The reliability of your solder joints are related to the environment which the 
assembly will see.  The harsher the environment (thermal cycling) the more you 
have to control the TCE mismatch.  The way we do it is to hard bond two board 
assemblies to both sides of a restraining core made of silicon carbide and 
aluminum.  I've measured the TCE of our bonded assembly and it is down to 7-8 
ppm/degrees C.  I've also thermally cycled a test BGA assembly while monitoring 
the resistance through the solder joints and have exceeded 1500 thermal cycles 
(-55 to +125 C) on a 1089 ceramic BGA, which confirmed our FEA (finite element 
analysis).  

My point is that you really cannot determine how reliable your design will be 
without evaluating the situation, although, one could hypothesize that a 47mm 
ceramic BGA on FR4 with any temperature variation will not last very long.

Jim Marsico
(516) 595-5879
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