Question

For a parallel structure of identical components, the system can succeed if at least one of the components succeeds. Assume that components fail independent of each other and that each component has a 0.12 probability of falure. 1. What is the probability that a parallel structure with 2 identical components will succeed? and 2. How many components would be needed in the structure so that the probabiltiy the system will succeed is greater than 0.9999

Answer 1

prob. of a system can be a failure is less than (1-0.9999) = 0.0001

now probability that the system will be failure when it has x components is
(0.2)^x

so, (0.12)^x < 0.0001
or, x*log0.12 < log0.0001
or, x > log0.0001/log0.12 [the sign changes coz log 0.12 is negative]
or, x > 5.7227

so, the no. of components (x) has to be around 6