False alarms defined

Sensitivity tells how accurately the device sounds true alarms, while specificity defines how accurately the device avoids false alarms. The concept may appear vague, but it vividly describes real situations. A sensitivity of 80% means that there are two undetected hypoglycemia events every eight times the alarm sounds. A specificity of 80% indicates that in every 10 alarms there are 2 false alarms. 

In a manufacturing setting, it is rate that the false alarm and miss errors will have equal weights. Thus, in inspection of fuel flow valves for a space shuttle, the consequences of a miss are potentially catastrophic, whereas a false alarm leads only to the delay of component replacement. The weighting of these consequences is an essential component of TSD and represents a form of knowledge-based behavior when consciously applied. An inspector can define an optimum strategy as one that maximizes the expected value of outcomes rather than maximizing the fraction of correct decisions. Expected value depends upon ... 

In order to avoid that false alarms are reported to a supervisor system or that true faults are not detected, ARR residuals should be significantly sensitive to tme faults but little sensitive to parameter variations given uncertain system parameter values. Parameter sensitivities of ARR residuals can be singled out by defining appropriate thresholds. As the dynamic behaviour of a real system described by a hybrid model can be quite different in different system modes, thresholds should be adapted to system modes. 

Similarly, for Type II, we define that is the probability of the false-alarming events, when the probability of failure is less than the threshold value L, that is ... 

The most important parameter to monitor here is the exhaust temperature spread, which is defined as the maximum thermocouple reading minus the minimum. Traditional monitoring systems compare this value (at steady state conditions) to a constant threshold and monitor it over time. However, this approach has proven fiiiitless, as it is prone to false alarms or alarms that appear too late. The main reason for this is that for hybrid premixed combustors, such as GE DLN (dry low NOx) combustors, the spread depends on the combustion mode and load and is not a constant value. Hence, a more robust approach is to monitor the combustion mode and the main thermodynamic parameters of the unit, and then set the threshold accordingly. Figure 7 shows how this spread changes with combustion mode and load for a multi-can DLN machine. 

Minimum detectable concentration clmin, is defined by previously determining the acceptable "p" percent false alarm rate. (Which we set to 5 corresponding to 2a variation for Gaussian variables). 

An important parameter for evaluating quality control cards and out-of-control situations is the average run length (ARL) which is defined as the average number of registrations in a quality control card for a single out-of-control situation [41]. A high ARL is required should the analytical process run under control. The probability of a false alarm is then very low. On the other hand, a true out-of-control situation should be indicated as quickly as possible, that is, the ARL has to be relatively small. 

Figure 21.9 provides a general comparison of univariate and multivariate SPC techniques (Alt et al., 1998). When two variables, xi and X2, are monitored individually, the two sets of control limits define a rectangular region, as shown in Fig. 21.9. In analogy with Example 21.5, the multivariate control limits define the dark, ellipsoidal region that represents in-control behavior. Figure 21.9 demonstrates that the application of univariate SPC techniques to correlated multivariate data can result in two types of misclassification false alarms and out-of-control conditions that are not detected. The latter type of misclassification occurred at sample 8 for the two Shewhart charts in Fig. 21.8.

Once the backscattering in the (s, v) plane has been estimated, scatterers are selected by looking for strong peaks in y. In this context, a tool for the effective selection of reliable scatterers is required since in real data the useful information is cormpted by noise, a detection stage is required to control the false alarm rate, defined as the probability to declare the presence of a scatterer, whereas the scatterer is not really present on the ground. With reference to the case of a single... 

If the alternate hypothesis is accepted at the detection phase, estimation of change by PCD method is initiated by reducing the forgetting factor to a small value at the detection instant. This will cause the filter to converge quickly to the new values of model parameters. Shewhart charts for each model parameter are used for observing the new identified values of the model parameters. At this point the out-of-control decision made at the detection phase can be reassessed. If the identified values of the parameters are inside the range defined by the null hypothesis, then the detection decision can be reversed and the alarm is declared false. 

---