k factor for one-sided normal tolerance limit

Matlab script:

%
% k_factor.m ver 1.0 by Tom Irvine
%
% k factor for one-sided normal tolerance limit
%
% p = probability percent
% c = confidence percent
% nsamples = number of samples
%
% k = tolerance factor
% Zp = Z limit corresponding to probability area in the normal
% distribution curve
%
% nu = degrees of freedom
% delta = Noncentrality parameter
% T = Noncentral T-distribution abscissa
%
% Matlab functions from Statistics and Machine Learning Toolbox:
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% norminv – Normal inverse cumulative distribution function
% nctinv – Noncentral t inverse cumulative distribution function
%

function[k,Zp,delta,T]=k_factor(p,c,nsamples)

nu=nsamples-1;

probability=p/100;
confidence=c/100;

Zp = norminv(probability);

delta=sqrt(nsamples)*Zp;

T = nctinv(confidence,nu,delta);

k=T/sqrt(nsamples);

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Maximum predicted environment (MPE) levels can be derived for acoustic, shock, and vibration levels where flight data is available.  The enveloping for multiple sets of data can be performed using tolerance factors as described in the following papers.

Normal Tolerance Factors for Upper Tolerance Limits:
normal_tolerance_factors.pdf & Alternate Link

Uncertainty Margins in Aerospace Vibroacoustic Levels:
uncertainty.pdf & Alternate Link

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Example for P95/50 Normal Tolerance Limit:

50% chance of one exceedance of the P95/50 level in 20 flights or ground tests.

– Tom Irvine