Multi-day precision reference

For each level, a multi-day precision study reports repeatability SD and CV (within-run imprecision), between-run SD within days, and between-day SD. It also gives within-laboratory SD and CV (the total imprecision; see within-laboratory precision) and the grand mean, with a confidence interval from the day means.

• One material per level.
• At least two days. One run a day is fine.
• At least two replicates in at least one run.
• A day, run and replicate on every included row, with each replicate ID used once per run.
• A planned design has the same number of runs each day and the same number of replicates in every run. When a result is lost or excluded, the remaining results are still calculated (see Unbalanced designs).
• Between-run SD (within days) needs two or more runs per day. With one run per day, the between-day component is reported as Between-day/run SD and combines day and run effects.

Confidence level, Measurement scale and Display decimal places are calculation settings.

Manufacturer precision claims (optional) holds one claim value per row: the level, the claim concentration, the manufacturer's SD or CV, and whether the claim is Repeatability or Within-laboratory. A CV is converted to SD at the included level mean. One-sided confidence starts at 95%.

Suggested design under Collection design on Set up offers 5 days × 1 run × 5 replicates and 20 days × 2 runs × 2 replicates and sets the counts in Lay out the grid on an empty grid. Once the grid has rows, the Precision design panel above Entered results offers the same two designs for Renumber day, run and replicate.

• Lay out the grid, on an empty grid, adds a row for every result the design needs, with material ID, level, day, run and replicate filled in.
• Renumber day, run and replicate replaces the day, run and replicate of all included rows in table order. The file still needs those three columns, and each level needs exactly 25 or 80 included rows. Its confirmation is Renumber day, run and replicate?.
• Add a day or run reuses a selected day's or run's materials and replicate labels with every measurement blank.

In Import a file, the column uses are Specimen or material ID, Level or group, Day, Run, Replicate and Result; Day, Run and Replicate are required.

The calculation stops, naming the level, if there is only one day, no run has two replicates, a level has two materials, a row has no day, run or replicate, or a replicate ID repeats within a run.

• An SD limit can use the study unit, a percentage of the level mean, or both. With the larger-allowance choice, the limit is the greater of the two. The saved result shows the resolved SD allowance at each mean. On an interval scale, Pass only when within both is Not met when the SD fails its study-unit allowance and Undecided otherwise.
• An analyzer profile can prefill this limit from the random share of its allowable error. See About allowable error.
• SD and CV decisions use the entered decimal results before display rounding; equality meets an inclusive limit.
• CV limits need a ratio scale (Measurement scale, the default). On an interval scale they are Undecided.
• With one run per day, a Between-run SD (within days) limit is Undecided. A Between-day SD limit then uses the combined between-day/run SD.
• The manufacturer claim comparison is a separate question. A laboratory limit remains Not met when its observed result exceeds it, even if the manufacturer claim comparison is consistent.
• A limit that is Not met makes the whole study Criteria not met.

See Set acceptance limits, including More statistics, and About acceptance decisions.

• Results: the mean with its confidence interval, repeatability SD and CV, and within-laboratory SD and CV, arranged as described in Reading results.
• Results by day: each day's mean and SD.
• Additional statistics: every variance component, including the between-run and between-day SDs, and the confidence interval for the grand mean.
• The report's Design line: the days, runs and replicates found, or the range of counts in an unbalanced design (for example 4–5 replicates per run).
• With an unbalanced design, the saved result and the report's study notes say that the unbalanced estimator was used and how many results the full design would have had (for example 24 of 25 results; day 3 has 4 replicates).
• The manufacturer claim comparison: the claimed SD, verification limit and Consistent with the claim or Higher than the claim. The precision summary gives the observed SD.
• Display decimal places under Calculation settings sets the number of digits shown.

The repeatability SDs can feed the Deming λ of a method comparison.

precision.csv has one control material (QC1), level 1, on 5 days with 1 run per day and 5 replicates per run (25 rows). The results are 5.4 or 5.5.

Setup: analyte Example analyte, unit mmol/L, 95% confidence. Limits:

• Within-laboratory CV at most 2 %.
• Repeatability CV at most 1 %.

The study status is Criteria met. A note says that with one run per day the between-day/run SD combines day and run effects. Results by day gives day means of 5.50, 5.46, 5.48, 5.50 and 5.50 mmol/L.

When you calculate Glucose · multi-day precision in the example project, LabRuns records these methods:

1. Random-effects model with days, runs within days and replicate error, one material per level. At least 2 days and at least one run with 2 or more replicates.
2. Balanced design: repeatability variance = MS(error). Run variance = [MS(run) − MS(error)] / n. Day variance = [MS(day) − MS(run)] / (r n). With one run per day, the combined day/run variance = [MS(day) − MS(error)] / n.
3. Unbalanced design (unequal runs or replicates): method-of-moments ANOVA estimators. With one run per day, day/run variance = [MS(day) − MS(error)] / n0, n0 = (N − Σnᵢ²/N) / (D − 1). With several runs per day, sequential sums of squares with E[MS(run)] = σe² + k1·σrun² and E[MS(day)] = σe² + k2·σrun² + k3·σday², where k1 = (N − ΣΣnᵢⱼ²/nᵢ) / (Σbᵢ − D), k2 = (ΣΣnᵢⱼ²/nᵢ − ΣΣnᵢⱼ²/N) / (D − 1) and k3 = (N − Σnᵢ²/N) / (D − 1).
4. A negative component is set to zero. Within-laboratory variance is the sum of the components.
5. SD allowances using a percentage require a ratio scale. With both limits required on an interval scale, a failed study-unit requirement fails the criterion; otherwise it is undecided.
6. Grand-mean CI uses Student t with D − 1 degrees of freedom and the SD of the D day means divided by √D. It assumes independent, normally distributed day means.
7. Distribution diagnostics: ordered values plotted against standard-normal quantiles at Blom positions pᵢ = (i − 3/8)/(n + 1/4).
8. Box: type-7 quartiles, IQR = Q3 − Q1. Whiskers end at the most extreme values within Q1 − 1.5 IQR and Q3 + 1.5 IQR. Values beyond the whiskers stay in the analysis.
9. Q–Q and box plots need at least 3 values that are not all identical. The strip plot shows every included value.

D is the number of days, r the runs per day and n the replicates per run. Each SD on the screen is the square root of its variance component. The grand mean is the mean of all included results (the mean of the day means in a balanced design). Within-laboratory CV = 100 × within-laboratory SD / grand mean, on a ratio scale.

A component set to zero shows as 0, with a note. See variance components.

In the unbalanced formulas, nᵢ is each day's count, N the total, bᵢ the number of runs on day i and nᵢⱼ the replicates in run j of day i. The sums of squares are taken in order: days, then runs within days, then replicates. In a balanced design k1, k2 and k3 equal n, n and r × n, so the balanced and unbalanced formulas give the same result.

The verification limit is the claimed SD × √[χ²(confidence, ν) / ν], which assumes normally distributed measurement error. For repeatability, ν is the residual degrees of freedom, N − R for N results in R runs. For within-laboratory precision, ν comes from a Satterthwaite approximation using the active variance components, their covariance and the observed day and run structure. The same approximation handles a lost replicate or a short run. A component estimated below zero stays at zero. The approximation follows Van den Heuvel's published statistical method.

Sources: NIST/SEMATECH e-Handbook, nested designs; Searle, Casella and McCulloch, Variance Components (1992), for the unequal-size estimators. Numerical examples from Chakravarthy et al. (2019). See Study reference.

Evidence references: CAP COM.40300, COM.40350 (9 December 2025). In a binder, the CAP evidence index lists the report sections behind each requirement and the laboratory records that go with them.