1668087601 Exam 22072021 AB

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First name and Last name: Student number: ______________________________________________________________________________________________________________ RELIABILITY SAFETY AND RISK ANALYSIS A+B 22/07/2021 Note: 1. Make sure you write your first name, last name, student number and sign every exam sheet; 2. The exam consists in 2 exercises and 2 open questions; 3. The exam time is 2 hours and 15 minutes. Exercise 1 [7.5 points] Consider a hot standby system of two identical units. The failure rate of the units is 𝜆 when they are operating and 𝜆𝑠 when they are in standby. Both units are healthy at time 0. In case of failure of the operating unit, the maintenance team starts immediately the repair, which is characterized by a constant repair rate, 𝜇. The failure of the unit in standby is unnoticed until it is asked to operate. In the case in which the operating unit had a failure and the standby unit had previously failed, the maintenance team starts repairing both units in parallel. This latter repair process, which will result in the repair of both units at the same time, is characterized by a constant repair rate 𝜇𝑠 < 𝜇. E1.1) Draw the Markov diagram of the system, upon proper definition of the system states. E1.2) Write the transition matrix and the Markov equation in the matrix form. E1.3) Find the Mean Time To Failure of the system. E1.4) Find the expected number of system failures in 1 year, considering steady state probabilities. E1.5) Repeat questions E1.1) and E1.2) assuming that an external event may occur with rate 𝜆𝑒 and that it has a probability 𝑝 of causing the failure of the operating unit and 𝑝𝑠 of the standby unit. Exercise 2 [7.5 points] Consider an emergency door with probability 𝑝 of failure to open on demand. Experts have estimated 𝑝 based on prior…