Assume that I need to determine the reliability of a service. The service includes component a (software reliability=0.95) and component b (software reliability=0.98). I have 2 computers: Computer A (hardware reliability=0.99) and Computer B (hardware reliability=0.99).
I have two following cases:

Case 1: Deploy both a and b on computer A. For this case, the service
reliability is around 0.923.
Case 2: Deploy a on computer A, and b on computer B. For this case, the service reliability is around 0.912

I really wonder why the service reliability in case 2 is lower than in case 1. The thing is A and B have the same hardware reliability. Can someone clarify that?

It depends where the logarithm is. If it is just a factor, then it doesn't make a difference, because big-O or $\theta$ allows you to multiply by any constant. 

If you take $O(2^{\log n})$ then the base is important. In base 2 you would have just $O(n)$, in base 10 it's about $O(n^{0.3010})$. 
