Accuracy, Precision, and Process Capability

A camera measurement, display luminance reading, or dimensional inspection is useful only when its uncertainty is small enough for the decision. Repeated values can agree closely and still be wrong. Equally, an average can lie near a reference while individual readings vary too widely to support acceptance.

Separate bias from precision

Accuracy describes how closely a measurement agrees with the quantity’s true value; it involves both trueness and precision. Trueness concerns the average result relative to a reference, while precision concerns agreement among repeated measurements under stated conditions. Neither accuracy nor trueness is itself a numerical error metric. Estimated bias and standard deviation provide quantitative descriptions:

A tight, displaced dart cluster illustrates small spread with bias. A broad, centered cluster illustrates small observed mean bias with poor precision; it does not establish accurate individual results. The reference also has uncertainty, and a finite sample does not reveal the exact long-run mean.

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State the conditions behind the spread

Repeatability holds the procedure, operator, measurement system, location, and operating conditions substantially fixed over a short period. Reproducibility evaluates precision across different locations, operators, and measurement systems, with the changed conditions stated. Intermediate precision commonly describes changes over time within one laboratory.

Precision is therefore the broader term. Manufacturing Gage R&R uses “reproducibility” for the operator-related component of its declared study; this does not automatically establish performance across laboratories. Repositioning a part, refocusing a camera, or changing a display fixture can introduce variation that repeated software reads alone miss.

Compare measurement spread with tolerance

For a two-sided engineering tolerance $T=USL-LSL$, define a six-standard-deviation precision-to-tolerance ratio:

The multiplier is a reporting convention, not a confidence interval for the estimated standard deviation. State whether $\sigma_{\mathrm{gage}}$ represents repeatability alone or total Gage R&R. P/T omits bias and other uncertainty contributions. A one-sided specification does not supply a tolerance width without an additional justified engineering bound.

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Keep process capability separate

Capability compares a stable process distribution with specification limits. Using its mean $\mu$ and a suitable within-process standard deviation $\sigma_p$:

$C_p$ describes potential spread relative to tolerance; $C_{pk}$ also responds to centering. A single upper or lower limit supports the corresponding one-sided index. These are process indices, not measurement-system approval scores. Measurement noise inflates observed spread, while bias can shift apparent centering. Check measurement suitability and process stability first; non-normal data may require another capability model. An overall standard deviation convention produces performance indices $P_p$ and $P_{pk}$ rather than within-process $C_p$ and $C_{pk}$.

Iris Optics can help separate instrument variation from product variation and establish measurement requirements that support defensible camera, display, and optical acceptance decisions.