a function of the misalignment roll angle, (3. The larger the value of 3, the larger the
difference between the magnitudes of If' and Pr'.
4.3. Propagation of Uncertainty in the Friction Coefficient
The friction coefficient (g) as defined in eqn 4.24 is calculated from the tribometer
read forward (rf') and reverse (tr') values and the misalignment angles (3, 4)). Values for
these parameters have to be determined to report a value for the friction coefficient.
4.3.1. Law of Propagation of Uncertainty
When measuring a quantity it should be recognized that there is no exact
measurement. Therefore, when reporting measurement values both the measured value
and the uncertainty in that value should be stated. A method for the evaluation of the
uncertainty in measurements is outlined in [30,31]. This method defines a systematic
procedure to incorporate uncertainties in all the measured values in a function to find the
overall combined standard uncertainty of that function value. The general expression to
determine the variance (combined standard uncertainty squared) of any function
G(x,y,z) is expressed in eqn 4.32 [30,31].
2 (aGG2 (GY 2
u c(xY= (uz)2 () z ) eqn 4.32
This expression assumes no covariance between the measured values in the
function. To use this method, a value for the uncertainty in the measured value of each
parameter (Ux,y,z) in the function of interest has to be determined. There are two
categories of methods for evaluating the uncertainty in a measured value; a Type A