ISO 9276-3:2008

Overview

ISO 9276-3:2008 - Representation of results of particle size analysis - Part 3 - specifies statistically grounded methods for adjusting an experimental particle size distribution curve to a chosen reference model and for evaluating the residual deviations after adjustment. The standard describes both analytical (quasilinear) and numerical (non‑linear) fitting approaches and explains how the fitted model can serve as a target size distribution for product quality control and process optimization.

Key topics

• Reference models covered
  • Normal distribution (Laplace–Gauss) - e.g., precipitation/condensation products
  • Log‑normal distribution (Galton–MacAlister) - e.g., powders from grinding/crushing
  • Gates–Gaudin–Schuhmann (GGS) - for extreme fine fractions (bilogarithmic)
  • Rosin–Rammler (RRSB) - for extreme coarse fractions
  • Any other model or model combinations when using non‑linear regression
• Regression methods
  • Quasilinear regression: transform cumulative sigmoid curves into straight lines with X(x) and Y(Q) transforms and apply linear regression (analytical, no start estimate required)
  • Non‑linear regression: numerical least‑squares optimization in the original scale (requires starting estimates - quasilinear results are recommended as initial values)
  • Weighted quasilinear options and numerical algorithms (e.g., Levenberg–Marquardt) are discussed
• Statistical evaluation
  • Goodness of fit, standard deviation of residuals, and exploratory data analysis procedures
  • Annexes include chi‑square testing for number distributions, influence of model/type of quantity on regression, and worked examples
  • Practical guidance on interpreting residuals (e.g., residual standard deviation thresholds indicating poor model fit)

Applications

• Quality assurance: define and maintain target particle size distributions for products (powders, suspensions, aerosols)
• Process optimization: monitor and adjust milling, classification, precipitation or crushing processes to meet distribution targets
• Data analysis: select suitable distribution models, compare experimental distributions statistically, analyze truncated or multimodal data
• Reporting and control: standardized methods for fitting and reporting particle size distribution results in R&D, production and QC labs

Who should use this standard

• Particle technology engineers, process engineers and QC/analytical scientists working with particle size analysis, sieving, laser diffraction, sedimentation or microscopy sizing methods
• Data analysts implementing distribution fitting, statistical validation and automated process control based on particle size distributions

Related standards

• ISO 9276‑1: graphical representation (context)
• ISO 9276‑2: calculation of average sizes and moments
• ISO 9276‑5: methods for log‑normal probability distribution calculations

Keywords: ISO 9276-3:2008, particle size analysis, particle size distribution, quasilinear regression, non-linear regression, log-normal, Rosin-Rammler, Gates-Gaudin-Schuhmann, quality assurance, process optimization.