This is a technique for calculating the equivalent value for a risk network reliability and the RDF. Use this technique to calculate the equivalent of three components connected in parallel, each with a Reliability of 0.8 alone.

Example:Example of Equivalence Analysis for a Risk Network [Updated 10-2007] Given the Risk Network below, find its equivalent overall RDF: Assuming that the numbers given are reliabilities, one can develop an equivalent reliability then find the RDF using the complement rule. Begin by combining the various series and parallel combinations using the addition and multiplication rules for probabilities. 1. D and I are simple series or serial combinations so we can use the multiplication rule to combine D and I into D D = D X I = 0.95 X 0.99 = 0.9405 2. F and H are a parallel combination (OR) so we can use the addition rule here where there is joint probability that both F and H will function simultaneously. F = F + H (F X H) = 1.5 (0.56) = 0.94 0.9 0.7 0.7 0.8 0.7 0.8 0.95 0.99 OUT IN A B C D E F H I Page 1 of 3 Risk Network Example 0.9 0.7 0.7 0.8 0.94 0.9405 OUT IN A B C D E F Redrawing the network to show D and F equivalents: 3. Now combine B and C as simple serial equivalents as: B = B X C = 0.7 X 0.8 = 0.56 4. And, E and F likewise as: E = E X F = 0.7 X 0.94 = 0.658 Redrawing showing B and E: 5. Now, B and E can be combined as a parallel combination as: B = B + E (B X E) = 0.56 + 0.658 (0.56 X 0.658) = 1.232 0.3685 = 0.84952 0.9 0.56 0.658 IN A B 0.9405 D OUT E Page 2 of 3 Risk Network Example 0.9 A 0.8495 B" 0.9405 D' OUT Redrawing now showing B : Finally, combining A with B and D as a simple serial combination as: A = A X B X D = 0.9 X 0.84952 X 0.9405 = 0.7191 This is the equivalent Reliability of the network. Now, to find the RDF we subtract the Reliability from 1 as: RDF = 1 R = 1 0.7191 = 0.2809 Therefore, the Final network looks like this where the RDF equivalent is shown: IN 0.2809 A OUT