Statistical tolerance intervals of distributions in tasks associated with acceptable risk
- Authors: Davydov A.R1, Noskova V.V1
- Affiliations:
- Perm National Research Polytechnic University
- Issue: No 2 (2025)
- Pages: 131–139
- Section: ARTICLES
- URL: https://ered.pstu.ru/index.php/amcs/article/view/4705
- DOI: https://doi.org/10.15593/2499-9873/2025.2.09
- Cite item
Abstract
The calculation of tolerance bounds for distributions is a necessary task to effectively address acceptable risk. This is reflected, among other things, in the requirements of international standards. The article provides theoretical information about statistical tolerance intervals and directions of their application. Formulas for calculating one-sided tolerance intervals are presented. As an example, the problem of calculating the characteristics of structural strength of materials in aircraft construction using experimental data is considered. A comparative analysis of the values of the lower tolerance limit using different laws of data distribution is carried out.The use of non-parametric methods for calculation of tolerance limits is shown. Using the basic relation for the calculated indices, the confidence probabilities are obtained, allowing to use the minimum elements of the samples as the left one-sided boundary. At given values of the confidence probability, the dependences of the data coverage values on the sample size are plotted. Statistical modelling methods were used to calculate the values of the lower tolerance boundary. The R software package was used for calculations.
Full Text
9About the authors
A. R Davydov
Perm National Research Polytechnic University
V. V Noskova
Perm National Research Polytechnic University
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