Table 2 Mathematical models of faults (Bhatti and Ochieng 2007)
Error type | Failure model | Remarks |
|---|---|---|
Step error/Bias | \(f\left( t \right) = A u\left( {t - t_{0} } \right)\) | Where, \(f\left( t \right)\) is the value of the fault at time \(t\); \(u\left( t \right)\) is the unit step function and \(t_{0}\) is the onset time of the failure; \(A\) is the amplitude of the fault; \(R\) is the slop of the fault; \(G \sim N\left( {\mu ,\sigma^{2} } \right)\) represents Gaussian distribution with mean \(\mu\) and variance \(\sigma^{2}\); \(\theta\) is the phase difference. |
Ramp error | \(f\left( t \right) = R \left( {t - t_{0} } \right) u\left( {t - t_{0} } \right)\) | |
Random noise | \(f\left( t \right) = G u\left( {t - t_{0} } \right)\) | |
Oscillation | \(f\left( t \right) = A \sin \left( {t - \theta } \right) u\left( {t - t_{0} } \right)\) |