Results for low to high cycle fatigue help to obtain design fatigue probability curves or the necessary number of tests for a given admissible error.
In the case of treated patients, working with a sample of 2606 patients afforded us a maximum admissible error of 1 = ±1.98% for sensitivity (70%) and δ2 = ±3.82% for specificity (70%).
In the case of untreated patients, working with a sample of 1968 patients afforded us a maximum admissible error of δ1 = ±2.28 percentage units for sensitivity (70%) and δ2 = ±4.4 percentage units for specificity (70%).
Assuming that, once the optimal point has been chosen, both scales have an S ≥ 70% and an Sp ≥ 70%, and that there would be no differences between patients on and those not on PPI treatment, then, based on a sample of 5621 patients, the sensitivity and specificity of each test could be estimated with a maximum admissible error of δ1 = ±1.35% and δ2 = ±2.60% respectively.
This means that we can approximate the set { H ~ : J ( H ~, H ) ≤ 1 / γ } of all admissible estimation errors H ~ by a (complex) ellipsoid in the parameter space [15]: D adm = { H ~ : vec H ( H ~ ) γ I adm vec ( H ~ ) ≤ 1 }.
Considering the definition of mean error and standard deviation, the condition (4) corresponds to an admissible relative error on the measured braking distances of about 6 %–6.5 %, which is thus larger than the one adopted for the TTBS01 validation procedure.
Moreover, the approach allows for the inclusion of a user generated error term (E) to account for the amount of error admissible along the true-positives axis (the omission error) [ 43].
The proposed control scheme is the first work on extension to MIMO second-order hyperbolic distributed parameter systems with admissible initial state error.
Observer performance is shown to be high with a mean absolute final carbon content estimation error for admissible heats equal to 0.0012%.
The purpose is to design a mode-dependent linear filtering which ensures that, for all admissible uncertainties, the filtering error system is not only stochastically asymptotically stable in the large, but also satisfies a prescribed H∞-norm level.
