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
probability of failure. Complete parts (a) through (c). (a) Would it be unusual to observe one component fail?
Would it be unusual to observe two components fail?
(b) What is the probability that a parallel structure with 2 identical components will succeed?
The probability that a parallel structure with 2 identical components will succeed is
(Type an integer or a decimal. Do not round.)
(c) How many components would be needed in the structure so that the probability the system will succeed is greater than 0.9999?
(Round up to the nearest whole number.)
Probability of both components failing = 0.19^2 → 0.0361
Probability of success for n components = 1 - 0.19^n
We want 1 - 0.19^n > 0.9999
Set 1- 0.19^n = 0.9999
n*ln(0.19) = ln(1-0.9999)
n = ln(1 - 0.9999)/ln(0.19)
n = 5.546
Round up: n = 6. You would need 6 components in parallel.