File:Regression lois statistiques fiabilite locotracteur.svg
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Summary
DescriptionRegression lois statistiques fiabilite locotracteur.svg |
Français : Régression pour trouver un modèle paramétrique de la fiabilité.
Créé avec Scilab, modifié avec Inkscape. English: Regression to find a parametric model for the Reliability.
Created with Scilab, modified with Inkscape. |
Date | |
Source | Own work |
Author | Cdang |
Other versions | same data as File:Exemple fiabilite F R lambda.svg |
Scilab source
This media was created with Scilab, a free open-source software. Here is a listing of the Scilab source used to create this file. |
// Ce script nécessite le module Atoms CASCI
clear;
// paramètres de la loi de Weibull
beta_forme = 0.845;
eta_echelle = 126;
// génération des données
// Y = linspace(0, 1, 30)
// Y = Y(2:$-1);
// t_orig = floor(idfweibull(Y, beta_forme, eta_echelle))';
t = [2, 5, 9, 13, 17, 22, 27, 39, 39, 39, 52, 64, 64, 76, 86, 97, 108, 121,...
135, 151, 169, 191, 215, 245, 282, 332]';
t_complet = [t ; 365 ; 365];
N = 28
// nombre cumulé
i = 1;
j = 1
n0 = 1;
nt = size(t, "*");
while i < nt
if t(i)<>t(i+1) then
dn(j) = n0; n0 = 1;
tt(j) = t(i);
j = j + 1;
else
n0 = n0 + 1;
end
i = i+1;
end
dn(j) = n0;
tt(j) = t(i);
ndn = j;
n(1) = dn(1);
for i = 2:ndn
n(i) = n(i-1) + dn(i);
end
// Fréquences cumulées
F = n/(N+1);
R = 1-F;
// loi exponentielle
lnR = log(R);
a_exp=sum(tt.*lnR)/sum(tt.^2);
Rexp = 1-cdfexponential(tt, -a_exp);
// tracé
scf(0);
clf;
subplot(2,2,1)
plot(tt, lnR, "o")
xpoly([tt(1), tt($)], [a_exp*tt(1), a_exp*tt($)]);
xtitle("Diagramme semi-logarithmique (loi exponentielle)", "t (j)", "ln R")
xstring(240, -0.2, "$\lambda ="+string(-a_exp)+"$");
// droite de Henry : quantiles loi normale
t_norm = idfnormal(F, 0, 1);
[a_norm, b_norm, sigmanorm] = reglin(tt', t_norm'); // régression linéaire
sigma_norm = 1/a_norm;
mu_norm = -b_norm*sigma_norm;
Rnorm = cdfnormal(tt, mu_norm, sigma_norm);
subplot(2, 2, 2)
plot(tt, t_norm, "o");
xpoly([tt(1), tt($)], [a_norm*tt(1) + b_norm, a_norm*tt($) + b_norm]);
xtitle("Droite de Henry (loi normale)", "t (j)", "quantile")
xstring(10, 1.15, "$\mu ="+string(mu_norm)+"\text{ ; } \sigma ="...
+string(sigma_norm)+"$")
// droite de Henry : quantiles loi log-normale
lnt = log(tt);
[a_lognorm, b_lognorm, sigmalognorm] = reglin(lnt', t_norm');
// régression linéaire
sigma_lognorm = 1/a_lognorm;
mu_lognorm = -b_lognorm*sigma_lognorm;
Rlognorm = 1-cdfnormal(lnt, mu_lognorm, sigma_lognorm);
subplot(2, 2, 3)
plot(lnt, t_norm, "o");
xpoly([lnt(1), lnt($)], [a_lognorm*lnt(1) + b_lognorm, a_lognorm*lnt($) + b_lognorm]);
xtitle("Droite de Henry (loi log-normale)", "ln t", "quantile")
xstring(0.2, 1.15, "$\mu ="+string(mu_lognorm)+"\text{ ; } \sigma ="...
+string(sigma_lognorm)+"$")
// loi de Weibull
Yweib = log(-log(R));
[a_weib, b_weib, sigma_weib] = reglin(lnt', Yweib');
beta_weib = a_weib;
lambda = exp(-b_weib/beta_weib);
Rweib = 1-cdfweibull(tt, beta_weib, lambda);
subplot(2,2,4)
plot(lnt, Yweib, "o")
xpoly([lnt(1), lnt($)], [a_weib*lnt(1) + b_weib, a_weib*lnt($) + b_weib]);
xtitle("Diagramme de Weibull", "t (j)", "ln R")
xstring(0.2, 0.55, "$\beta ="+string(beta_weib)+"\text{ ; } \lambda ="...
+string(lambda)+"$");
scf(1);
clf;
subplot(2,2,1)
plot(tt, R, "o")
plot(tt, Rexp)
xtitle("Loi exponentielle", "t (j)", "R")
subplot(2,2,2)
plot(tt, R, "o")
plot(tt, 1-Rnorm)
xtitle("Loi normale", "t (j)", "R")
subplot(2,2,3)
plot(tt, R, "o")
plot(tt, Rlognorm)
xtitle("Loi log-normale", "t (j)", "R")
subplot(2,2,4)
plot(tt, R, "o")
plot(tt, Rweib)
xtitle("Loi de Weibull", "t (j)", "R")
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
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- You are free:
- to share – to copy, distribute and transmit the work
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- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
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Items portrayed in this file
depicts
27 June 2013
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 09:30, 1 July 2013 | 584 × 456 (242 KB) | Cdang | + parameters values in log-normal case | |
09:01, 1 July 2013 | 584 × 456 (280 KB) | Cdang | Wrong method for the Henry's lines | ||
15:54, 27 June 2013 | 610 × 460 (282 KB) | Cdang | User created page with UploadWizard |
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- Usage on fr.wikipedia.org
Metadata
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If the file has been modified from its original state, some details may not fully reflect the modified file.
Short title | Régression sur des lois paramétriques en fiabilité |
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Width | 584.0459 |
Height | 455.63477 |