How much is an incandescent lamp's filament stressed by an on/off cycle?

Domestic filament lamps are produced in their thousands on (generally) automated factory production lines. Buying one lamp with a rated life of, say, 1,000 hours does not mean it will last (about) 1,000 hours. It means that the average life of a sample of several 100 lamps will be 1,000 hours. Some in the sample will last longer, some shorter. This will be due to minor differences in materials and manufacturing, tolerance of machinery, wearing of jigs, etc. The factory intends to make bulbs with an average life of 1,000 hours (it says so on the box !) so they test batches and confirm it. A certain percentage of any batch will last a lot longer than the average which is why you sometimes see articles in newspapers about a consumer who e.g. bought a bulb in 1940, left it on in their outside toilet, and it is still on today.

If a particular bulb has a weak spot in it, such as a slightly dodgy spot weld, it is quite possible that the cycling of on/off thermal shocks will cause a premature failure. However without a forensic examination of your failed bulb (possibly requiring an electron microscope) you will never know the exact cause of failure. The factory obviously does do examination to some extent of failures and tries to ensure that the quality of manufacturing processes such as spot welding are acceptable and not likely to adversely affect the rated average life. Their testing will probably include some on/off cycling tests approximately representative of intended use. For a domestic lamp this might be 3 or 4 on/off cycles a day. If you leave a lamp on permanently with no on/off cycles it is likely (but not guaranteed) to last longer than it otherwise would. Whether the otherwise would is 100, 1000 or 10,000 hours you will never know.

The manufacturers will probably have very little interest in knowing about extended life with an atypical number of switching cycles unless the lamp is for some very specialised application where the number of cycles is large e.g. traffic lights.