Question

Many electronics follow a failure rate described by an exponential probability density function (PDF). Solar panels are advertised to last 20 years or longer, but panels made in China are failing at a higher rate. The time-to-failure of this device is usually exponentially distributed with mean 12 years What is the probability of failure in the first 8 years?

Answer 1

Given: Many electronics follow a failure rate described by an exponential probability density function (PDF). Solar panels are advertised to last 20 years or longer, but panels made in China are failing at a higher rate. The time-to-failure of this device is usually exponentially distributed, with a mean of 12 years.

Required: To determine the probability of failure in the first 8 years.

Explanation: Acording to the question,

`\begin{gathered} (1)/(\lambda)=12 \\ \lambda=(1)/(12) \end{gathered}`

As we know,

The cumulative distributive function will be:

`1-e^(-\lambda x)`

Hence, In the first 8 years the probability of failure is

`\begin{gathered} P(X<8)=1-e^{-(8)/(12)} \\ =1-0.5134 \\ =0.4865 \end{gathered}`

Final Answer: The probability of failure in the first 8 years is 0.4865.