Esary-Proschan formula is an approximation formula used for FTA top event probability calculation after Minimal Cut Sets generation. It is able to take into account common basic events and calculate the result in reasonable time.

 

The calculation procedure using this formula consists of several steps:

 

1. Minimal Cut Sets Generation

 

2. Common basic events factor calculation

 

Common basic events are basic events which appear in all Minimal Cut Sets.

We need to calculate the common basic events factor using the following formula:

,

where e(x) is common basic event appearing in all MCS and Q(e(x)) is its probability.

 

3. Top event probability calculation

,

where MCS(y) is Minimal Cut Set number y and Q(MCS(y)) is its probability.