FORM (First Order Reliability Method) and SORM (Second Order Reliability Method)
You may find this article useful:
http://www.ntu.edu.sg/home/cbklow/documents/Conference/BKLow_2012_APSSRA.pdf
You might be interested in PERMAS.
http://www.intes.de/kategorie_support/download/shortdescription/permas-v15-prod-E.pdf
You may find the following paper useful if you need to calculate system reliability with correlated components: https://ascelibrary.org/doi/abs/10.1061/%28ASCE%29EM.1943-7889.0001280
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