Calculate t1 and t2 pairs that have the same p-Value

Calculates pairs of t1 and t2 values, which have the same p-value for the two-sample equivalency test. See p_equiv_two_sample().

Usage

iso_equiv_two_sample(n, m, alpha, t1max, t2max, n_points)

Arguments

n

the size of the qualification sample

m

the size of the equivalency sample

alpha

the desired p-value

t1max

the maximum value of t1 (only approximate)

t2max

the maximum value of t2 (only approximate)

n_points

the number of returned points is twice n_points

Value

A data.frame with values of t1 and t2

Details

The values t1 and t2 are based on the transformation:

t1 = (X_mean - Y_min) / S

t2 = (X_mean - Y_mean) / S

Where:

• X_mean is the mean of the qualification sample

• S is the standard deviation of the qualification sample

• Y_min is the minimum from the acceptance sample

• Y_mean is the mean of the acceptance sample

References

Kloppenborg, S. (2023). Lot acceptance testing using sample mean and extremum with finite qualification samples. Journal of Quality Technology, https://doi.org/10.1080/00224065.2022.2147884

See also

p_equiv_two_sample(), k_equiv_two_sample()

Examples

# \donttest{
if(requireNamespace("tidyverse")){
  library(cmstatrExt)
  library(tidyverse)
  curve <- iso_equiv_two_sample(24, 8, 0.05, 4, 1.5, 10)
  curve

  curve %>%
    ggplot(aes(x = t1, y = t2)) +
      geom_path() +
      ggtitle("Acceptance criteria for alpha=0.05")
}
#> ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
#> ✔ dplyr     1.1.4     ✔ readr     2.1.5
#> ✔ forcats   1.0.0     ✔ stringr   1.5.1
#> ✔ ggplot2   3.5.1     ✔ tibble    3.2.1
#> ✔ lubridate 1.9.3     ✔ tidyr     1.3.1
#> ✔ purrr     1.0.2     
#> ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
#> ✖ dplyr::filter() masks stats::filter()
#> ✖ dplyr::lag()    masks stats::lag()
#> ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors

# }