I am a rock climber. Climbing relies on skill, strength, knowledge, a bit of luck, and good gear. Falling is a part of the sport and with the right gear the sport is safe.
I do not know, nor want to know, the MTBF (or MTTF) of any of my climbing gear. Not even sure this information would be available. And, all of the gear I use does have a finite chance of failing every time the equipment is in use. Part of my confidence is the that probability of failure is really low.
The equipment manufacturers tend to stress the robustness of the equipment, the strength of the design to shock loading and so on. The equipment is very strong relative to the load a falling climber may cause. There is very little overlap between the stress and strength distributions – meaning the equipment has a large safety margin or safety factor.
The equipment does wear out with use and time. The literature and climbing community stresses the use of equipment that is in good condition. As harnesses and ropes age the strength reduces and we tend to retire this equipment while it still has potentially years of useful life remaining. Again, we use a safety margin (if paying attention).
The expectation is the equipment will not fail during a reasonable duration of use and stress. This isn’t the only industry that enjoys this goal. AND, they do not use MTBF.
In the climbing industry, a failure tends to lead to death or very serious injury. Again, this isn’t the only industry where this is true. Yet, in the medical equipment, aerospace and transportation industries we commonly see the use of MTBF. That is unfortunate.