Dear SciLab Friends:

I have an object consisting of many (~10,000) small components that can fail in 
a statistical way during long-term operation at extreme conditions.

My primary failure model is described by PHI(t) going monotonically from zero 
to one at times from t=0 to T. In the computer, this is realized in n timesteps.

Mechanism 2: There is a secondary failure mechanism that starts only when a 
component has previously failed by mechanism 1 and occurs after some delay. The 
delay function is f(t) and final expression for the evolution of the mechanism 
2 failure is given by:

F(t)  = Int_{0}^{T}  PHI(t) . f(T-t) . dt

a classical convolution Faltungsintegral.

In Scilab, I write

F= conv(PHI, f, "same")/ n;

and the resulting function F looks reasonable for most of the time. Under some 
conditions, however, I can have


at early stages, but this is physically impossible. Because it comes later, F 
must always be below PHI.
What do I do wrong?

PS: massively simplified code below......

k=1E-7;              // corrosion rate(s-1) in mechanism #1
n=100;               // number of timesteps
t=(1:n)';             // time in days
ts= 3600*t;          // time in seconds
PHI= 1 - exp(-((k*ts)^2));   // failure fraction in mechanism #1
plot("nl", t, PHI, 'r--');
f= 1 - exp(-ts/3E5);         // "pure" failure fraction in mechanism #2
F=conv(PHI,f,"same")/length(t); //"convoluted" failure fraction mechanism #2
legend('failure fraction #1','subsequent failure fraction #2',4);
xlabel('time (hours)');
ylabel('failure fraction');
title('Component failure evolution #1 is followed by #2');
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