Originally Posted by
cyccommute
That’s not how probability works. “one in X” where X can be any number is a statement of how common something is. Consider a coin toss. The chance of tossing heads is 1 in 2 chances. Each toss of the coin can be either of 2 results. But that doesn’t mean that you can’t toss heads 3 times in a row. Tossing 50 heads in a row has a far smaller probability but it could still happen.
If frame breakage were 1 in 2 that would mean that frame breakage is a common occurrence. That doesn’t mean it happens every time the bike is taken for a ride but you shouldn’t be surprised if the frame fails. But we know that bicycle frames aren’t that delicate. Even the lightest of bicycle frames don’t break very often. There are literally hundreds of millions of bicycles in the world and only a very small percentage of them ever break. The conversational phase “one in a million” shouldn’t be taken as a statistical analysis of bicycle frame breakage but more as a way of saying “frame breakage is rare”.
Even in a rather small community like bicycle touring, a thread like this that reports 6 frame breakages shouldn’t be taken as a sign that frames break with any regularity. While I have broken 4 frames, I’ve owned 40 bikes, 36 of which haven’t broken. Even at a 10% failure rate, I don’t think that bicycles are particularly prone to breakage. I consider all but one of the breakages due to engineering and manufacturing errors. Using a Hell Bent seatpost with about 2” of setback on my Flashback was my fault.
Your probability discussion is still incomplete; you forgot to mention confidence levels, for instance.
Your one in a million broad-brush "conversation" still doesn't hold up. For instance, if the Mean (bike) Trips Before Failure (MTBF) was 1,000,000, even if you made one bike trip per day on average, it'd be over 2,700 years an average cyclist would ride before, on average, one bike failed by frame breakage. How long you been riding again?
Now if you want to get down into the details of reliability and sparing analysis, that might be relevant to touring. It's going to be tougher to fix or replace a bike while on tour than riding around home, where you've got default SAG support available -- friends or family to pick you up and take you and your bike home. So if a touring bike has an MTBF of one in 10,000, and you're going for a 100 day tour, the chances of the bike breaking on tour is 1%; uncomfortable, perhaps, compared to your mythical 1,000,000, but probably not worth carrying a spare frame. It's much less than your chance of getting a flat, for instance, where it's worth carrying something to get you back on the road because the probability is much higher. Now if you're @
mev and going on a three year trip around the world, you want to at least think about how you're going to finish the trip, or even get home, if your bike breaks.
If we could get some honest input from one of the major bike brands, you'd have a better idea what the true failure rate. They're more likely to have run the numbers, and figured out that they're going to need X% spares in the warehouse to address frames breaking within the warranty period. I don't have a reference, but I've got it stuck in my head that "X" was about 1% -- at least before Covid cleared the warehouses.