scientiairanica.sharif.edu/article_22092_15321f2f76194a8ea5887b246ff5484a.pdf}
}