Equivalency Threshold Calculator • cmstatrExt

This page provides an online calculator to determine one- and two-sample equivalency factors and thresholds. This calculator gives the factors $k_1$ and $k_2$ as well as determining the power of the test for detecting reduction in mean. The one-sample factors and thresholds are based on the paper by Vangel below and the two-sample factors and thresholds are based on the paper by Kloppenborg below. More details are given at the bottom of this page.

M. Vangel, “Lot Acceptance and Compliance Testing Using the Sample Mean and an Extremum,” Technometrics, vol. 44, no. 3. pp. 242–249, Aug-2002.

S. Kloppenborg, “Lot acceptance testing using sample mean and extremum with finite qualification samples,” Journal of Quality Technology, 2023. DOI: 10.1080/00224065.2022.2147884

This calculator is provided as-is without any warranty. Users are advised to review the code to verify correctness.

Calculator

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	Qualification Sample	Equivalency Sample
Material & Property
Mean	$\bar{x}_{qual}$	$\bar{x}_{equiv}$
Standard Deviation	$s_{qual}$
Sample Size	$n$	$m$
Minimum		$x_{min\,equiv}$
Significance ( $\alpha$ ):

One-Sample Method
k-Factors	$k_1$	$k_2$
Thresholds	Minimum Individual $W_1 = \bar{x}_{qual} - k_1 s_{qual}$	Minimum Average $W_2 = \bar{x}_{qual} - k_2 s_{qual}$
Result
Two-Sample Method
k-Factors	$k_1$	$k_2$
Thresholds	Minimum Individual $W_1 = \bar{x}_{qual} - k_1 s_{qual}$	Minimum Average $W_2 = \bar{x}_{qual} - k_2 s_{qual}$
Result

Details

The functionality of this page is provided by the same C++ code that is used by the cmstatrExt R package. This code is compiled to WebAssembly so that it can run inside a web browser without the user installing any special software. This software is licensed under the AGPL-3 license. Source code is available here.