The P–F Interval Is a Measurement Hypothesis

A gearbox alert fires on a Tuesday. The first question in the room is always the same: how long have we got?

The honest answer is not a number. It is a list of things that would each have to be true before a number would mean anything.

Most engineers have seen the P–F diagram — a curve declining across a page, P marked where the fault becomes detectable, F marked where the function is lost, a comfortable gap between them. Drawn that way, the gap looks like a property of the machine, the way a bore diameter is a property of the machine.

It is not. It is a proposition about one failure mode, one functional boundary, one measurement method, one operating context, and one decision process. Change any of those and the gap you drew moves, or closes.

P and F are definitions you chose, not features you found

Three terms, stated precisely, do most of the work.

F — functional failure is the defined point at which the asset no longer meets a required function or performance criterion in the stated operating context. The equipment may still be turning. The required function is the boundary, not the noise.

P — a defined potential-failure condition is the point at which a chosen method, sensor or sample location, operating state, acquisition procedure, detection criterion and confirmation rule can identify evidence of that developing failure with acceptable measurement performance. Every word in that list is a decision somebody made.

The P–F interval is the observed or estimated time, cycles, distance or other exposure between that defined P and that defined F. It is conditional on those definitions, and it should be represented with uncertainty rather than treated as a fixed characteristic of the machine.

Move the accelerometer to a different bearing housing and P moves. Take the reading in a different load state and P moves. Change the threshold, the sampling method, the analyst’s confirmation rule, or where the business decides the required function has been lost, and P moves again. Change the deterioration rate — new duty, different product, contaminated lubricant — and the interval compresses while your measurement stays exactly the same.

This is why a nominal warning window cannot be transferred from one asset class, site or failure mode without evidence. A window that held at another plant is a fact about that plant’s definitions.

No technique is first in line

There is no stable, general sequence in which ultrasound, oil analysis, vibration, temperature and human senses must detect every developing failure. Technique performance depends on the failure mechanism, the signal path, the sensor or sample location, the operating state, acquisition settings, the threshold, the confirmation method, and the quality of the baseline.

The public technical record makes the point without supplying a ladder. NREL reports that different wind-turbine failure modes call for different monitoring techniques, and that particle-count results can depend on sensor location. In a separate NREL gearbox reference, vibration detection is reported earlier than oil debris analysis for specified high- and intermediate-speed damage modes, while the same reference notes difficulty in the planetary stage. NASA’s tapered-roller-bearing experiment found value in combining oil-debris and vibration features, but its rules were built from a limited test-rig dataset and were expected to change as more failure-progression data became available.

Read those for what they are: demonstrations that technique performance is conditional, in named test contexts, on named modes. They are not a transferable ranking of technologies, and a wind-turbine gearbox in a slide deck is not your gearbox.

The record that has to exist before the interval does

Before assigning a P–F interval, the reviewable artefact is a detection evidence record. Six fields, each answering a question the interval silently assumes has been answered.

Decision field	What the record must state	Why it matters
Function and failure mode	required function, performance boundary, failure mechanism, consequence context	prevents an asset-level interval from hiding unlike modes
Measurement contract	technique, sensor or sample location, operating state, acquisition settings, data-quality checks	defines what “detectable” means in practice
Detection criterion	baseline, threshold, persistence or confirmation rule, analyst or system decision	makes P reproducible and exposes false-negative risk
Warning evidence	field or test observations, population and conditions, spread, censoring, missing data, transfer limits	distinguishes an uncertain estimate from a borrowed number
Response path	alert review, diagnosis, decision authority, parts, access, isolation, work window, execution	shows how much of the warning is consumed after detection
Governance	consequence class, applicable law and regulation, OEM or controlled-procedure requirements, owner, approvers, review triggers	keeps the reference from becoming unauthorised instruction

The fourth row is the one most programmes cannot fill, and the fifth is the one that decides whether the interval was ever usable. A warning that arrives with a genuine lead time, into an organisation that needs longer than that to raise a permit and find the part, has not created time to act. It has created a record of what you failed to do.

If the evidence cannot support a warning interval for the specified conditions, record the result as NOT DEMONSTRATED. Do not invent a low-side value by intuition, and do not lengthen an established task merely because recent measurements were quiet.

What the DoD manual says, and the fraction it does not prescribe

DoDM 4151.25, dated 16 February 2024, describes an on-condition task in its DoD reliability-centred-maintenance context as needing four things: a detectable potential-failure condition, a relatively consistent P–F interval, practical monitoring at an interval shorter than P–F, and enough time to act.

It does not prescribe a universal one-half fraction.

The review that replaces the missing fraction keeps four questions separate, so uncertainty and missing information stay visible rather than dissolving into arithmetic.

What warning evidence exists? Record the relevant population and conditions, the exposure basis, the observed spread, censored or missing observations, transfer limits, and the reasons the evidence may no longer apply. A mean, one anecdote, or a borrowed asset-class number is not a defensible lower bound.

When can a valid measurement actually occur? Include operating-state opportunity, physical access, missed or invalid readings, analysis, confirmation, escalation, and failure of the monitoring system itself.

What does the response path demand? Review, diagnosis, decision authority, parts, access, permits and isolation, work-window alignment, repair, and return-to-service controls — under credible adverse conditions, not only the best case.

What uncertainty and consequence controls apply? Mandated and OEM tasks, protective functions, safe-state and shutdown rules, independent safeguards, change control, decision authority, and the site-approved basis for any additional conservatism.

The result is a governed evidence judgement, not a calculation of safety or residual risk.

The most-cited counter-example is worth stating precisely, because it is usually made to say the opposite of what it says. The NTSB’s investigation of Alaska Airlines Flight 261 found that insufficient lubrication of the jackscrew assembly caused excessive wear, and that extended lubrication and end-play-check intervals contributed to the accident; the report also addressed measurement error, systemic maintenance deficiencies, oversight, and the absence of a fail-safe mechanism. Its recommendation for at least two opportunities to detect excessive wear applied to that specific aircraft jackscrew and its potentially catastrophic condition. It is not evidence for a universal 50% P–F rule, a general industrial inspection interval, or a sensor ordering. The transferable lesson is governance: where consequences are material, interval changes warrant task-specific technical evidence, measurement-reliability review, missed-task consideration, consequence treatment, and competent approval. That reading is an authorial inference, not an NTSB endorsement.

An exercise that costs an afternoon

Take one asset you already act on by condition — one where somebody would raise a job if a number moved. One failure mode, not the whole machine.

Fill the six fields of the detection evidence record from what is genuinely written down today. Not what people believe. What a stranger could read.

Then time the response path against real records rather than against the plan: from the reading, to the review, to the decision, to the parts, to the access and isolation, to the work window, to return to service. Use the last two or three jobs of that type, including the awkward one.

Two things usually happen. The warning-evidence row comes back empty or borrowed, which tells you the interval was inherited rather than established. And the response path turns out to consume most of the warning, which tells you the constraint was never the sensor.

Neither finding costs capital, and both change what the next purchase should be.

If you cannot defend the mode, the measurement, the warning evidence and its limits, the response path and the approval basis, you do not have a P–F task yet. You have a hypothesis to test under controlled conditions.

Which of your inspection intervals could survive being asked where its warning evidence came from?

The P–F definitions, the detection evidence record, and the bounded readings of DoDM 4151.25 and NTSB AAR-02/01 are from Predictive Maintenance: Practitioner Reference Frameworks and Planning Guide (Part 1: Predictive Maintenance Foundations).