You can generalise this for other required accuracies. If instead of 25% we use “a” then the optimal guess is 100%+a of the current life which is correct 2a100%+a of the time.
If we use an alternative optimisation criterion where we compare any two prediction methods and see, over the life of the bathing machine, which is closer to the correct answer most often then 200% (i.e. the halfway rule) is best.
So which rule of thumb you use depends on what you’re looking to achieve—a guess which will be fairly good for as much of the lifetime as possible or a guess which is better for most of the lifetime, even if sometimes it’s way off.
You can generalise this for other required accuracies. If instead of 25% we use “a” then the optimal guess is 100%+a of the current life which is correct 2a100%+a of the time.
If we use an alternative optimisation criterion where we compare any two prediction methods and see, over the life of the bathing machine, which is closer to the correct answer most often then 200% (i.e. the halfway rule) is best.
So which rule of thumb you use depends on what you’re looking to achieve—a guess which will be fairly good for as much of the lifetime as possible or a guess which is better for most of the lifetime, even if sometimes it’s way off.