tolint

Free core of TolInt: tolerance intervals for normal data.

The problem You need an interval that covers a stated proportion of the population with stated confidence, for a spec limit or a capability claim. A confidence interval covers a parameter, a prediction interval covers one future point. Neither answers "where do 95% of the parts fall". This does.

What it does norm_tol_int(x) gives a two-sided tolerance interval by Howe's approximation (the form Minitab reports), and one-sided intervals are exact via the noncentral t distribution. norm_k_factor(n) gives the k-factor directly (interval = xbar +/- k*s). lognormal=True handles lognormal data through the standard log transform. Search terms: tolerance interval Python, normal tolerance interval, k factor tolerance, Howe tolerance interval.

Limits Normal data only (lognormal through the log transform). The exact two-sided interval (Witkovsky) is not in this free core, and neither are distribution-free intervals or sample-size planning. No CLI.

Install

pip install tolint

Needs Python 3.9 or newer, NumPy, and SciPy.

from tolint import norm_tol_int
import numpy as np
x = np.array([10.1, 9.8, 10.3, 10.0, 9.9, 10.2, 10.1, 9.7, 10.0, 10.2])
iv = norm_tol_int(x, P=0.95)
print(iv.lower, iv.upper)

This is the free core: normal tolerance intervals (Howe two-sided, exact one-sided) and k-factors, with lognormal support. The full version ($30, one-time) adds the exact two-sided Witkovsky interval, two-sided nonparametric Wilks intervals, and sample-size planning: https://groundplane0.gumroad.com/l/zxhmnx