CIVL 181 tutorial 10 Value of information, expected utility

E[L|CN]?

Adopted from Question 2.8 In order to protect an $8M dam from overtopping, two spillway systems are proposed. Spillway A ~ 3.5 M, Spillway B ~ 3 M If fail, the spillway and the dam will be destroyed. P (F A ) = 0.15, P (F B ) = 0.3 A test, cost 0.3M, give the following result: If “A is preferred”, P (F A ) = 0.2, P (F B ) = 0.6 If “B is preferred”, P (F A ) = 0.5, P (F B ) = 0.1 The engineer thinks 70% chance will be “B is preferred”

Question 2.8 a)Draw a decision tree, include all relevant alternatives Test No test A preffered (0.3) B preffered (0.7) System A System B System A System B System A System B Probability of failure Loss

Question 2.8 b) Determine whether the test should be conducted based on EMV No test: E(A) = 0.15 x x 3.5 = 4.7, E(B) = 0.3 x x 3 = 5.4A* Test and if A is preferred: E(A) = 5.1, E(B) = 7.8 A* Test and if B is preferred: E(A) = 7.5, E(B) = 3.8B*

Question 2.8 Test No test A preferred (0.3) B preferred (0.7) System A* System B System A System B* System A* System B Probability of failure Loss

Question 2.8 E (no test) = E (A*) =4.7 E (test) = E(A|A*)P(A*) + E(B|B*)P(B*) = (5.1)(0.3) + (3.8)(0.7) [no test cost] = 4.19 E (test) with test cost = = 4.49 So, test c) What is the value of the test? = 4.7 – 4.19 = 0.51

Question 2.8 d) Suppose the designer is Risk aversive, such that u(x) = x 1.5, should the test be conducted? Test No test A prefered (0.3) B prefered (0.7) System A* System B System A System B* System A* System B Probability of failure Loss utility

Question 2.8 No test: U(A) = 0.15 x x = , U(B) = 0.3 x x 3 2 = A* Test and if A is preferred: U(A) =, U(B) = A* Test and if B is preferred: U(A) =, U(B) = B* …