Bathtub curve
The bathtub curve refers to a theory about the likeliness of product failure, particularly applied to electronics:
Depending on the product, there is a certain likeliness something 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 a while (on the order of magnitude of two to five years for most electronics) the likeliness 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 rises slowly, but somewhat exponentially.
If you plot a curve that drops rapidly, stays low for a while, then rises, this looks roughly like the profile of a classical bathtub, with the curve one one side that you can lie on. Hence the name.
The bathtub curve is an interesting-sounding theory. It's probably more approximate than it having a name suggests, in that it also largely describes the fact that some components (and thereby the devices they are in) can be expected expected to fail in under a dozen years, depending a lot on the product.
Various companies have a Dead On Arrival policy (if it doesn't work and you send it back immediately, they'll just send out another)
since it's often easier and/or cheaper for them to occasionally send out a replacement, than to spend a lot more time testing each unit.
At the same time, it means that a year of warranty is otherwise very low risk for the producer, and even 'extended' warranty of three-or-so years is, arguably, still relatively meaningless. Of course, it's nice in the few cases of failure (and for the company, since it produces some basic goodwill).
It is also why you may want to be concerned if they reduce warranty from three years to one. 'Extended warranty' can be a bit of a scam, depending on the product; usually the extra two years still lie in relatively safe territory.