assume I have 1 disposable product (a pump for example). It fails according to exponential distribution.
plant 1 <----- local depot 1 <--- |---- central depot plant 2 <----- local depot 2 <---
local depot 1 & 2 are supplied from central depot. plant 1 inventory is supplied from local depot 1 and same is true for local depot 2 and plant 2 .
Each failure of pump creates a demand at a rate of $\lambda$.
My opinion is that even rates at plant 1 & 2 are exponential and each rate is same as $\lambda$, one can NOT say that result demand rate at central depot is also exponential and rate is 2$\lambda$
my reason: distribution of demand of pump in central inventory will be something different than exponential
Am I correct? If I am not correct can you please explain at least basically why i am not correct? (for the details I can read sources over web)