The question i want answered is: Compute and compare the probabilities that the
ID: 3269599 • Letter: T
Question
The question i want answered is:
Compute and compare the probabilities that the system fails when the probability that component C3 functions is improved to a value of 0.99 and when the probability that component C4 functions is improved to a value of 0.94. Which improvement increases the system reliability more?
6. Consider the following system made up of functional components in parallel and series. C2 0.85 C1 C4 0.95 0.90 C3 0.95 6-1. (2 points) What is the probability that the system operates? Answer:Explanation / Answer
Case 1: In case the reliability of C3 increases to 0.99
Here the probability that the system operates fine
= Probability that C1 operates * (Probability that at least one out of C2 and C3 works ) * (probability that C4 operates )
= 0.95 * ( 1 - 0.15*0.01) * 0.9
Here the middle term represents 1- 0.15*0.01 means that probability at least one of C2 and C3 works. ( as they are in parallel )
Now the probabiltiy here is computed as:
= 0.95 * ( 1 - 0.15*0.01) * 0.9
= 0.8537175
Therefore the reliability of the system here is 0.8537175
Case 2: In case the reliability of C4 increases to 0.94
Here the reliability of the system is computed as:
= Probability that C1 operates * (Probability that at least one out of C2 and C3 works ) * (probability that C4 operates )
= 0.95 * ( 1 - 0.15*0.05) * 0.94
= 0.8863025
Therefore the reliability of the system here is 0.8863025
Therefore the reliability of the system in case 2 is more than in case 1.
Therefore improvements in the reliability of C4 improves the system reliability more.
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