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Solved: Reliability For a parallel structure of identical
Chapter 10, Problem 21AYU(choose chapter or problem)
For a parallel structure of identical components, the system can succeed if at least one of the components succeeds. Assume that components fail independently of each other and that each component has a 0.15 probability of failure.
(a) Would it be unusual to observe one component fail? Two components?
(b) What is the probability that a parallel structure with 2 identical components will succeed?
(c) How many components would be needed in the structure so that the probability the system will succeed is greater than 0.9999?
Questions & Answers
QUESTION:
For a parallel structure of identical components, the system can succeed if at least one of the components succeeds. Assume that components fail independently of each other and that each component has a 0.15 probability of failure.
(a) Would it be unusual to observe one component fail? Two components?
(b) What is the probability that a parallel structure with 2 identical components will succeed?
(c) How many components would be needed in the structure so that the probability the system will succeed is greater than 0.9999?
ANSWER:Step 1 of 3
Given, for a parallel structure of identical components, the system can succeed if at least one of the components succeeds. Assume that components fail independently of each other and that each component has a 0.15 probability of failure.
(a)
We know that, P(one failure) = 0.15
It is not unusual to observe one component fail.
\(\mathrm{P}(\text { two failure })=0.15^{2}=0.15 \times 0.15=0.0225\)
It is unusual to observe two components fail.