Bootstrap-based estimation and inference for measurement precision under ISO 5725

TL;DR

The paper addresses bootstrap-based estimation of ISO 5725 precision measures within a one-way random-effects framework, where practical guidance has been limited. It systematically compares five bootstrap schemes and three CI methods, introducing Wiley-based bias corrections to yield accurate point estimates and reliable interval estimates, validated by extensive simulations across realistic sample sizes and variance ratios, plus a case study on ISO 5725-4 data. Key findings show that adjusted within-laboratory resampling (boot-$j_r$, boot-$j_s$) provides accurate point estimates in small-to-moderate designs, while a two-stage resampling strategy with BCa intervals (boot-$ij_r$ with BCa) delivers near-nominal or conservative CIs across many scenarios; performance degrades under extreme designs. The study provides concrete, actionable guidance for implementing resampling-based precision analysis in interlaboratory studies, including when to prefer adjusted within-lab estimators for point estimation and BCa-based two-stage resampling for interval estimation, with cautions for dominant between-laboratory variation and imbalanced designs.

Abstract

The ISO 5725 series frames interlaboratory precision through repeatability, between-laboratory, and reproducibility variances, yet practical guidance on deploying bootstrap methods within this one-way random-effects setting remains limited. We study resampling strategies tailored to ISO 5725 data and extend a bias-correction idea to obtain simple adjusted point estimators and confidence intervals for the variance components. Using extensive simulations that mirror realistic study sizes and variance ratios, we evaluate accuracy, stability, and coverage, and we contrast the resampling-based procedures with ANOVA-based estimators and common approximate intervals. The results yield a clear division of labor: adjusted within-laboratory resampling provides accurate and stable point estimation in small-to-moderate designs, whereas a two-stage strategy-resampling laboratories and then resampling within each-paired with bias-corrected and accelerated intervals offers the most reliable (near-nominal or conservative) confidence intervals. Performance degrades under extreme designs, such as very small samples or dominant between-laboratory variation, clarifying when additional caution is warranted. A case study from an ISO 5725-4 dataset illustrates how the recommended procedures behave in practice and how they compare with ANOVA and approximate methods. We conclude with concrete guidance for implementing resampling-based precision analysis in interlaboratory studies: use adjusted within-laboratory resampling for point estimation, and adopt the two-stage strategy with bias-corrected and accelerated intervals for interval estimation.