In "acceptance sampling" by (Gaussian) variables, computes, for given sample size, n, and AQL, the non-central t-distribution (NCT) related to the quality index, Q (t = Q√n), in order to find a critical value, k, for it, according to a given producer's risk ("Type I"), α.
 †In the form of the NCT adopted, the interior integral is numerically computed here from 0 to M, instead of to infinity. If a negative default value is given, it will be M = ⌊√(5 n)⌉ (i.e., rounded).
 The values t_low and t_upp may have to be adjusted so as to include the computed t, which can be done by simple trials. A wide interval such as (1, 50), although sufficient, produces a less suggestive graph.
 Plots F, the NCT, vs. t, for the given sample size.
 For the base data, the standard gives k = 1.30 [or (n, AQL, α, M) = (10, 1.5 %, 10 %, 9): k = 1.58].

• ANSI/ASQ Z1.9, "Sampling procedures and tables for inspection by variables for percent nonconforming", ASQ, Milwaukee, WI (USA).

• Google: Mil-Std-414

• Google: "acceptance sampling"

• 1629-04-14: Biot, Jean Baptiste (1862-02-03).