Holger:
4x indeed sounds like a good practical limit. Do you know any literature which we can refer to for this? An specification that limits shot peening to 4 times without any basis is a bit tricky. Rejection of part solely based on the fact that it already has been peened 4 times is probably not acceptable, unless there is research that backs up such limit.

Regarding the operating temperature, we know this will affect the compressive stress somewhat, but we like to quantify this. Any literature available? Anything known about the impact of this stress reduction on the number of the times a part can be peened?