Repeatability and Reproducibility Studies for the HORIBA LA-950 Laser Diffraction Analyzer

Repeatability, reproducibility, and instrument to instrument agreement are important performance characteristics of any analytical instrument. This technical note presents multiple data sets that prove the excellent performance analysts should expect from the HORIBA LA-950 laser diffraction analyzer.

Introduction

Two studies are presented in this technical note; one performed at multiple HORIBA Application Labs using polydisperse standards, and one performed by a customer analyzing their own sample. Both studies tested the repeatability, reproducibility and/or instrument to instrument variation of the LA-950.

Definitions

The word precision is often used as a catch-all to describe the results from any kind of repeated test. Understanding the different types of precision is important because some tests are more diffi cult (and meaningful) than others.

  • Repeatability - Measurement variation with a single operator and single instrument on the same sample, over a short amount of time with all other variables held constant (i.e. location). Think of this as taking a sampling, loading it into the LA-950, and taking three consecutive measurements without draining.
  • Reproducibility - Measurement variation with either multiple operators on multiple instruments with the same sample (but possibly multiple lots) in multiple locations. Not all of these conditions must be satisfied. This is a much more taxing test than repeatability and is the test performed for this study. When a manufacturer makes a claim about precision, make sure to know which type.
  • Intermediate Precision - Measurement variation with multiple operators on either single or multiple instruments, in the same location across multiple days.

The table on the next page summarizes how these three tests differ. This information appears courtesy of ASTM and can be found in ASTM E177, Practice for Use of the Terms Precision and Bias in ASTM Test Methods (1), and E456, Terminology Relating to Quality and Statistics (2).

Repeatability Condition Intermediate Precision Condition Reproducibility Condition
Laboratory Same Same Different
Operator Same Different Different
Apparatus Same Same* Different
Time between Tests Short** Multiple Days Not Specified

* This situation can be different instruments meeting the same design requirement.
** Standard test method dependent, typically does not exceed one day.

HORIBA Study

A reproducibility study was performed on 40 unique, randomly selected LA-950 systems; 20 for wet measurements, 20 for dry measurements. Two NIST traceable polydisperse (range of sizes) glass bead reference samples were used in this study. The challenge samples were PS-202 (3-30 µm) and PS-215 (10-100 µm) from Whitehouse Scientific. The PS-202 sample was measured as an aqueous wet dispersion according to the method outlined in Analytical Test Method 102 (3). The PS-215 sample was measured as a dry powder using the PowderJet accessory according to the method outlined in Analytical test method 103 (4). The instrument settings used are shown below.

PS-202:

Circulation: 3;
Agitation: 2;
Liquid level: LOW;
Refractive index: STD-GLASS BEADS (1.51-0.00i);
Distribution base: VOLUME;
Form of distribution: Manual (15 iterations);
Data acquisition time LD=5000, LED=5000

PS-215:

Refractive index STD-GLASSBEADS (1.51-0.0i);
Distribution Base VOLUME;
Form of distribution Manual (15 iterations);
Data sampling times: LD=50000;
T% for Sampling ; Max T%:= 99%, Min T%= 95%;
Air pressure; 0.3 MPa (3 bar)

Figures 1 and 2 and Tables 1 and 2 show the results for the PS-202 wet measurements and PS-215 dry measurements.

Overlay of 20 wet results from 20 systems.

Figure 1. Overlay of 20 wet results from 20 systems.

Overlay of 20 dry results from 20 systems.

Figure 2. Overlay of 20 dry results from 20 systems.

Table 1. Results from 20 wet analyses on 20 systems.

PS-202 (µm)
D10 D50 D90
PS202 (5JW).NGB 9.291 14.066 20.312
PS202 (A6K).NGB 9.484 14.42 21.052
PS202 (D00).NGB 8.992 14.202 20.467
PS202 (E1W).NGB 9.712 14.61 20.925
PS202 (F00).NGB 9.327 14.373 21.348
PS202 (XD1).NGB 9.403 14.125 19.957
PS202 (H00).NGB 9.236 14.226 20.363
PS202 (HVY).NGB 9.417 14.271 20.429
PS202 (J31).NGB 9.199 13.976 20.164
PS202 (PWW).NGB 9.333 13.916 19.462
PS202 (R8X).NGB 9.366 14.241 20.712
PS202 (RP2).NGB 9.24 14.253 20.917
PS202 (S1N).NGB 9.426 14.36 20.431
PS202 (SBJ).NGB 9.717 14.545 20.704
PS202 (U12).NGB 9.086 13.875 20.164
PS202 (UB6).NGB 9.207 13.824 19.612
PS202 (USL).NGB 9.356 14.189 20.133
PS202 (VB1).NGB 9.103 13.844 19.768
PS202 (WFU).NGB 8.971 13.318 18.634
PS202 (WTF).NGB 9.58 14.382 20.541
Average 9.322 14.151 20.305
Std. Dev 0.21 0.3 0.62
CV (%) 2.21 2.11 3.05

Table 2. Results from 20 dry analyses on 20 systems.

PS-215 (µm)
D10 D50 D90
PS215 (2PN).NGB 27.002 38.445 60.784
PS215 (5JW).NGB 26.863 39.97 62.391
PS215 (5TT).NGB 26.986 38.913 59.778
PS215 (7P0).NGB 28.293 41.117 64.453
PS215 (A6D).NGB 27.912 39.891 60.961
PS215 (CX6).NGB 27.415 38.752 58.1
PS215 (E2W).NGB 25.324 38.49 58.739
PS215 (GB5).NGB 28.12 40.758 63.033
PS215 (M0F).NGB 27.337 40.909 64.624
PS215 (P7B).NGB 27.493 40.165 62.889
PS215 (P9G).NGB 27.326 39.725 61.375
PS215 (R8X).NGB 28.653 41.501 64.832
PS215 (RDC).NGB 28.474 41.411 64.42
PS215 (RP2).NGB 25.324 38.49 58.739
PS215 (SX6).NGB 27.147 38.466 57.976
PS215 (WFU).NGB 27.058 39.48 61.334
PS215 (WHK).NGB 26.967 39.014 60.804
PS215 (XHM).NGB 27.087 40.974 66.039
PS215 (EGX).NGB 27.898 41.059 63.956
PS215 (G00).NGB 28.434 41.771 65.232
Average 27.356 39.983 62,023
Std. Dev 0.9 1.14 2.53
CV (%) 3.28 2.84 4.08

Additional statistical information including graphs showing the 1 standard deviation errors bar are shown in Figures 3 and 4 and Tables 3 and 4.

Statistical analysis of 20 wet results on 20 systems.

Figure 3. Statistical analysis of 20 wet results on 20 systems.

Statistical analysis of 20 dry results on 20 systems

Figure 4. Statistical analysis of 20 dry results on 20 systems

Table 3. Statistical analysis of 20 wet results on 20 systems.

Particle Size Percentile [D10] Percentile [D50] Percentile [D90]
Mean 9.322 14.151 20.305
Std. Dev 0.206 0.296 0.62
COV 2.21% 2.11% 3.05%
Lower 95% 9.226 14.011 20.014
Upper 95% 9.419 14.291 20.595
Minimum 8.971 13.318 18.634
Maximum 9.717 14.61 21.348

Table 4. Statistical analysis of 20 dry results on 20 systems

Particle Size Percentile [D10] Percentile [D50] Percentile [D90]
Mean 27.328 39.915 61.843
Std. Dev 0.917 1.246 2.743
COV 3.36% 3.12% 4.44%
Lower 95% 26.898 39.332 60.56
Upper 95% 27.757 40.498 63.127
Minimum 25.324 38.445 57.194
Maximum 28.653 41.771 66.039

ISO 13320:2009 (5) section 6.4 states that the coefficient of variation (CV %) should be less than 3% at the D50 and less than 5% at the D10 and D90 when testing reproducibility. In the context of the ISO document this pass/fail criteria refers to testing a single instrument. This study was performed across 20 different instruments and still exceeded the ISO guidelines.

Customer Case Study

An existing LA-910 user studied LA-950 performance when considering upgrading to the newer model. To begin the user used two LA-950 systems and one sample (Formulation 1) to test repeatability. The results for these studies are shown in Tables 5 and 6 with size expressed in nm. The CV% values are extremely low, partly due to the nature of the sample which was small, narrow, and easily dispersed, but also because of the high performance level shown by the LA-950 systems.

Table 5. Repeatability of sample Formulation 1 on LA-950 Unit 1

Formulation 1 Dmean D5 D10 D50 D90 D95
1 156 113 120 154 195 209
2 155 112 119 153 194 208
3 155 112 119 153 194 208
4 156 113 119 154 195 209
5 154 111 119 152 193 207
6 155 112 119 152 194 208
Average 155 112 119 153 194 208
Std. Dev. 0.8 0.8 0.5 1 0.8 0.7
CV% 0.5 0.7 0.4 0.6 0.4 0.4

Table 6. Repeatability of sample Formulation 1 on LA-950 Unit 2

Formulation 1 Dmean D5 D10 D50 D90 D95
1 154 112 119 152 192 208
2 154 112 119 152 192 208
3 155 113 119 152 192 208
4 155 115 119 152 193 208
5 154 112 119 152 193 107
6 155 112 119 153 193 208
Average 155 112 119 152 192 208
Std. Dev. 0.5 0.5 0 0.6 0.3 0.5
CV% 0.3 0.5 0 0.4 0.1 0.3

Impressed with this performance, the user purchased four LA-950 systems and investigated the instrument to instrument variation using two samples, Formulation 1 and Formulation 2. The results from these studies are shown in Tables 7 and 8. The user was satisfied with these results.

Table 7. Instrument to instrument variation across four LA-950 systems for Formulation 1.

Formulation 1 Dmean D5 D10 D50 D90 D95
Average (nm) 155 112 119 152 193 208
Std. Dev. (nm) 0.8 0.8 0.7 1 1.1 0.7
CV (%) 0.5 0.7 0.6 0.6 0.6 0.3

Table 8. Instrument to instrument variation across four LA-950 systems for Formulation 2.

Formulation 1 Dmean D5 D10 D50 D90 D95
Average (nm) 193 136 147 187 247 264
Std. Dev (nm) 1.5 0.5 0.4 0.6 0.4 1.1
CV (%) 0.8 0.4 0.3 0.3 0.2 0.4

Conclusions

These studies mimic real-world conditions for many users who must reconcile results from multiple operators, units, and locations. This is particularly important for users with units across the world where the challenge of supporting across multiple time zones and languages grows quickly.

In this context the LA-950 Particle Size Analyzer data proves an excellent solution with superb data correlation for realistic (polydisperse) samples. In the HORIBA study this was proven across:

  • 40 randomly selected units
  • 2 locations
  • 6 operators
  • and acquired over 6 years (i.e. no drift)

This is accomplished without any unit-matching technique and at normal performance (i.e. no low sensitivity data processing). Such performance is unmatched on the market today.

In the customer study instrument to instrument agreement was proven across four systems measuring their own real world samples.

References

1. ASTM E177-10, Standard Practice for Use of the Terms Precision and Bias in ASTM Test Methods, available at www.astm.org.

2. ASTM E456-12, Standard Terminology Relating to Quality and Statistics, available at www.astm.org.

3. Analytical Test Method 102, Test Method for PS-202 Polydisperse Glass Bead Standards on Partica LA-950 available in the Download center at http://www.horiba.com/scientific/products/particle-characterization/.

4. Analytical Test Method 103, Setup of Automatic Dry Measurement Partica LA- 950 with PowderJet available in the Download center at http://www.horiba.com/scientific/products/particle-characterization/.

5. ISO13320 Particle size analysis – Laser diffraction methods, available at www.iso.org

This information has been sourced, reviewed and adapted from materials provided by HORIBA Scientific.

For more information on this source, please visit HORIBA Scientific.

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