TY - JOUR
ID - 22092
TI - An alternative expression for the constant c4[n] with desirable properties
JO - Scientia Iranica
JA - SCI
LA - en
SN - 1026-3098
AU - Munoz, J. F.
AU - Moya-Fernandez, P. J.
AU - Alvarez, E.
AU - Blanco-Encomienda, F. J.
AD - Faculty of Economics and Business, Campus Cartuja s/n. 18071 Granada, Spain
Y1 - 2022
PY - 2022
VL - 29
IS - 6
SP - 3388
EP - 3393
KW - Bias
KW - standard deviation
KW - gamma function
KW - Control chart
KW - Process capability index
DO - 10.24200/sci.2020.52702.2846
N2 - 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.
UR - https://scientiairanica.sharif.edu/article_22092.html
L1 - https://scientiairanica.sharif.edu/article_22092_15321f2f76194a8ea5887b246ff5484a.pdf
ER -