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First name and Last name: _________________________________________________________________________________________________ RELIABILITY, SAFETY AND RISK ANALYSIS EXAM: 11/07/2022 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); 3. The exam time is 2 hours and 30 minutes for students of Part A+B, who also have to solve Q1.4, and 2 hours and 15 minutes for Part C. Exercise 1 [E1] A pipeline (P) of a liquid natural gas production system connects an extraction platform with a liquefaction plant. The pipeline has a constant failure rate 𝜆𝑃. Due to the high corrosivity of the gas residues, the pipeline is periodically cleaned. The time interval between the end of the cleaning and the beginning of the next cleaning is 𝑇 and the cleaning intervention lasts 𝜏. You are required to: E1.1) Plot the time evolution of the system instantaneous unavailability; E1.2) Evaluate the system average unavailability over the maintenance cycle (you can assume 𝜆𝑇 ≪ 1); E1.3) Find the optimal interval between cleaning interventions (𝑇𝑜𝑝𝑡) that minimizes the average unavailability; E1.4) Assume that 𝑝𝑒 is the probability that the maintenance team fails to correctly reconnect the pipeline after the cleaning intervention. Repeat E1.3) and comment the results. The plant manager considers the possibility of replacing the pipeline P with two pipelines P1 and P2 working in parallel and with constant failure rate 𝜆1 and 𝜆2, respectively. Assuming that: • P2 is cleaned after P1; • the time interval between the end of the cleaning of P1 and the beginning of the next cleaning of P2 is 𝑇 2; • the time interval between the end of the cleaning of P2 and the beginning of…