# Reliability of Parallel System (Example UQLab Documentation)

Hi All,

Thank you so much for the amazing software. I was looking at the reliability of the parallel system (MCS approach) example in the UQlab documentation section and was quite concerned why the results were not the same as using the know reliability formulation for parallel systems.

The example had two limit state functions in parallel.

1. g1(r,s) = 1.2r - 0.9s
2. g2(r,s) = r-s

The max (g1(r,s),g2(r,s)) approach was used to obtain the Probability of Failure of the system which was 2.03E-4.

However, if you obtain the probability of failure of the individual limit state function and multiply them together (Parallel System) you obtain :

g1(r,s) = 2.028E-4
g2 (r,s) = 2.2699E-2
if we multiply this two together we obtain (POF= 4.6 E-6). The question why can’t we multiply the POF of the two limit state function to obtain the POF of the parallel system?

Appreciate your thoughts. Reference if to UQlab example on the reliability of parallel systems.