# How to compute probability of failure based on built PCE?

Greeting, PCE model of response Y is built,
then how to define the limit state equation based on built PCE and compute probability of failure?

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Hi @AmosJoseph ,

A bit late but better than never…
You can use the PCE model just like any other model. Is the PCE a metamodel for your true limit state function? Then you can just perform the reliability analysis as in this example: Two-dimensional hat function. If the limit state function is a function of your model/metamodel, there are several options: see Section 2.1 of the Model user manual.

By the way, it is not recommended to compute probabilities of failure using PCE metamodels. The reason is that by design, PCE metamodels are accurate in those regions of the input space where there is a lot of probability mass. But they are not guaranteed to be accurate in the regions of low probability (the tails), which are exactly what you are interested in when you ask for the probability of failure. Instead of a PCE metamodel, you should use your original model and a specialized reliability technique such as FORM, SORM, or subset simulation (see the reliability user manual).

Good luck!

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OK. Thank you for your kind reply!