An alternative expression for the constant c4[n] with desirable properties

Document Type : Article

Authors

Faculty of Economics and Business, Campus Cartuja s/n. 18071 Granada, Spain

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

References

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Scientia Iranica
Volume 29, Issue 6 - Serial Number 6
Transactions on Industrial Engineering (E)
November and December 2022
Pages 3388-3393

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History

  • Receive Date: 15 January 2019
  • Revise Date: 07 February 2020
  • Accept Date: 07 December 2020

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