Electronic – Hardware reliability Test

If you use appropriate derating guidelines for electrolytic capacitors (keeping the ripple current in check, ensuring they stay well below their maximum temperature rating) they can last a very long time and still provide adequate performance. I've seen capacitors come out of 15 year-old equipment and still 'work' to some degree.

Fans have a limited lifespan depending on how fast you operate them. They tend to gradually fail over time.

If you have a primarily surface-mount design, consider conformal coating to help limit exposure to the elements and mitigate oxidation, etc. Products in the field for years which have some air exposure can very easily get several millimeters of dust, which makes a very effective thermal blanket.

Make sure that, if you're using RoHS parts, that you're not using parts prone to tin whiskering. (This is another area where conformal coating can be helpful).

The simple way of thinking:

Each component has a failure rate. It can be measured in MTBF (mean time between failure) (as @Nick T said) or Failure Rate. Reliability is a number which states the probability that a component would still being working after an amount of time. In general for eletronic components it follows an exponential distribution. You can use it to calculate the probability of a component still being functional after a given time.

For a circuit with no security systems (back-ups, redundant circuitry, etc) the overall reliability is the product of each reliability.

If you have a backup circuit, for example two redundant capacitors on the power supply, the probability that the capacitor bank is still working is the sum of the two probabilities.