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Exact one-tailed 100p% upper limits for future sample repeatability relative standard deviations obtained in single-

Foster D McClure¹, Jung K Lee

¹U.S. FDA, Center for Food Safety and Applied Nutrition, Office of Food Defense, Communication and Emergency Response, Division of Public Health and Biostatistics, Biostatistics Branch, College Park, MD 20740-3835, USA. fdmc5100@yahoo.com

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Summary

New formulas provide exact upper limits for future sample repeatability relative standard deviations in analytical method validation. These calculations are essential for ensuring method accuracy and reliability in both single and multi-laboratory studies.

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Area of Science:

Analytical Chemistry
Statistical Methods
Method Validation

Background:

Repeatability relative standard deviation is a critical metric in analytical method validation.
Accurate estimation of future performance is necessary for reliable method application.
Existing methods may lack precision for establishing robust upper limits.

Purpose of the Study:

To derive exact one-tailed upper limits for future sample repeatability relative standard deviations.
To provide formulas applicable to both single- and multi-laboratory repeatability studies.
To enhance the statistical rigor of analytical method validation.

Main Methods:

Derivation of formulas based on the noncentral t-distribution.
Application of derived formulas for calculating kappa(p) and nu(p) upper limits.
Utilizing statistical theory for precise estimation of variability.

Main Results:

Exact one-tailed 100p% upper limits (kappa(p) and nu(p)) were derived.
Formulas are presented for single-laboratory and multi-laboratory repeatability studies.
The noncentral t-distribution provides a robust theoretical basis for the limits.

Conclusions:

The derived formulas offer precise statistical tools for assessing future repeatability.
These methods improve the reliability of analytical method validation.
The findings support more confident application of validated analytical methods.