Models that are so vague they are barely an idea

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Bathtub curve

The bathtub curve refers to a theory about the likeliness of product failure, particularly applied to electronics but potentially to anything made of many components.

The idea is that

there is a certain likeliness the whole will fail almost immediately, often due to a randomly faulty component.

after this possibility of immediate failure, the probability stays low, as components and design should last a few years.

After maybe five years, the likeliness of failure slowly starts rising again due to wear, and minor wear/quality differences between components

if various critical components are rated for the same length of service, the probability of failure would start curving up noticeably after that interval

"Why the name?"

If you plot a curve that drops rapidly, stays low for a while, then rises more slowly.

This looks roughly like the profile of a one-person bathtub, with the curve one one side that you can lie on. Hence the name.

"Is it true?"

The bathtub curve is an interesting-sounding theory, but is it true?

Vaguely. Depends. Too crude to use as a general model, though.

Its two often-mentioned ingredients are based in something real, but that does not imply that either is used accurately, nor that the combination is complete.

Prime reasons it might be useful is often about estimating maintenance and replacement cost.

Say, when industry starts to use many copies of the same device, you know you'll be needing to do more maintenance overall, so you start doing calculations like Mean Time To Repair.

That calculation will work better when you consider what all your critical components are, and what their typical lifespan is.

At the same time, this reminds us we need to think about complexity.

Even if the failure rate of each component is an extremely curve up so gentle that you can't see it for the first ten years, the risk of the device containing many of them is roughly all those curves multiplied. This makes the overall curve both higher, and curve up faster.

So just describing that shape doesn't have a lot of predictive power.

Especially since the shape changes.

Another thing it seems to point out is that, in certain fields, companies may have a Dead On Arrival policy (meaning "if it doesn't work and you send it back immediately, they'll just send out another"), which is based on some cost-benefit analysis saying that it is cheaper for them to occasionally send out a complete replacement, than to spend a lot more time testing each unit thoroughly for more exceptional faults.

...while in other fields, e.g. where things relate to safety, that same approach is the best way to quickly stop existing as a company.

See also

• http://www.itl.nist.gov/div898/handbook/apr/section1/apr124.htm
• http://en.wikipedia.org/wiki/Bathtub_curve