clear;
clf;

// lambda

pas_t = 0.5
lambda0 = 0.15;
lambda1 = 0.015;
lambda2 = 1.5;
t1 = 5;
t2 = 40;
tmax = 50
T1 = 0:pas_t:t1;
T2 = (t1+pas_t):pas_t:t2;
T3 = (t2+pas_t):pas_t:tmax
T = 0:pas_t:tmax;
n = size(T, "*");

n1 = size(T1, "*");
n2 = size(T2, "*");
n3 = size(T3, "*");

lambda(1:n1) = lambda1 + (lambda0/t1^2)*(T1 - t1).^2;
lambda(n1+1:n1+n2) = lambda1;
lambda(n1+n2+1:n1+n2+n3) = lambda1 + (lambda2/(tmax - t2)^2)*(T3 - t2).^2;

// fiabilité

lambda_cumul(1) = lambda(1);
for t = 2:n
    lambda_cumul(t) = lambda_cumul(t-1) + lambda(t);
end
R = exp(-lambda_cumul);
F = 1-R;

// densité

for t = 1:n-1
    f(t) = (R(t)-R(t+1))/pas_t;
end

// Tracé Weibull

Yweib = log(-log(R(2:$)))
Tweib = log(T(2:$));

// Tracé

subplot(2,2,1)
plot(T, [F, R])
xtitle("Fréquences cumulées", "t", "Fréquence")
legend("F (mortalité)", "R (survie)", 2)

subplot(2,2,3)
plot(T(2:$), f)
xtitle("Densité", "t", "$f$")

subplot(2,2,2)
plot2d(T, lambda, rect=[0, 0, 50, 0.3])
xtitle("Taux de défaillance", "t", "$\lambda$")

subplot(2,2,4)
plot(Tweib, Yweib)
xtitle("Tracé ""Weibull"" ", "ln(t)", "ln(-ln(R))")