1. The following system has three components. Component 1 has 85.5% reliability, component 2 has 80% reliability with a 64.5% reliable backup, and finally component 3 has 99.9% reliability. Using this system, answer parts (a) and (b). 2 a. 0.855 0.645 0.800 0.855 What is the reliability of the system? (Round to 4 decimals, i.e. 0.4456 or 44.56%) b. If the system costs $600 to fix every time it breaks down, what is the expected fixing cost if the system runs for 1000 times? 0.999 0.645 0.800 0.999 c. Assume that the system still costs $600 to fix every time it breaks down, and you are going to run the system 1000 times. You are considering improving your system. You have contacted a backup supplier of component 1. She tells you that the machinery necessary to implement the backup will cost $50,000. What would the minimum reliability of the backup need to be to make the purchase worthwhile? (keep 4 decimals for intermediate calculations)

Calculation Questions (Will be translated into Multiple Choice Questions. Detailed Solutions are Provided in the end) 1. The following system has three components, Component 1 has 85.5% reliability, component 2 has 80% reliability with a 64.5% reliable bathup, and finally component 3 has 99.9% reliability. Using this system, answer parts (a) and (b) Tnoic 7 a. What is the reliabitity of the system? (Round to 4 decimals, i.e. 0.4456 or 44.56% ) b. If the system costs $600 to fix every time it breaks down, what is the expected fixing cost if the system runs for 1000 times? c. Assume that the system still costs $600 to fix every time it breaks down, and you are going to run the system 1000 times, You are considering improving your system. You have contacted a backup supplier of component 1 . She tells you that the machinery necessary to implement the backup will cost $50,000. What would the minimum reliability of the backup need to be to make the purchase worthwhile? (keep 4 decimals for intermediate calculations)