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Failure of a system of components logically arranged in series and parallel

  • Thread starter abba02
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The performance of the valves in (V1 OR V2 OR V3) AND V4 AND V5 has been assessed in more detail under conditions
closer to those experienced in-service and the distribution functions of the random time
to failure have been quantified. The useful life period, prior to wear-out, occurs from
installtion to 5years. During this period, all of the distribution functions are modelled
using an exponential distribution function of the form:
FT (t) = 1 − exp[−_λit] where i=1,2,3,4,5
If _λ1 = λ_2 = _λ3 = 0.05; λ_4 = 0.267; λ_5 = 0.189 (all in years−1), calculate the probability
of a loss of flow from the manifold sometime in the period (0,3)years.
ANSWER[P[F]=0.08643]

2. Homework Equations
FT (t) = 1 − exp[−_λit] where i=1,2,3,4,5

3. The Attempt at a Solution
Assummed that V1,V2 AND V3 ARE IN SERIES AND ARE IN PARALLEL WITH V4 AND V5
= 1- exp [-λ1+λ2+λ3+λ4+λ5*3]
Have tried to substitute .05,.267 and .189 for lambada, *3 for t in the given equation but my answer is still very different from the given answer of 0.08643[/QUOTE]
 

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