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 0.11 probability of failure.
(a) Would it be unusual to observe one component fail?
(b) Would it be unusual to observe two components fail?
(c) What is the probability that a parallel structure with 2 identical components will succeed?
(d) How many components would be needed in the structure so that the probability the system will succeed is greater than 0.9999? Round to nearest whole num

Answer 1

im not sure how many components a parallel structure has, if it has thousand, one or two failed is usual. if it has only a few, question a&b is relative unusual.

for c the possiblility of the structure fail is 0.11*0.11(all component fail lead structure fail)=0.0121
the possiblility of success is 1-0.0121=0.9879

for d if you want to let the possiblility of success is greater than 0.9999, it means the possiblility of fail is less than 0.00001
we can write \[0.11^{n}\le 0.00001\]
so \[n \ge \log_{0.00001} 0.11\] n belongs to integer
u can use calculator to solve it then.

Answer 2

@OliviaS