Int. J. Metrol. Qual. Eng.
Volume 13, 2022
|Number of page(s)
|29 November 2022
A double integration method for generating exact tolerance limit factors for normal populations
Nuclear Technology Expert Committee, Korean Agency for Technology and Standards, 93, Isu-ro, Maengdong-myeon, Eumseong-gun, Chungcheongbuk-do 27737, Korea
* Corresponding author: firstname.lastname@example.org
Accepted: 13 October 2022
This article introduces a new method for generating the exact one-sided and two-sided tolerance limit factors for normal populations. This method does not need to handle the noncentral t-distribution at all, but only needs to do a double integration of a joint probability density function with respect to the two independent variables “s” (standard deviation) and “x” (sample mean). The factors generated by this method are investigated through Monte Carlo simulations and compared with the existing factors. As a result, it is identified that the two-sided tolerance limit factors being currently used in practical applications are inaccurate. For the right understanding, some factors generated by this method are presented in Tables along with a guidance for correct use of them. The AQL (Acceptable Quality Level) is a good, common measure about quality of a product lot which was already produced or will be produced. Therefore, when performing sampling inspection on a given lot using a tolerance limit factor, there is a necessity to know the AQL assigned to the factor. This new double integration method even makes it possible to generate the AQLs corresponding to the one-sided and two-sided tolerance limit factors.
Key words: AQL / acceptable quality level / sampling inspection / sample size / tolerance limit factor / tolerance interval
© P. Kang, Published by EDP Sciences, 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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