Hi all,
I hope you are doing well!
I have problems understanding a vital thing. If I have a machine running with a failure rate (i.e. to first failure) of f(s)=(1/(24θ^5))s^4*e^(-s/θ). After the first failure, a second machine is brought up automatically, having the same failure rate.
How would I now express a new variable (T) which is the combination of the two machines and calculate its density function?
I am not looking for the solution of this exact problem but I would like to understand if I just sum up the two functions or if I have to convolve it with itself. Or maybe something completely different I am not seeing here. What is the difference of adding the functions together and the convolution? What is the appropriate calculation in this case?
Thank you very much in advance!
I hope you are doing well!
I have problems understanding a vital thing. If I have a machine running with a failure rate (i.e. to first failure) of f(s)=(1/(24θ^5))s^4*e^(-s/θ). After the first failure, a second machine is brought up automatically, having the same failure rate.
How would I now express a new variable (T) which is the combination of the two machines and calculate its density function?
I am not looking for the solution of this exact problem but I would like to understand if I just sum up the two functions or if I have to convolve it with itself. Or maybe something completely different I am not seeing here. What is the difference of adding the functions together and the convolution? What is the appropriate calculation in this case?
Thank you very much in advance!