# Equivalency Factor Calculator

Source:`vignettes/articles/compute-equiv-factors.Rmd`

`compute-equiv-factors.Rmd`

This page provides an online calculator to determine two-sample equivalency factors. 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 basis of this method is the following paper. More details are given at the bottom of this page.

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.*

## Details

Based on a user selected qualification sample size (\(n\)), equivalency sample size (\(m\)) and significance level (\(\alpha\)), the factors \(k_1\) and \(k_2\) are calculated. Equivalency limits are set as:

\[ W_{min\,indiv} = \bar{x} - k_1 \cdot s \\ W_{avg} = \bar{x} - k_2 \cdot s \]

The power of this equivalency criteria is investigated through simulation. In this simulation, 2500 qualification samples are drawn from a standard normal distribution (\(N(\mu, \sigma)\)) and equivalency limits are computed based on each qualification sample. Next 2500 equivalency samples are drawn from a \(N(\mu-\delta\sigma, \sigma)\) distribution. Each of the equivalency samples are compared against each of the equivalency limits and the proportion of equivalency samples rejected are reported. Thus, a total of 6,250,000 comparisons are made. This is repeated for several values of \(\delta\).

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.

Graphing is provided by the Plotly JavaScript library, which is licensed under the MIT license.