|
|
| n |
|
Sample size. |
| AQL |
% |
AQL, in percent (e.g., 0.10 means
AQL = 0.10 % or 0.001). |
| k |
|
Acceptability constant (as in ANSI/ASQC Z1.9-1980
[1980]) |
| r |
|
Indicates an approximation to the lower limit of
integration, −∞, which will become
μ − r.σ
(see below). |
| h |
|
Numerical integration interval [not so small
that the number of intervals becomes greater than a certain limit (see
below)]. |
Calculates the probability [cumulative distribution function (cdf)]
underlying a given acceptability constant, k, such as the one in
each sampling plan in the ANSI document mentioned. Numerical
integration is used to compute the probability, from the definition
formulas [Resnikoff et al., 1957].
The parameters μ and σ are the moments of a
non-central t, given f (degrees of freedom) and
δ (non-centrality). (The problem data
determine the values of the two parameters.) Namely, the mean
is [MathWorld]
μ = δ √
(f/2) Γ[(f−1)/2] / Γ(f/2)
To find out the minimum h —leading to the maximum number
of integration intervals and maximum acceptable execution time—, run
e.g. the default problem.
For comparison, related results are calculated for the same
t: Student's t cdf (both via a library and by the same
numerical techniques) and Gauss. |
(03-Sep-2002) |
References
• Anonymous, 1980,
ANSI/ASQC Z1.9-1980,
(...)
• Resnikoff, G. J., G. J. Lieberman, 1957, "Tables of the
non-central t distribution: density function, cumulative
distribution function and percentage points", Stanford University Press,
Stanford, CA
• MathWorld:
Noncentral
Student's t-Distribution
|
|