Proof test coverage (PTC) is the fraction of dangerous undetected failures that a proof test actually reveals. A full-stroke test of a valve finds a stuck valve, but not necessarily a seat that leaks too much or a spring that is too weak at process conditions. Whatever the test misses stays hidden until the device is overhauled or replaced.
The arithmetic
Split λDU into two parts:
- PTC · λDU, revealed at every proof test (interval T1),
- (1 − PTC) · λDU, revealed only at renewal (interval MT, often the mission time).
PFDavg ≈ PTC·λDU·T1/2 + (1 − PTC)·λDU·MT/2
Worked example
The valve from the single-channel article: λDU = 2 × 10⁻⁶ per hour, T1 = 1 year, mission time 20 years.
| Proof test coverage | Revealed part | Hidden part | PFDavg | Band |
|---|---|---|---|---|
| 100 % | 8.8 × 10⁻³ | 0 | 8.8 × 10⁻³ | SIL 2 |
| 90 % | 7.9 × 10⁻³ | 1.8 × 10⁻² | 2.5 × 10⁻² | SIL 1 |
| 80 % | 7.0 × 10⁻³ | 3.5 × 10⁻² | 4.1 × 10⁻² | SIL 1 |
The hidden 20 % of failures accumulates for twenty years and contributes five times more than everything else. Halving T1 hardly helps; only better coverage or more frequent renewal does.
Where coverage values come from
- The device certificate or FMEDA report sometimes states the coverage of a described test.
- Otherwise the engineer estimates it by asking, failure mode by failure mode, whether the test would reveal it. Be specific about the test: a stroke test from the control room, a stroke test with timing, a test at process pressure, a seat leak test.
- Record the basis. A reviewer will ask.
Typical qualitative picture (orders of magnitude, not data): a full stroke with stroke-time check reveals most valve failure modes but not seat leakage; adding a tight shut-off test where tightness matters raises coverage further; a transmitter test that only injects a signal at the electronics does not test the sensor or the impulse line.
What to do when coverage drives the result
- Improve the test: add timing, leak tests, test at process conditions, test the solenoid separately.
- Shorten the renewal interval for the part the test misses (overhaul the valve every few years).
- Add partial stroke testing for valves, which clears part of λDU often.
- Add redundancy, accepting the common cause term.
In First Out AI
PTC is a field on each group (Pro). Free assumes 100 %, which is why a Free result can look better than reality; the Pro panel shows the difference. The proof test draft lists the coverage each test must achieve.
Written for First Out AI as engineering guidance. It supports engineering work and does not replace it; check every value against your standards, certificates and company rules with a competent functional safety engineer.