The P-F Curve, and What Sits Where On It
Every "how early can you detect it?" conversation is really an argument about one picture. This is the picture.
A machine that is going to fail rarely fails without warning. It emits evidence, and the evidence arrives in a fixed order: first as very high frequency energy that nothing but a dedicated instrument can hear, and last as a noise loud enough that someone walks over to investigate.
P is the earliest point at which failure is detectable. F is functional failure — the point at which the machine can no longer do its job. The gap between them is the P-F interval, and it is the only thing that determines whether condition monitoring buys you a planned outage or a slightly better-documented breakdown.
Positions are indicative, not measured. Ordering follows conventional practice; the intervals vary enormously by machine, duty and failure mode, and the caveats below are not decoration.
How to read it
The curve is deliberately flat at the left and steep at the right. Damage does not progress linearly — a spall spends a long time being microscopic and then a short time being catastrophic, and the steepening slope is what makes late detection so much less valuable than it looks.
Every technique is a horizontal choice about where to stand. Ultrasound and enveloping stand far left and buy months. Overall RMS stands well right and buys days to weeks. Neither is better; they cost differently, they need different skill, and they fail differently.
The sales conversation that sounds like it is about accuracy is almost always about position on this slope.
What the map does not tell you
Earlier is not automatically better. A technique that detects six months out gives you six months of a fault you now have to track, re-measure and argue about, on an asset that may be replaced for unrelated reasons before it fails. Detection you cannot act on is a cost.
The intervals are not fixed. A slow-speed paper machine bearing and a 3,600 RPM pump do not share a P-F interval, and neither shares one with a bearing that is starved of lubricant rather than spalled. The ordering is far more stable than the durations.
The curve assumes there is a curve. Some failures have no meaningful P-F interval at all — a bearing that seizes from sudden contamination, a winding that fails from a voltage transient. Those are run-to-failure or design problems, and no monitoring position on this diagram helps. Being able to say which of your assets are on this curve and which are not is worth more than any single technique.
Position on the curve is not the same as coverage. Ultrasound sits furthest left but hears only certain failure modes. A technique's value is where it stands multiplied by what it can see from there, and this diagram only shows the first factor. A proper gap analysis needs the second.
The uncomfortable part
Everything above assumes you can tell where on the curve you currently are — which requires knowing what this machine looked like when it was healthy.
That assumption fails more often than the techniques do. A baseline learned from a machine that was already degrading is not a baseline, and no amount of sensitivity in the instrument recovers it. Working through a public run-to-failure dataset, I hit exactly this: one feature carried a clean signal from the first minute of recording, and the detector could not use it, because there was no undegraded period to learn "normal" from.
The write-up is in the bearing prognostics study. It is the failure mode nobody puts on the diagram, and it is structural to essentially every learn-normal-then-alarm product on the market.
Definitions for everything named here are in the glossary.