Exact False-Alarm Risk for p-Chart Limits — pchart_alpha

Compute the actual false-alarm probability of p-chart limits under the in-control binomial model. The calculation respects the discreteness of \(X \sim Binomial(n, p)\) and treats a signal as \(X/n < LCL\) or \(X/n > UCL\).

Usage

pchart_alpha_risk(p, n, lcl, ucl)

Arguments

p: In-control nonconforming proportion.
n: Positive integer sample size or vector of sample sizes.
lcl: Lower control limit or vector of limits.
ucl: Upper control limit or vector of limits.

Value

A numeric vector with the exact false-alarm probability for each sample size and pair of limits.

Examples

limits <- pchart_limits(0.015, 20, type = "cf2")
pchart_alpha_risk(0.015, 20, limits$lcl, limits$ucl)
#> [1] 0.003178083