Question: Question 2 (25 Points) You are analyzing a plant with 8 machines, organized into 4 in series work stations, as presented in the following structure:

Question 2 (25 Points) You are analyzing a plant

Question 2 (25 Points) You are analyzing a plant with 8 machines, organized into 4 in series work stations, as presented in the following structure: A D G B E H These 8 machines have constant failure rates and their failure probabilities are statistically independent. Work station Machines Failure rate per hour A 0.0004 1 B 0.0004 0.0004 D 0.0002 2 E 0.0002 3 F 0.0005 G 0.0003 4 H 0.0003 1. Find the survival probability of the plant at 1000 hour of running time. (12 Points) 2. Redesign the plant to reach the required reliability of 0.7 at 1000 hours of running time. You cannot improve the machines reliabilities. You can change the structure of only one work station during this improvement (13 Points) Solution

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