Problem 4S-1 Consider the following system: 0.71 0.71 Determine the probability
ID: 461474 • Letter: P
Question
Problem 4S-1 Consider the following system: 0.71 0.71 Determine the probability that the system will operate under each of these conditions:
The system as shown. (Do not round your intermediate calculations. Round your final answer to 4 decimal places.)
Each system component has a backup with a probability of .71 and a switch that is 100% percent reliable. (Do not round your intermediate calculations. Round your final answer to 4 decimal places.)
Backups with .71 probability and a switch that is 96 percent reliable. (Do not round your intermediate calculations. Round your final answer to 4 decimal places.)
The system as shown. (Do not round your intermediate calculations. Round your final answer to 4 decimal places.)
Explanation / Answer
a) - System Operational Probability=0.71*0.71=0.5041
b) - System Operational Probability= {1 – ((1 – 0.71)*(1 – 0.71))}* {1 – ((1 – 0.71)*(1 – 0.71))} =0.0424
C) - Each component has [as was just computed in b. – previously, above] Operational Probability = {1 – ((1 – 0.71)*(1 – 0.71)) = 0.0841. And since the back-up switch [previously assumed perfect] is only 0.99 reliable, the back-up switch is actually a “series” element.
This means that for each component there is a back-up in parallel and that there is also a “series “switch.
Component Operation Probability = [Operational Probability of “series” Switch] * [Operational Probability of Component/Back-up] = [((1- 0.71)*(1 -0.0841))] * [(1-((1-0.71)*(1-0.71)))] = 0.0547
System Operational Probability = 0.0547 * 0.0547 = (approx) 0. 0031