Bathtub failure curve

Why is a brand-new machine more likely to break this week than a six-month-old one?

Take a pump out of its crate and a pump that has run since January. Which is more likely to fail this week? The new one, and often by a wide margin. Reliability engineers have a name for that early stretch of elevated, falling failure rate — infant mortality — and it is the left-hand wall of the bathtub curve.

The explanation everyone reaches for is that a machine needs to bed in: it starts fragile and toughens up with use. That is worth testing rather than repeating, because it makes a strong claim. It says a particular machine becomes less likely to fail as it runs. What, physically, would have got better?

Run through what use does to hardware. Surfaces abrade, fasteners loosen, seals harden, insulation embrittles, metal accumulates fatigue cycles. Nearly every process you can name runs one way. A few genuinely do improve early — bearing surfaces conforming to each other, a seal seating properly, electrical contacts wiping clean — and it would be wrong to say bedding-in is a myth. But it is a minority of mechanisms, and it cannot carry a curve that falls this steeply across nearly everything manufactured, including electronics with no moving parts at all.

So try assuming the opposite: that no individual unit improves. Can the failure rate still fall?

Here is the move that unlocks it. The falling rate is not a measurement of a machine. It is a measurement of a batch. And a batch is not uniform — it is a mixture. Most units left the factory built correctly. A small fraction left with a latent defect: a cold solder joint, an O-ring nicked on assembly, a bolt at the wrong torque, a contaminant trapped in a casting. Those two groups have completely different prospects, and only one of them is fragile.

Now watch the mixture over time. The defective units fail quickly, because their defects are the sort that show up under the first load cycles. The sound ones do not. Week by week, the survivors contain a smaller and smaller share of defectives — not because anything healed, but because the weak members have been removed from the population being counted.

The arithmetic is sharper than the picture suggests. Suppose you have two subpopulations, each with a constant failure rate — no ageing whatsoever in either group, so no individual item's prospects change by a hair. Mix them and the observed failure rate of the mixture declines over time regardless, because the high-rate members are eliminated first and the average drifts towards the low-rate ones. Decreasing risk, built entirely out of components with no decreasing risk in them.

That reframes the original question. The six-month-old machine is not tougher than the new one. It is evidence. It has sat an examination the new one has not sat, and passed. "It has run since January" is data about which subpopulation it was drawn from.

Three things follow that the bedding-in story cannot explain. Burn-in — running units hard before shipping them — works, and what it does is cull rather than strengthen; the manufacturer is deliberately spending some of the good units' life to buy out the defective ones before they reach a customer. Replacing a working part with a fresh one moves you from a proven unit back into the unfiltered population, which is why "we serviced it and then it broke" is a real pattern rather than bad luck. And early failures should be concentrated in a minority of units and traceable to specific defects rather than spread evenly across the fleet — which is what failure analysis actually finds when it opens them up.

One honest complication: a large share of early failures are not the machine's fault at all. They are installation errors, wrong commissioning settings, and an operator who has not yet learned the thing. That produces the same falling shape — a fixed stock of mistakes surfacing early and then running out — from a completely different cause.

This cuts against the way the bathtub is usually taught. Drawn as a single curve against age, it invites you to read it as one machine's biography: fragile youth, steady middle age, worn-out old age. It is nothing of the kind. It is a composite — the left wall belongs to a population containing defectives, the flat floor to failures triggered by external events rather than by age, and the right wall to genuine accumulating wear. Different mechanisms, different subsets of items, superimposed on one axis.

And most items never show all three. In the study that founded reliability-centred maintenance, Nowlan and Heap's 1978 analysis of United Airlines component data, failure modes sorted into six patterns, and the full bathtub was the rarest but one. The dominant pattern, at about 68 percent, was early failures followed by a flat line that never rises — items for which there is no wear-out region to schedule against at all. Only around 11 percent showed any age-related wear-out zone. Those figures are much quoted and much over-extrapolated: they describe aircraft components under one airline's maintenance regime, not machinery in general.

• How burn-in duration is chosen, given that it consumes life from the good units too.
• Why some software shows the same early-failure shape despite nothing physical wearing out.
• What changes in the reasoning when a fleet is repaired rather than replaced, so units re-enter the population part-aged.

Every term the collection defines is gathered in the glossary.