Worked Example

Consider the power-distribution board of a small satellite: the card that takes the regulated bus, protects it, and feeds the payload and the avionics. It is deliberately none of the systems the industry examples carry. The ratings and the limits below are illustrative teaching values in the shape the standards use, and a real analysis takes them from whichever of the five documents the contract names.

The policy, settled once:

The board, on both axes

Eight parts, each with its applied stress, its own temperature from the thermal model, and the two checks:

Three violations in eight parts, and they are not the same kind of finding.

C12 and K1: over on the stress ratio

The capacitor is the classic. Somebody needed a 12 V rail decoupled, found a 16 V tantalum in the library, and used it: 12 / 16 = 0.75 against a ceiling of 0.50. Nothing about the board is hot, nothing is unusual, and the part is inside its own rating. It is a procurement decision that was never checked, and it is fixed by a part number: a 35 V part on the same rail gives 12 / 35 = 0.34.

The relay is the same shape with a twist. Its contacts are rated 5 A resistive, and the 3.2 A they carry is into a capacitive payload load, which is the condition its rating was not quoted at. Even on the resistive number it is 0.64 against 0.50.

U5: over on temperature, with every ratio comfortable

The regulator's input voltage is half its rating, its output current is half its rating, and every stress ratio on the row passes with room to spare. It is a linear regulator dropping 2.4 watts in a package with a 28 K/W junction-to-ambient resistance, in a local ambient of 85 °C:

Tj = 85 + 28 × 2.4 = 152 °C

against a 110 °C cap: 42 degrees over, on a part that a ratio-only review passes without comment. This is the case the foundations chapter means by the second axis, and it cannot be found on a schematic.

What the two fixes are worth

Derating is not a margin for its own sake, and the prediction says what each fix returns.

C12, through the voltage stress factor πV = (S/0.6)⁵ + 1:

at S = 0.75: (1.25)⁵ + 1 = 4.05 · at S = 0.50: (0.833)⁵ + 1 = 1.40

Changing one part number divides that capacitor's failure rate by 2.9, and the part costs the same.

U5, through the Arrhenius factor at Ea = 0.35 eV:

Replacing the linear regulator with a switcher takes the dissipation from 2.4 W to about 0.6 W, which puts the junction at 85 + 28 × 0.6 = 102 °C: inside the cap, and 3.6 times less failure rate than as built. The switcher costs board area and some EMC work, and that is the trade the number is there to inform.

The margin on everything else

The passing parts are worth reading too. L2 at 0.70 against 0.75 and D2 at 0.63 against 0.75 are inside policy and have almost no headroom left: a load increase, a hotter orbit or an end-of-life tolerance moves either of them over. A derating report that lists only the violations has thrown away the early warning, which is the whole reason to keep the margins in the deliverable.

What the board looks like after the fixes

Three part changes, no redesign, and they were available at schematic stage for the cost of noticing. That is the argument for running derating early: the same three findings after qualification are three requalifications.