ISO 9276-3:2008 PDF

Representation of results of particle size analysis — Part 3: Adjustment of an experimental curve to a reference model

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Title (English):

ISO 9276-3:2008

Representation of results of particle size analysis — Part 3: Adjustment of an experimental curve to a reference model

Document status:: Active
Format:: Electronic (PDF)
Number of pages:: 23
Publication date:: June 24, 2008
Edition:: ISO IS 9276 edition 1 version 1
ICS:: 19.120

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Description (English):

ISO 9276-3:2008 specifies methods for the adjustment of an experimental curve to a reference model with respect to a statistical background. Furthermore, the evaluation of the residual deviations, after the adjustment, is also specified. The reference model can also serve as a target size distribution for maintaining product quality. ISO 9276-3:2008 specifies procedures that are applicable to the following reference models: a) normal distribution (Laplace-Gauss): powders obtained by precipitation, condensation or natural products (pollens); b) log-normal distribution (Galton MacAlister): powders obtained by grinding or crushing; c) Gates-Gaudin-Schuhmann distribution (bilogarithmic): analysis of the extreme values of the fine particle distributions; d) Rosin-Rammler distribution: analysis of the extreme values of the coarse particle distributions; e) any other model or combination of models, if a non-linear fit method is used. ISO 9276-3:2008 can substantially support product quality assurance or process optimization related to particle size distribution analysis.

Technical details

Technical committee: ISO/TC 24/SC 4 - Particle characterization
SKU: ISO 9276-3:2008

Abstract

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.

Related standards

Standards mentioned in the description

Abstract

Overview

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

ISO 9276-3:2008 PDF

Technical details

Abstract

Overview

Key topics

Applications

Who should use this standard

Related standards

Related standards

Abstract

Overview

Key topics

Applications

Who should use this standard

Related standards

Related standards

Representation of results of particle size analysis - Graphical representation

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