Repeatability and Reproducibility

Compares variation in repeated measurements under unchanged and changing conditions.

Conceptual context

Repeated measurement does not produce a perfect copy of the same number. Each $x_i$ carries the combined influence of the object, instrument, method, environment, and operator. Repeatability examines what happens when nearly everything is kept unchanged. Reproducibility broadens the scene and allows relevant conditions to change. The central question is not merely how scattered the data are, but which part of that scatter belongs to the measurement process itself and which part appears when the procedure moves across operators, instruments, laboratories, or times. The $s$ acts as a statistical lens that summarizes the width of the result cloud and makes both regimes comparable.

🟢 Essential level

Repeatability describes how close results are when the same method is used under nearly identical conditions. Reproducibility asks whether that closeness survives when important parts of the experiment change. In both cases, the $x_bar$ marks the approximate center of the results, while the $s$ describes how widely the $x_i$ values spread around that center. A small $s_r$ means the procedure is stable within one setting. A larger $s_R$ shows that changes in operator, instrument, laboratory, or time add variability. The difference does not by itself prove bias, but it does reveal dependence on external conditions. The $CV$ is useful for relative comparisons when scales differ and the $x_bar$ remains safely away from zero.

Repeatability is therefore a local property of a procedure, whereas reproducibility tests whether that property survives transfer to a wider experimental setting. A procedure with good repeatability but poor reproducibility usually signals that something in the instrument, the operator, or the environment is not sufficiently controlled or documented, even though each individual session looks perfectly stable.

🔵 Formal level

Basic formulas

For a series containing $n$ observations, the $x_bar$ is obtained by dividing the $\textstyle\sum x_i$ by the number of observations:

Sample mean

Sample spread is quantified by dividing the $\textstyle\sum(x_i-\bar x)^2$ by the degrees of freedom:

Sample standard deviation

Both expressions are the mandatory starting point of any repeatability study: without a reference $x_bar$ and a measure of its spread, one set of repetitions cannot be compared with another, and random variation cannot be distinguished from a genuine change of conditions.

Real student questions

Does good repeatability guarantee good reproducibility? No. An instrument may be stable in one laboratory and change when temperature, operator, or calibration changes.

Does a small $s$ mean the result is correct? It means the measurements are tightly grouped. They may still be grouped around a biased value.

Why is reproducibility usually worse? Because it includes more sources of variation than repeatability.

Should I always use $CV$? No. Use it only when relative comparison is meaningful and $x_bar$ is not near zero.

What if $s_R$ is smaller? Review grouping, formulas, units, component estimates, and whether the same measurand is being compared.

Final synthesis

Repeatability studies spread under nearly unchanged conditions. Reproducibility adds controlled changes. The $s$ usually increases because new sources of variation appear. Correct interpretation requires separating precision, bias, and experimental structure.