Failure rate of two identical item

Question

I have two identical pipelines and the failure rate of a leak in one of them expressed in event/year. The two pipelines are identical and not interconnected. I want to know the failure rate of the situation where I have a leak in both pipelines. Initially I multiplied the frequencies, I asked my boss for help and he said that it is not possible because the unit of measurement cannot be ev^2/y^2. He explained the solution to me, but I don't remember the answer but I'm sure I have to somehow multiply some frequency and some probability. And the other piece of data I need to use is that the estimated life of the plant is 20 years. 20 years is the observation time of the system and should be a necessary data for calculating the probability. I need help, thank you very much!! <3

Answer 1

If the breakdown rate is $\lambda$ per year then the one year reliability of that item (in its simplest model) is $R=e^{-\lambda}$. You have a system of two such items in parallel. The one year unreliability of an item is $U=1-R$ and the unreliability of the system is $U^2$. The one year reliability of this system is $1-U^2$. You can calculate this figure to give a number between 0 and 1, let's call it $R_s$. If $\lambda_s$ is the breakdown rate of the system then $R_s=e^{-\lambda_s}$ and taking logs will give you your system breakdown rate. You should read up on reliability and the exponential distribution for more examples.