A sampling plan, i.e., n, sample size, and k,
acceptability constant, is determined for the type of variable and
solution method selected, from the two equations
P(AQL) = 1− α, with
α the Type I (producer's) risk, and
P(LTPD) = β, with
β the Type II (consumer's) risk. The quality index is:
for Gaussian, the classical (MIL-STD 414) statistic;
and for exponential,
(U − xbar) ⁄
xbar.
Solution methods available, with
f1 = P(AQL) − (1 − α)
and f2 = P(LTPD) − β, are:
(i) minimization of
maxi |fi|, for
i = 1, 2; and
(ii) Newton-Raphson to solve the two equations.
Tolerance addresses the minimization or the Newton-Raphson convergence.
Exponential: LTPD and calculated n and k
(β = 10 %)
| LTPD) n, k | AQL |
| Code letter | α | 1 % | 4 % |
10 % |
| D | 10 % | 28) 4, 2.80 |
39) 5, 1.99 | 50) 5, 1.44 |
| H | 8 % | 9.3) 17, 3.38 |
18) 18, 2.40 | 29) 19, 1.72 |
| P | 1 % | 3.9) 103, 3.70 |
8.4) 185, 2.73 | 17) 185, 1.95 |
Gaussian: pairs LTPD, k from the standard
[ANSI/ASQC Z1.9, 1980] (β = 10 %)
| LTPD, k | | AQL |
| Code letter, n | α | .65 % |
1 % | 1.5 % | 2.5 % | 4 % |
6.5 % | 10. % |
| D 5 | 10 % | 26, 1.65 | 28, 1.53 |
31, 1.40 | 35, 1.24 | 39, 1.07 | 44.5, .874 |
50, .675 |
| F 10 | 10 % | 13.2, 1.84 | 15.2, 1.72 |
18, 1.58 | 21.5, 1.41 | 25.5, 1.23 | 31, 1.03 |
37, .828 |
| H 20 | 8 % | 7.5, 1.96 | 9.3, 1.82 |
11.2, 1.69 | 14.3, 1.51 | 18, 1.33 |
23, 1.12 | 29, .917 |
| K 50 | 5 % | 4, 2.08 | 5.4, 1.93 |
6.7, 1.80 | 9.2, 1.61 | 12.4, 1.42 | 16.7, 1.21 |
22, 1.00 |
| P 200 | 1 % | 2.2, 2.18 | 3.9, 2.04 |
4.1, 1.89 | 5.95, 1.70 | 8.4, 1.51 | 12.2, 1.29 |
17, 1.07 |
|
