A.7.3 Performance Metric Equations
Statistical formulae used to compute performance measures are given below:
Bias (CIS) = Bias in estimate of CDU = E (CIS – CDU)
The estimate CIS of CDU is unbiased when Bias (CIS) = 0
Relative bias (CIS) = Abs (E (CIS – CDU)) / CDU = |E (CIS – CDU)| / CDU
FE in mean estimate = FE (CIS) = Relative Bias (CIS) = |E (CIS – CDU)| / CDU
From the above, it is noted that reduction in FE and its variance are directly related to reduction in the bias in the estimate of DU mean.
MSE and RMSE associated with the ISM mean estimate CIS are given by
MSE(CIS) = E(CIS - CDU)2 = Var(CIS) + (Bias(CIS))2;
S2FE = Var (FE) = MSE / c2DU ; and
Standard Deviation (FE) = Sd (FE) = sqrt (MSE) / CDU
The (1 – α) 100% Chebyshev UCL of the mean based on r ISM replicates is given by
Student’s-t-statistic based (1 – α) 100% UCL of mean is given by