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This document was prepared by Technical Committee ISO/TC 69, Applications of statistical methods, Subcommittee SC 6, Measurement methods and results.

This second edition cancels and replaces the first edition (ISO 5725-3:1994), which has been technically revised. It also incorporates the Technical Corrigendum ISO 5725-3:1994/Cor.1:2001.

The main changes are as follows:

A list of all parts in the ISO 5725 series can be found on the ISO website.

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0.1   ISO 5725 uses two terms “trueness” and "precision” to describe the accuracy of a measurement method. “Trueness” refers to the degree of agreement between the average value of a large number of test results and the true or accepted reference value. “Precision” refers to the degree of agreement between test results.

0.2   General consideration of these quantities is given in ISO 5725-1 and is not repeated here. It is stressed that ISO 5725-1 provides underlying definitions and general principles should be read in conjunction with all other parts of ISO 5725.

0.3   Many different factors (apart from test material heterogeneity) may contribute to the variability of results from a measurement method, including:

0.4   Two conditions of precision, termed repeatability and reproducibility conditions, have been found necessary and, for many practical cases, useful for describing the variability of a measurement method. Under repeatability conditions, none of the factors a) to h) in 0.3 are considered to vary, while under reproducibility conditions, all of the factors are considered to vary and contribute to the variability of the test results. Thus, repeatability and reproducibility conditions are the two extremes of precision, the first describing the minimum and the second the maximum variability in results. Intermediate conditions between these two extreme conditions of precision are also conceivable, when one or more of the factors listed in b) to g) are allowed to vary.

To illustrate the need for including a consideration of intermediate conditions in method validation, consider the operation of a present-day laboratory connected with a production plant involving, for example, a three-shift working system where measurements are made by different operators on different equipment. Operators and equipment are then some of the factors that contribute to the variability in the test results.

The standard deviation of test results obtained under repeatability conditions is generally less than that obtained under intermediate precision conditions. Generally, in chemical analysis, the standard deviation under intermediate precision conditions may be two or three times larger than that under repeatability conditions. It should not, of course, exceed the reproducibility standard deviation.

As an example, in the determination of copper in copper ore, a collaborative study among 35 laboratories revealed that the standard deviation under intermediate precision conditions (different times) was 1,5 times larger than that under repeatability conditions, both for the electrolytic gravimetry and Na2S203 titration methods.

0.5   This document focuses on intermediate precision and alternative designs for collaborative studies of a measurement method. Apart from the determination of intermediate precision measures, the aims of these alternative designs include reducing the number of required measurements, increasing the reliability of the estimates for precision and overall mean and taking into account test material heterogeneity.

Indeed, a $t$-factor fully-nested experiment with two levels per factor (inside each laboratory, there are $t-1$ factors) and two replicates per setting requires $2·2^{t-1}$ test results from each laboratory, which can be an excessive requirement on the laboratories. For this reason, in the previous version of ISO 5725-3, the staggered nested design is also discussed. While the estimation of the precision parameters is more complex and subject to greater uncertainty in a staggered nested design, the workload is reduced. This document offers alternative strategies to reduce the workload without compromising the reliability of the precision estimates.

As far as the special designs for sample heterogeneity are concerned, they were discussed in the previous version of ISO 5725-5. However, it is convenient to have one part of this standard dedicated to the question of the design of experiments.

0.6   The repeatability precision as determined in accordance with ISO 5725-2 is computed as a mean across participating laboratories. Whether it can be used for quality control purposes depends on whether the repeatability standard deviation can be considered to remain constant across laboratories. For this reason, it is important to obtain information on how the repeatability standard deviation varies within and between the laboratories under different conditions.

0.7   In many collaborative studies, the between-laboratory variability is large in comparison to the repeatability, and it would be useful to a) decompose it into several different precision components, b) reduce, if possible, some sources of variability which are due to the intermediate precision conditions. This can be done by identifying factors (e.g. time, calibration, operator or equipment) which contribute to the variability under intermediate precision conditions of measurement, by quantifying the corresponding variability components and, wherever achievable, decreasing their contribution. In this manner, the intermediate precision component of the overall variance is enlarged while the between-laboratory component of the overall variance is reduced. Only random effects are considered: it is only reasonable to model a factor as a fixed effect after a method or calibration optimization study has been conducted. In this standard, different relationships between factors are taken into account, e.g. whether a particular factor is subsumed under another factor or not.

0.8   Estimates for precision and overall mean are subject to random variability. Accordingly, it is important to determine the uncertainty associated with each estimate, and to understand the relationships between this uncertainty, the number of participants and the design. Once these relationships are understood, it becomes possible to make much more informed decisions concerning the number of participants and the experimental design.

0.9   Provided different factorial effects do contribute to the variability, determining the respective precision components may make it possible to reduce the required number of participating laboratories, since the between-laboratory variability can be expected to be less dominant. However, it is highly recommended to have a reasonable number of participating laboratories in order to ensure a realistic assessment of the overall method variability obtained under routine conditions of operation.

0.10   In the uniform-level design according to part 2 of this standard, there is a risk that an operator will allow the result of a measurement on one sample to influence the result of a subsequent measurement on another sample of the same material, causing the estimates of the repeatability and reproducibility standard deviations to be biased. When this risk is considered to be serious, the split-level design described in this document may be preferred as it reduces this risk. Care should be taken that the two materials used at a particular level of the experiment are sufficiently similar to ensure that the same precision measures can be expected (in other words: the question arises whether the precision component associated with a particular factor remains unchanged across a range of similar matrices).

0.11   The experimental design presented in ISO 5725-2 requires the preparation of a number of identical samples of the material for use in the experiment. With heterogeneous materials this may not be possible, so that the use of the basic method then gives estimates of the reproducibility standard deviation that are inflated by the variation between the samples. The design for a heterogeneous material given in this document yields information about the variability between samples which is not obtainable from the basic method; it may be used to calculate an estimate of reproducibility from which the between-sample variation has been removed.