Consider the following system made up of functional components in parallel and s
ID: 3204477 • Letter: C
Question
Consider the following system made up of functional components in parallel and series.
a) What is the probability that the system operates?
b) What is the probability that the system fails due to the components in series? Assume parallel components do not fail.
c) What is the probability that the system fails due to the components in parallel? Assume series components do not fail.
d) Compute and compare the probabilities that the system fails when the probability that component C1 functions is improved to a value of 0.99 and when the probability that component C2 functions is improved to a value of 0.89. Which improvement increases the system reliability more?
lder the following system made of functional components in parallel and series. up C2 0.85 C1 0.95 0.90 0.95 ts) What is the probability that the system operates?Explanation / Answer
6-1)
Probability that system functions = P(C1)*P(C2)*P(C4)+P(C1)*P(C3)*P(C4) - P(C1)*P(C2)P(C3)*P(C4) { we are subracting P(C1)*P(C2)P(C3)*P(C4) becuase we are adding case when C2 and C3 functions twice}
Probability that system functions = 0.95*0.85*0.9 +0.95*0.95*0.9 -0.95*0.85*0.95*0.9 = 0.848
6-2)
P(parallel components fail) = (1-0.85)(1-0.95) = 0.15*0.05 = 0.0075
P(parallel components does not fail ) = 1-0.0075 = 0.9925
probability that the system fails due to the components in series
= (1-0.95)(0.9925) +(1-0.9)(0.9925) -(1-0.95)(0.9925)(1-0.9) = 0.144
6-3)
P(series component doesnot fail) = 0.95*0.9 = 0.855
probability that the system fails due to the components in parallel = (1-0.85)(1-0.95)(0.855) = 0.0064125
6-4)
Probability that system functions = P(C1)*P(C2)*P(C4)+P(C1)*P(C3)*P(C4) - P(C1)*P(C2)P(C3)*P(C4) { we are subracting P(C1)*P(C2)P(C3)*P(C4) becuase we are adding case when C2 and C3 functions twice}
Probability that system functions = 0.95*0.85*0.9 +0.95*0.95*0.9 -0.95*0.85*0.95*0.9 = 0.848
i)when C1 is improved to 0.99
Probability that system functions = 0.99*0.85*0.9 +0.99*0.95*0.9 -0.99*0.85*0.95*0.9 = 0.884
Probabiltiy that system fails = 1- 0.884 = 0.116
ii)when C2 is improved to 0.89
Probability that system functions = 0.95*0.89*0.9 +0.95*0.95*0.9 -0.95*0.89*0.95*0.9 = 0.850
Probabiltiy that system fails = 1-0.85 = 0.15
increasing C1 probabbility inceases the system failure decreases more so increasing C1 probabilty is reliable