I have a system with two components, component A and component B. Let $X$ be the random variable representing time between failures of component A and $X$ is exponentially distributed. Let $E[X]=m$. Now we want to test the following hypothesis:
null hypothesis: $m\le m_0$ where $m_0$ is some given constant alternate hypothesis: $m>m_0$
To test the hypothesis we need samples of $X$ which are not available. But, we have the information that A has a failure rate lower than B (time between failures for B is also exponentially distributed). MTTF of component B is $n_0$. Can we use samples generated from B and use as samples of A to test the above hypothesis?