2024 05 31 full written exam

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First name and Last name: Student number: Person code: ______________________________________________________________________________________________________________ RELIABILITY, SAFETY AND RISK ANALYSIS EXAM SIMULATION FULL WRITTEN EXAM Note: 1. Make sure you write your first name, last name, student number or person code, and sign every exam sheet; 2. The exam consists of 2 exercises (E1, E2) and 2 open questions (Q1, Q2). E1 and E2 cover the same topics of Test 2 (i.e., Markov Chain) and Test 4 (i.e., Fault Tree), respectively. 3. If you took Test 2 and/or Test 4, you have the option to keep your original test grade or use the grade that you will obtain on Exercises 1 and 2 of this exam, respectively. Note that if you opt to keep your Test 2 grade, Exercise 1 will not be graded; similarly, choosing to keep your Test 4 grade will result in Exercise 2 not being graded. Please indicate your preference in the following table by marking a single choice per column. Topic Evaluation Markov Chain Fault Tree Exam Exercise Exercise 1[E1] Exercise 2[E2] Test Test 2 Test 4 4. The exam time is 2 hours and 15 minutes for students of Part A+B, who also have to solve E2.5, and 2 hours for Part C. 5. The Professor can require that the student performs the oral exam. Exercise 1 [E1] (Markov Chain) A new item starts operating at time t=0 with failure rate 𝜆𝜆1 = 𝜆𝜆. When it fails, the operator performs a partial repair (repair rate 𝜇𝜇), which enables the item to continue its operation although it is partially degraded. Its failure rate after the partial repair (in the partially degraded state) is 𝜆𝜆2 = 2𝜆𝜆. You are required to: E1.1) Compute the item reliability and Mean Time to Failure; E1.2) Compute the asymptotic availability; E1.3) Suppose now that when the item fails, the operator…