6-2. (2 points) What is the probability that the system fails due to the compone

Question

6-2. (2 points) What is the probability that the system fails due to the components in series? Assume parallel components do not fail.

6-3. (2 points) What is the probability that the system fails due to the components in parallel? Assume series components do not fail.

6-4. (2 points) 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?

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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

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