The simple answer is: “they got too hot”, but, there are supple details to consider. Most of these are outside of the control of the lamp manufacturer. The equipment designer must address these problems.
At full power operation the temperature of the quartz wall of the main body should be between 800°C and 1000°C. The ends of the lamp should be no greater than 350°C. The reason for the lower temperature of the lamp ends is to keep the electric leads from oxidizing and failing. The metal inside the quartz is molybdenum which, if too hot, will expand enough to shatter the ends and/or start to oxidize and no longer conduct electricity. This leads to arcing and lamp failure.
The reason for the higher temperature on the body is to keep it below the strain point of fused silica. The strain point of a glass is a temperature below which you will not cause permanent strain to build into the glass. The strain point of fused silica is roughly 1070°C. Keep the body at 1000°C or below and you should be fine.
The problem comes in when the lamp is put in a fixture where it must be cooled. These fixtures are designed to focus the energy to a work surface, but, also trap the heat near the lamp. How much extra heat can a quartz lamp take? That is the problem. For long lamps it is a very important problem.
Glasses have a characteristic temperature called the annealing point. At this temperature the glass is still too “rigid” to deform, but, the molecules have enough energy to move slightly. This is enough to allow built up strain to relax and is also a point where you can force strain into the glass. Unfortunately, the annealing point for fused silica is roughly 1140°C, only around 60°C above its strain point. Not a lot of difference and easy to build up in an enclosed fixture.
Well, in addition to temperature we also must consider the WEIGHT of the lamp. The HID lamps are basically rods only held by the ends. The longer the lamp the more mass it has. When you hold it by the ends, all that mass puts the force in the center of the rod. Short HID lamps rarely bow during use even at high temperatures as there is so little force pulling is down. Longer lamps are easy to bow if too hot. (To illustrate this point, go to a home improvement store. Find metal rods. Find a short one and hold it up on each end. It will probably look straight. Try again with a much longer piece. Bet ya it sags in the middle!)
The next defining characteristic of any glass is a value called the glass transition temperature. Once you hit this point the glass lose its “rigidity” and can become more “plastic”. Get the glass to this temperature, add some force (like its own weight) and it is possible to deform (bow) it. Unfortunately, the glass transition temperature of fused silica is only around 1200°C. Again, not much higher than its annealing point of 1140°C.
So, if you have a long HID lamp, which weighs a lot, and it gets too hot by just a little, it will bow. Not only will it bow, but since the pressure inside a full power lamp is usually greater than the air pressure, the lamp gets bigger in diameter. It blows up like a balloon.
Why don’t the lamps just go “bang”?
Well, very luckily it’s a slow process. If the lamp is overheated by the reflector it will bow and get slightly bigger in diameter. As it bows it moves away from the accumulated heat of the reflector. So it will get cooler. Also, as it gets bigger in diameter its power goes down which also makes it cooler. Once the lamp cools to below its strain point, everything stops and the lamp is happy. Bowed, but stable and happy.
So, if your lamps bow you may have to redesign the enclosure or decide on reducing the lamp power. It’s just too much heat.