**[SOLVED] Failure probability**

**1. The problem statement, all variables and given/known data[/b**

The performance of the valves in Q5 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]

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

ATTEMPT

Have tried to substitute .05 for lambada and 3 for t in the given equation but my answer is still very different from the given answer of 0.08643

The performance of the valves in Q5 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. Relevant equations**FT (t) = 1 − exp[−_λit] where i=1,2,3,4,5

**3. The attempt at a solution**ATTEMPT

Have tried to substitute .05 for lambada and 3 for t in the given equation but my answer is still very different from the given answer of 0.08643

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