What Is Sensor Repeatability and How Is It Measured?

What does repeatability tell you—and what does it leave out?

Repeatability tells you how much results scatter when you repeat the same task without intentionally changing the measurement conditions. It does not tell you whether those results are centered on the correct value.

The JCGM metrology vocabulary treats repeatability as precision under a defined set of conditions: the same procedure, operators, measuring system, operating conditions and location, over a short interval. For an industrial sensor, that means describing the input or target, fixture and acquisition settings—not simply writing “tested ten times.”

A tight cluster can still be in the wrong place

Illustrative example: suppose a pressure reference is 50.00 kPa. Sensor A gives five readings from 49.98 to 50.02 kPa; Sensor B gives the same pattern shifted upward by 0.50 kPa. Both have a 0.04 kPa observed range, but their means are 50.00 and 50.50 kPa. For this comparison, assume reference uncertainty is negligible relative to that offset.

Subtracting a constant correction can shift Sensor B’s readings toward the reference without reducing their spread. Calibration establishes the relationship to a reference; it is not the same operation as adjustment, and it does not by itself remove random variation.

Resolution, hysteresis and drift answer different questions

Resolution concerns the smallest discernible change or output increment. Hysteresis concerns the difference associated with approach direction or prior state. Drift concerns a change over time. None can be replaced by one repeatability number. For a switch, measure repeated switch-on events separately from switch-off events; combining both can make a stable hysteresis gap look like random scatter.

What should you record for an analog sensor or an ON/OFF sensor?

Record a quantity that can reveal variation: repeated measured values for a measuring sensor, or repeated transition positions or times for a switching sensor. Ten identical ON bits do not reveal how closely the switching boundary repeats.

For a measuring sensor, define the input and acquisition rule

At a declared pressure, temperature, force or distance, record the analog or digital process value using the same settling time, sampling rate and averaging settings. Distinguish two useful tests:

• Fixed-input test: leave the reference unchanged and record fresh measurements. This characterizes short-term variation of that stationary measurement setup.
• Repeated application test: remove and reapply the input, or reposition the same part, between readings. This also includes the effects of the stated loading or positioning cycle.

Choose the test that matches the intended use. Re-reading a cached register is neither a new acquisition nor a new operating cycle. Fast samples from a filtered signal may also be correlated, so their count is not automatically the number of independent observations.

For a switching sensor, record the same edge each cycle

Move a defined target through the detection boundary and record the position where the chosen output transition occurs. Return far enough to restore the starting state, then approach again in the same direction at the same speed. Record release events separately if needed.

State whether motion is toward the sensing face or across it. An axial operating-distance result cannot simply be transferred to a side-passing edge at an arbitrary gap. OMRON’s proximity guidance identifies approach geometry, temperature, supply and differences between individual sensors as relevant influences.

If timing is the quantity of interest, measure each output edge relative to a repeatable reference event. A PLC timestamp includes the acquisition path unless that contribution has been independently characterized.

How do you run a repeatability test that means something?

First define the event, then hold its conditions stable and record complete, traceable cycles. The following is a practical test-planning sequence, not a substitute for a model-specific or contractual acceptance procedure.

1. Define the result. Specify, for example, “pressure indication at a 50 kPa reference” or “rising-edge position during an axial approach.” Identify the sensor model, unit and output mode.
2. Check the reference and fixture. Use a reference with known uncertainty and enough resolution for the variation of interest. For switching positions, the motion axis, position reference and edge-capture method are part of the test.
3. Fix the conditions. Record target material and geometry, direction, speed, temperature, supply, mounting, warm-up and filter settings. For optical sensing, include the surface, angle, background and lighting.
4. Define one cycle and collect the sequence. State the reset, reapplication and settling rules. Preserve results in acquisition order, together with timestamps or cycle numbers and any missed transitions.
5. Look at the sequence before summarizing it. A steady trend suggests changing conditions; alternating values may indicate two mechanical states. Investigate unusual points rather than deleting them to improve the result.
6. Report the method with the number. Include cycle count, units, statistic, reference, operating point and settings. Keep standard-target and production-target trials separate.

Before changing fixtures or connections, prevent unintended motion and follow the machine’s isolation procedure. Any powered motion test needs a controlled, authorized setup; an ordinary process sensor is not a personnel-protection safeguard.

How many cycles are enough?

There is no universal count for every sensor and decision. Follow the applicable test method where one is specified; otherwise choose the number and repetitions needed for the decision’s risk and confidence. Ten readings can teach a calculation or reveal an obvious problem, but they do not establish a rare-failure rate or a guaranteed production limit.

How do you calculate repeatability from the readings?

Use the statistic required by the specification. For a basic data summary, report the sample standard deviation and observed range, with the mean and cycle count alongside them. They describe different features of the same data—not interchangeable definitions of repeatability.

Here x_i is one result and n is the number of results. Standard deviation describes dispersion around the mean; range uses only the two extremes. Both retain the original unit. The mean locates the group but does not describe its spread.

A complete example using ten pressure readings

Illustrative data, not a product test: assume ten separate applications of a stable 50.000 kPa reference, unchanged setup, negligible reference variation at the displayed scale, and a 0–100 kPa measuring span.

50.02, 49.98, 50.05, 49.97, 50.01, 50.03, 49.99, 50.04, 49.96, 50.00 kPa

To express a chosen metric as a percentage of span, divide that metric by the stated span and multiply by 100. Here 3s / 100 kPa × 100 = 0.09083% of span. This is not 0.09083% of the reading. A specification may use rated span, configured span or another stated reference: use its denominator.

Do not replace single-reading scatter with the standard error

For independent observations from a stable process, the estimated standard error of the mean is s / √n. In this example it is about 0.009574 kPa. That describes the random uncertainty of the estimated mean—not the scatter of the next individual reading and not the total measurement uncertainty.

Likewise, x̄ ± 3s is not a guaranteed worst-case limit. The familiar 99.7% coverage concerns a normal population within three population standard deviations of its mean; a small sample does not prove that distribution or future coverage. Report the observed data and assumptions without turning a statistical band into a guarantee.

How can you compare repeatability specifications fairly?

Match the measured quantity, statistic and test conditions before comparing the number. A value in micrometers can describe a different event, spatial average or acquisition mode from another value with the same unit.

A real specification shows why the footnote matters

KEYENCE lists 0.1 µm repeatability for height difference for the WI-001, WI-004 and WI-010 heads in the WI-5000 series. Footnote 4 defines it as a σ value for the average height difference between two rectangular areas, measured for 30 seconds on a KEYENCE standard target, with Auto Maintenance Mode OFF and Capture Timing set to “Prioritize Accuracy.”

For WI-001, each specified rectangle is 0.3 × 0.9 mm. On the same page, a separate 1 µm height-resolution statement refers to a ±3σ definition for a different quantity. These are not two conflicting descriptions of the same measurement. Nor is the 0.1 µm value a promise about a single point on any moving production surface. This is a documented third-party example, not an xsz sensor rating. See the specification and footnotes.

Before accepting a comparison, resolve three questions:

• What repeats? One point, an averaged area, a switch-on coordinate or a trigger time—and for one sensor or several units?
• What does the value mean? Standard deviation, maximum deviation, full observed range, ± band or a product-specific definition? If it is a percentage, what is the reference quantity?
• Which conditions produced it? Target, working distance, direction, speed, sample count, filtering, temperature and supply. Compare the settings you can actually use.

Do not divide an undefined “±” value by three to manufacture a standard deviation. Also keep one unit’s cycle-to-cycle spread separate from unit-to-unit differences: a replacement sensor can repeat tightly around a different switching point.

Why can a repeatable sensor still give variable machine positions?

The machine records an event through a chain: target motion, sensing, electrical output, input acquisition and control logic. Variation anywhere in that chain can change the recorded position, even when the sensor’s own short-term behavior is consistent.

Separate a delay from variation in that delay

At constant speed, an additional delay corresponds to an additional distance:

Illustrative calculation: at 1 m/s, a 1 ms difference in acquisition delay corresponds to 1 mm of travel. A fixed delay at fixed speed mainly shifts the recorded position; a changing delay can add scatter. This does not calculate a particular PLC’s timing or isolate the sensor’s response time.

Where suitable test equipment and the machine’s approved procedure allow it, compare the sensor output edge with the controller’s captured event. Stable electrical transitions but variable recorded coordinates direct attention toward acquisition timing or motion feedback. Variation already present at the output calls for investigation of target presentation, fixture movement, sensing conditions and electrical influences.

Keep changed conditions in separate results

Compare a rigid, unchanged target with the actual part presentation; then examine relevant changes such as mounting temperature, target angle or surface condition. Change one factor at a time where practical. Averaging may reduce some visible noise, but a filtered measurement must still respond quickly enough for the application.

Under VIM terminology, extended testing at the same location with specified changes can be an intermediate precision study. Reproducibility addresses a different declared set of conditions, including different locations, operators and measuring systems. A changed day is not, by itself, a reason to relabel every result “reproducibility.” Preserve the short-term baseline and describe exactly what changed.

What repeatability is good enough for your application?

The repeatability contribution must fit the application’s allowed measurement or position variation, together with the other contributors. There is no universal “good” value or mandatory ten-to-one ratio that applies to every sensor task.

For part-position triggering, consider switching-point spread, part-position variation and acquisition timing. For dimensional inspection, include reference uncertainty, fixture effects, bias, resolution and the decision rule near the tolerance limits. A small repeatability figure is only one part of either assessment.

Specify the result you need in an observable form: the event or input, operating point, relevant conditions, allowed metric and acquisition settings. If the controller acts on individual readings, do not qualify the system using only the stability of a heavily averaged result that the process cannot wait for.