Can some please explain "What exactly is Derating?"
Operating the part at lower values than rated specifications
How it is related to positive and negative temperature coefficient.
Running a part at a lower voltage or current means less heat is generated. Powering a 16v max capacitor, at 16v, is stressing it. Running a 20mA led at 20mA will only provide x number of hours of life, while running it at 10mA will provide y hours, where y is greatly larger than x.
Derating is limited to only resistors and capacitors or it applies to ASICs also.
Derating can apply to almost anything. Resistors, LEDs, Other Diodes, Capacitors, ICs, CPUs. Another common word for derating, in the context of computers and CPUs, is underclocking. As opposed to overclocking, where you run a cpu at a higher than rated speed, underclocking (aka derating) runs it at a lower speed, allowing for less heat and longer life. Mainly used when modders want to remove noisy fans.
As a note, some devices demand derating in certain situations. Resistors listed as x wattage, expect the resistor to be in free air at ambient temperatures with air movement over it. If you put it in a sealed case, or in heat shrink, or in a hot environment, you NEED to derate it down. Same with Solar Panels. The given rating is for IDEAL sunlight. Average sunlight will derate the output current and voltage.
Don't get thrown off by having multiple voltage sources attached to the same node: just follow the super-node procedure, and recognize that it's ok to combine a super-node with another node/super-node to make a "super-super-node" (or just a bigger super-node).
In your case, you will eventually have a super-node which contains nodes 1, 2, and 3, and 2 other equations which describe the relationship between (v1,v2) and (v1,v3).
This gives you 3 equations and 3 unknowns, which can be solved using some algebra.
Finding these equations is left as an exercise for the reader (feel free to ask questions if you get stuck somewhere)
Best Answer
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_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.