Hi, I had a problem that the APU on B737-800 was not starting on ground. The APU initially starts and then does a protective shut-down with a fault light and a msg ” NO ACCELERATION SHUT DOWN “. At that time Pitot Static system trouble-shooting was also going on. We never correlated these two events and were in a problem till we actually got the solution. When Pitot Static System check is going on and you happen to simulate a higher altitude e.g. 10000 ft the Electronic control unit of APU takes the altitude information from ADIRU and compares this from inlet pressure sensors of APU. Upon mismatch of both these inputs the APU itself does a protective shut-down. As such it is advised that never start APU when a Pitot Static system test is going on.