Poisson Process Problem. A system is made up of two subsystems, A and B, connect
ID: 3124246 • Letter: P
Question
Poisson Process Problem.
A system is made up of two subsystems, A and B, connected in-series (i.e., the system fails if either subsystem fails). Subsystem A is made up of components 1 and 2, connected in series. Component 1 fails according to a Poisson process with rate 2.5 per year, whereas component 2 fails as a Poisson process with rate 2.8 per year. Subsystem B is made up of a single component 3, which is subject to repeated disruptions. The disruptions arrive as a Poisson process with rate 17 per year but only 10% of them cause the failure of component 3. Find the probability that the entire system will not fail during a year. Find the probability that there will be no more than one failure of the entire system during a year. Find the probability that the next system failure will occur within a year.Explanation / Answer
System is made up two sub systems A and B in series , System A has components with 1 and 2 with failure rate 2.5 and 2 fails in a year
system B with 17 per year disruptions and among them 10% of cause the failure
failure rate = 17*0.1 = 1.7
Probability system that not fail during a year =P(both system should not fail) =P(A not fail)*P(B not fail)
= [exp(-2.5)(2.5)^0 ] * [exp(-2)(2)^0 ]*[exp(-1.7)(1.7)^0 ] =0.0020029
b) Probability that no more than one failure of the entire system during a year =
= [exp(-0.0020029)(0.0020029)^0 ]+ [exp(-0.0020029)(0.0020029)^1 ]=0.9999
C)Probability that system failure within a year = 1-P(system will not failure) =1- 0.0020029=0.997971