# Reliability - Calculate importance factor of random variables in system

I have a system that can fail by 3 different modes. These fail modes functions are ff1, ff2 and ff3. The fail functions have 3 random variables (x, y, z).

I can calculate the probabilities of failure mode 1, 2, 3 and the combined failure modes (ff1 and ff2, ff1 and ff3, ff2 and ff3).

My question: how do I calculate the "importance factor" of each random variable for each mode?

xd = NormalDistribution[0, 1.];
yd = NormalDistribution[1, 2.];
zd = NormalDistribution[3, 1.];
dist = {x \[Distributed] xd, y \[Distributed] yd, z \[Distributed] zd};
ff1 = x - y <= 0;
ff2 = z - .5 x <= 0;
ff3 = z - .8 x - .1 y <= 0;

pf1 = NProbability[ff1, dist]
pf2 = NProbability[ff2, dist]
pf3 = NProbability[ff3, dist]
(*
0.67264
0.00364518
0.0126302
*)
Pf12 = NProbability[ff1 \[And] ff2, dist]
Pf13 = NProbability[ff1 \[And] ff3, dist]
Pf23 = NProbability[ff2 \[And] ff3, dist, Method -> {"MonteCarlo", PrecisionGoal -> 10}]
(*
0.0016
0.0067742
0.00365613
*)

• You should define the "importance factor" ... – Dr. belisarius Sep 17 '15 at 16:19
• Use the built-in functionality (and for the overall reliability distribution too)? – ciao Sep 17 '15 at 16:51
• perhaps something like reference.wolfram.com/mathematica/example/… – Dr. belisarius Sep 17 '15 at 17:04
• What I want to do is a sensitivity analysis, that is, what is the influence of each random variable in the final probability of fail. I saw Mathematica's importance functions but they don't accept fail functions (ff1, ff2, ff3) as arguments. – LeoRon7 Sep 17 '15 at 18:25