What’s more likely to break down: a car with 200 miles or 20,000 miles?

In manufacturing/engineering, there is a concept known as the bathtub curve.  In theory, something that is brand new (including a human being!) is more likely to have failures than something that is a little older and has worked out those early kinks.  Of course, once the product gets old, you’ll start having new reasons for failure (things wearing out).

I don’t have much to add on this topic, but I created this post this for two simple reasons:

  • First, it’s a nice example of a Cartesian graph that makes intuitive sense.  The aggregate blue curve indicates that new things can be lemons, then they work smoothly, and then they wear out and start breaking again.
  • Also, I think its a great example of an authentic real-life piecewise function.   As you can see, it has three very different sections.


Question: In terms of cars, do you think the blue curve above would be so symmetric?