Precision, accuracy, stability: the vocabulary of metrology#
Why#
The previous chapter shows figures like “RMS offset ~0.07 to 1.7 µs” and “drift 0.007 to 0.05 ppm” without rigorously defining them. These two numbers actually measure two completely different qualities of a clock, often conflated in everyday language. Understanding this distinction changes how you interpret everything else in this guide, in particular why a value can be “good” on one criterion and “bad” on another, at the same time.
Three quantities, three different questions#
| Quantity | Question asked | Typical example |
|---|---|---|
| Precision | What is the smallest increment I can resolve? | 1 ns on a modern PHC (PHC chapter) |
| Accuracy | How close am I to the “true” value (UTC)? | ~100 ns on a direct GPS PPS |
| Stability | How much does my measurement vary over time? | Allan deviation σᵧ ≈ 1.8×10⁻⁸ (see Performance chapter) |
Analogy: a simple mechanical watch. A precise watch has a second hand and a finely graduated dial: the second, even a fraction of a second, can be read on it. An accurate watch shows the correct time, the one given by a reference (not three minutes fast at all times). A stable watch always gains or loses the same amount, day after day: its error stays regular, even if it isn’t zero. A watch can be precise (second hand and detailed dial) without being accurate (always five minutes fast), exactly like a clock can display nanoseconds (precise) while being off by about ten minutes from UTC (not very accurate).
What RMS offset and skew actually measure#
The two metrics highlighted throughout this guide map directly onto two of these three quantities:
- RMS offset (
chronyc tracking) measures accuracy: the standard deviation of the error between the server’s clock and the GNSS reference. A value around a microsecond means the server is, on average, very close to true UTC. - Skew (
chronyc tracking) measures the frequency stability of the local oscillator, in parts per million (ppm). A low, steady skew means the clock drifts little between two successive chrony corrections, which is what makes thermal stabilization (dedicated chapter) relevant: frequency stability depends directly on the oscillator’s temperature.
It is entirely possible to have an excellent instantaneous RMS offset together with a high, unstable skew, a server that is constantly well corrected, but whose underlying oscillator wanders a lot and therefore needs frequent, large corrections. Conversely, a very stable but badly calibrated oscillator will show an excellent skew with a disappointing RMS offset. These are two different defects, with different causes and different remedies.
Frequency stability can be quantified even more rigorously, beyond the instantaneous skew, with the Allan deviation σᵧ(τ). This tool, its measurement on this server (σᵧ ≈ 1.8×10⁻⁸ at τ=4 s, along with the quartz stability graph), and its comparison against the Paris Observatory’s atomic references are covered in the Performance chapter.
Pitfalls to avoid#
- Mistaking a good instantaneous RMS offset for a guarantee of
long-term quality. A single
chronyc trackingreading says nothing about stability, two measurements several hours apart, watching the skew, give a far more reliable picture (see the Munin chapter for observation over time). - Optimizing one metric while degrading the other without noticing.
The
poll 2vspoll 4anecdote in the Chrony chapter is a good example: a theoretical hypothesis about statistical filtering improved one aspect on paper while degrading the RMS offset measured in practice.
Verify#
chronyc tracking | grep -E "RMS offset|Skew"Watch these two values several hours apart, ideally at different ambient temperatures (day/night): it’s the most telling test to distinguish instantaneous accuracy from real stability.
📚 Going further
- The precision/accuracy/stability distinction is formalized in IEEE Std 1139-2008 (Standard Definitions of Physical Quantities for Fundamental Frequency and Time Metrology, Random Instabilities).