My first guess on this would be defective light bulbs. The first bulb that exploded was probably manufactured on the same production run as the second bulb that exploded.
My second guess would be an over-voltage condition caused by an open (or intermittently open) neutral. Examining each and every neutral connection on the circiut would be the only way to eliminate this possibility.
My third guess is that you have been given all the details of the problem.
