Testing of industrial products - Aggregates for construction

Formulae

Cochran's test, and standardised ranges (k-statistics), for ranges of two test results, or ranges of two determinations.

Cochran's test statistic = W2 / Sum W2

k - statistic = W/Wpooled

where

W = the range for a laboratory

Sum W2 = the sum of squared ranges for a level

Wpooled = the pooled range for a level

Cochran's test for standard deviations of three determinations
and standardised standard deviations of three determinations.

Cochran's test statistic = S2 ÷ (Sum S2)

Standardised standard deviation = S ÷ { Sum S2/(2N) }½

where

2N = the number of standard deviations

S = the standard deviation of three determinations

Sum S2 = the sum of squared standard deviations for the level

Grubbs' test, and standardised laboratory biasses (h-statistics).

Grubbs' test statistic = h-statistic = (X - Xave) / Xsd

where

X = a laboratory average

Xave,Xsd = the average and standard deviation

Grubbs' test for a pair of outliers both exceeding the average:

test statistic = (Sp-1,p)2 / (S0)2

where

(Sp-1,p)2 = the corrected sum of squares of the p-2 values that do not include the two suspect values;

(S0)2 = the corrected sum of squares of all p values.

Note: The use of Cochran's and Grubbs' tests for outliers is described in the standard on precision (ISO 5725, 1994).

Repeatability and reproducibility standard deviations.

These are calculated using formulae for a uniform-level precision experiment with an unequal number of replicates per cell, given in the standard on precision (ISO 5725, 1994).

Repeatability and reproducibility limits.

R1 = 2.8 SR1

r1 = 2.8 Sr1

When two determinations are made on a test portion:

Wc = 2.8 Sspec

When three determinations are made on a test portion:

Wc = 3.3 Sspec

where Sspec is the between-specimen standard deviation

Functional relationships.

These are calculated using formulae for weighted regression analysis given in the standard on precision (ISO 5725, 1994).

Coefficients of variation.

Cr1 = 100 Sr1 / Xave

CR1 = 100 SR1 / Xave

Coefficients of variation for the Sand Equivalent test, Percentage of Crushed Particles, Percentage of Totally Crushed Particles.

Cr1 = 100 Sr1 / (100 - Xave)

CR1 = 100 SR1 / (100 - Xave)

Sensitivity ratios.

The sensitivity ratio for "Level 2 - Level 1" and repeatability is calculated as:

Sensitivity ratio = (Xave,1 - Xave,2) / sqrt{ (Sr1,1)2 + (Sr1,2)2 }

where

Xave,1 and Xave,2 are the averages for Levels 1 and 2

Sr1,1 and Sr1,2 are the repeatability standard deviations for Levels 1 and 2

The other sensitivity ratios are calculated similarly.