The failure rate is the one number you already have: the share of units that come back within the warranty window. The shape is the one that decides everything, and it is the one nobody measures.
| Burn-in | Field rate after | Change | Screened out | Cost | Failures avoided | Net |
|---|---|---|---|---|---|---|
| none | 4.00% | +0.00 pp | 0 | 00 | 0-0 | 0-0 |
| 24 h | 3.89% | -0.11 pp | 6 | 018,732 | 02,147 | 0-16,586 |
| 2 d | 3.84% | -0.16 pp | 9 | 037,143 | 03,192 | 0-33,951 |
| 7 d | 3.68% | -0.32 pp | 19 | 0128,769 | 06,422 | 0-122,348 |
| 1.0 mo | 3.31% | -0.69 pp | 46 | 0550,439 | 013,747 | 0-536,692 |
| 3.0 mo | 2.86% | -1.14 pp | 89 | 01.66M | 022,889 | 0-1.64M |
What burn-in removes, by hazard shape
Reduction in the field failure rate over a one-year window, in percentage points, against a baseline of 4 percent annual returns. Read the shape 1.0 row first: it is zero at every duration, and it stays zero however long the chamber runs.
| Hazard shape | 24 h | 48 h | 7 d | 1 mo | What it means |
|---|---|---|---|---|---|
| β = 0.4 | -0.37 | -0.48 | -0.78 | -1.33 | Strong infant mortality |
| β = 0.5 | -0.20 | -0.28 | -0.51 | -0.97 | Infant mortality |
| β = 0.6 | -0.11 | -0.16 | -0.32 | -0.69 | Mild infant mortality |
| β = 0.8 | -0.03 | -0.04 | -0.11 | -0.28 | Weak infant mortality |
| β = 1.0 | -0.00 | +0.00 | +0.00 | +0.00 | Memoryless |
| β = 1.2 | +0.01 | +0.02 | +0.06 | +0.19 | Early wear-out |
| β = 1.5 | +0.02 | +0.03 | +0.10 | +0.40 | Wear-out |
Negative numbers, shown with a plus, are burn-in raising the field failure rate. Against a 4 point baseline, even strong infant mortality at a month of burn-in removes 1.33 points, and the conventional 48 hours removes between nothing and half a point across every shape in the table.
A worked example
A 5,000 unit run. Four percent come back within the first year with no burn-in, the fitted shape is 0.6, and the line runs the conventional 48 hours. Chamber time costs 15 cents per unit-hour, a unit costs 120 to build, and a field failure costs 400 by the time the truck roll and the support time are counted.
Those 48 hours take the field failure rate from 4.00 percent to 3.84 percent. Across 5,000 shipped units that is 8 field failures avoided, worth 3,192. The burn-in costs 36,065 in chamber time and screens out 9 units that never ship, a further 1,078. Thirty-seven thousand spent to avoid three.
The natural next question is how much longer it would have to run. To halve the field failure rate on this curve takes 10,113 hours of burn-in per unit, which is 421 days. Burn-in is not the lever here, and no amount of extending it becomes one.
Now move the shape slider to 1.0 and the reduction goes to exactly zero. Not small, zero, at every duration, because a memoryless process cannot be screened on hours already survived. Move it to 1.2 and the number goes negative: the burn-in is now raising the field failure rate, because it ships a unit that has already spent part of its life in a chamber.
Burn-in does earn its place, and the tool will say so. Set the shape to 0.4, the field rate to 15 percent and the failure cost to 5,000 — a young line with real workmanship problems and an expensive product — and 48 hours removes 1.7 points, which is 85 field failures worth 427,500 against about 49,000 of chamber time and scrap. The point is not that burn-in is useless. It is that the duration has to come from the curve, and almost nowhere does it.
The arithmetic, so you can check it
Reliability is Weibull, R(t) = exp(-(t/eta)^beta). The characteristic life is derived from the field rate you enter rather than asked for, because nobody knows their eta: eta = W / (-ln(1 - F))^(1/beta). The field failure rate for a unit that survived burn-in is 1 - R(T + W) / R(T), against 1 - R(W) with no burn-in.
At beta = 1 those two expressions are algebraically identical, which is why the reference row is exactly zero rather than nearly zero. Costs are normalised per shipped unit, so a longer burn-in cannot look cheaper by quietly shipping fewer: the run is scaled up by the screened-out fraction and the extra units are charged at cost.
A single Weibull is one population with one failure mechanism, and real fleets are usually a mixture: a small badly-built subpopulation with a low shape sitting inside a large well-behaved one. A mixture is exactly the case where burn-in works best and where a single fitted shape understates it, so this model is conservative about burn-in when the defect is concentrated in a small batch. It also assumes chamber conditions accelerate the same mechanism that fails in the field, which is the assumption most burn-in programmes never verify and the reason some of them screen out nothing at all.
Why a passing board still fails in the field is in the BOM passes, the board is wrong. For what the test rig cannot reproduce at all, use the bench-to-field coverage tool, and for staged rollout once units are out there, the OTA rollout planner.
Questions
There is no duration that is right in general, because the answer depends on the shape of the hazard curve rather than on the hours. Below a Weibull shape of one, units fail early and burn-in removes some of them. At exactly one the process is memoryless and no duration changes anything. Above one, burn-in ships an older unit and raises the field failure rate.
Yes, whenever the shape parameter is above one. Then the hazard rate rises with age, so every hour in the chamber is an hour of useful life consumed before the unit reaches a customer. The field failure rate over the warranty window goes up rather than down, and you have paid chamber time for the privilege.
Because an exponential failure process has no memory. The probability a surviving unit fails in the next thousand hours is the same whether it has run for one hour or one thousand, so screening on hours already survived selects nothing. This is exact rather than approximate: the reduction is zero at every duration.
From return data you already keep. Fit a Weibull to the times-to-failure of warranty returns, or plot the cumulative return rate against age on log-log axes and read the slope. It is roughly a week of work on existing records, and it is the input that decides whether the burn-in line is worth running at all.
Then it is a commercial term rather than a reliability control, and it is worth being clear about which. That distinction changes the negotiation: a contractual duration can be met at the cheapest qualifying condition, whereas a reliability screen has to be designed against the failure mode it removes.