The plot in Figure 1 shows replicate values from each participant for the first cement. The true values are indicated by the arrows and the SRM uncertainty intervals are indicated by the line segments at each arrow's base. It should be noted that this example is only one of four materials in the study so conclusions from any single case may not be reasonable. Precision calculations are pooled for each phase across the four cements and bias estimates, when completed, will be done similarly. For the silicates and calcium sulfates, most participants' data fell within the 2σ ranges for the SRMs and the true values for calcium sulfates, suggestive of no significant bias among test results for these constituents. The plot in Figure 1 appears to indicate participants with relatively low alite estimates have correspondingly high belite estimates. This apparent correlation is not clearly evident in examining a correlation matrix on testing in our laboratory. Another possible bias may be seen in the under-estimation of ferrite and over-estimation of periclase, and may be attributable to microabsorption. Additional work is necessary to assess these errors and develop a consistent correction scheme for the test method.
Figure 1. Replicate data from eleven participants for Cement #1. Arrows denote true values and the tail segment denotes the uncertainty of that phase in the SRM used in Cement #1.
Based upon these data and calculations, a provisional precision statement may be developed using the pooled values in Table 1. Precision levels are all expressed as percentage points by mass relative to the total cement. Comparison with results from earlier round robins [4, 5] shows an improvement in both within- and between-laboratory repeatability and reproducibility (Fig. 2). This improvement most likely stems from the whole-pattern approach, from being both a consistent means of measurement and providing better counting statistics over single peak area measurement.
| Table 1. Repeatability (provisional values) expressed as within-laboratory standard deviation (sr) and repeatability limit for two tests of the same cement by the same lab (r, and reproducibility expressed as the multi-laboratory standard deviation (sR), and reproducibility limit for two tests on the same cement by two different laboratories (R). | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Alite | Belite | Aluminate | Ferrite | Periclase | Gypsum | Bassanite | Anhydrite | Calcite | |
| sr | 0.7 | 0.6 | 0.5 | 0.5 | 0.2 | 0.2 | 0.4 | 0.3 | 1.0 |
| r | 2.0 | 1.8 | 2.3 | 1.4 | 0.6 | 0.6 | 1.1 | 0.7 | 2.7 |
| sR | 1.9 | 0.9 | 0.8 | 0.7 | 0.3 | 0.6 | 0.7 | 0.7 | 0.5 |
| R | 5.2 | 2.5 | 2.2 | 1.9 | 0.9 | 1.5 | 2.0 | 2.0 | 1.5 |
Figure 2. Multi-laboratory standard deviations (sR ) for alite, belite, aluminate, and ferrite from the 2003 round robin [6], from Moore [4], and from Aldridge [5] shows improvement with the application of Rietveld pattern fitting approach used in the two ASTM round robins.