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Help me calculate a function for warranty period

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danesh

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Can any one help to solve:


The time to failure of a certain product is a continuous random variable with probability density function:(given in attchment)




Where t is time to failure in years

The manufacturer of that product is considering to offer a warranty; however they are willing to replace only 1% of all the products they sell. How long a warranty period should they offer?
 

Re: Solve function

I will try to help without solving it.

The question asking to find guarantee time \[T\] such that only 1% of the product failed before T. This means find
\[T\] such that \[P(\]fail at time \[t \leq T) \leq \frac{1}{100}\]

\[P(\]fail at time \[t \leq T) = \int_{0}^{T}F(t) dt = 0.01\]
 
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