How to do derating analysis
The only de-rating analysis I've ever done is with using MIL-HDBK-217F. Here's a copy. It's getting a tad old now but still covers all the main parts you might use and each component is detailed and explained. It covers all the environmental scenarios from "ground, benign" thru "airborne", "space, flight", "missile launch" and finally the top one "canon launches".

De-rating can be done by inference from this document - it'll guide you how to calculate the expected failure rate of components used in a particular circuit configuration and then you have the option of de-rating that component to either a bigger component of two sharing the same load. Bridge rectifiers, as I remember are one of the more troublesome elements.

EDIT - simple example

For a wire-wound resistor you use section 9.1 of the document and it tells you that the basic reliability of the component is: -

\$\lambda_P = \lambda_b\cdot\pi_T\cdot\pi_P\cdot\pi_S\cdot\pi_Q\cdot\pi_E\$

Then if you look further down the page you can start to choose values that are appropriate for the circuit that component is used in. For instance, I've chosen these: -


\$\lambda_b = 0.0024\$
\$\pi_T = 1.5\$ (I've assumed it's at 70degC)
\$\pi_P = 1.0\$ (I've assumed it's a 1 watt resistor)
\$\pi_S = 1.5\$ (I've assumed it's running at 50% wattage)
\$\pi_Q = 1.0\$ (Category M supplier i.e. has an established reliability)
\$\pi_E = 1.0\$ (I've assumed the application is ground benign i.e. the least onerous application)


\$\lambda_P = 0.0054\$ - this means failure rate per million hours. And if your design has 100 resistors like this then the overall failure rate from the resistors in your design is 0.54 failures every million hours or a MTTF of 1.85 million hours.