Good Day all,

First, I want to thank the UQLab team for such a great job putting together this software. I had a look at the example on reliability of parallel system as well as time variant reliability. However, I have a few concerns and will be grateful if anyone can be of help as I do not even know where to start. Appreciate any help on below example for the purpose of clarity.

**Problem**: Considering a simply supported beam of span L= 5m with uniformly distributed load w(t) modeled as a Standard Gaussian Process. The beam is subject to Flexural and Shear failure which are in SERIES. Degradation of the beam with time is gives as

Flexural : M(t) = M exp(-0.0005t)

Shear: V(t) = V exp(-0.0005t)

variable distribution are M (Normal : mean 500kN, CoV 10%) , V (Normal : mean 700kN, CoV 15%)

w(t) which is the load follows a Standard Gaussian Process ( Mean 90kN/m , CoV 25%)

The beam is treated as a SERIES system of the shear and bending failure.

LSF:

g1 = M(t) - (1/8 * w(t)* (L^2))

g2 = V(t) - (1/2*w(t)*L)

Determine the Failure probability for a 10 years design time (interval of 1yr)

**Questions:**

- First this system is in SERIES how can this be approached?
- Also from the uqlab example the deterioration was linear but in this case it is exponential how can this be dealt with?
- Two resistance variable are being considered M and V and one load variable w(t); how can we approach this given that we have been given 2 separate limit state function for M and V ?
- How can the out-crossing rate be obtained for the series system
- How can the failure probability be obtained for year 1,2,3… 10 from the out-crossing rate
- If we have a complex system ( series and parallel together) can the approach described in the time -variant reliability uqlab example still be applied?

Your help on this is appreciated. I really want to understand how to approach and set-up this problem in Uqlab for series system as well as a combination of parallel and series.

**Example Paper Source:** An out-crossing rate model and its efficient calculation for time dependent system reliability analysis by C Jiang, X.P.Wei , Z.L.Huang . Yr 2017.