Multiple detection decisions

Currie LA (1997) Detection International update, and some emerging dilemmas involving calibration, the blank, and multiple detection decisions. Chemometrics Intell Lab Syst 37 151... 

Gamma spectrometry multiple detection decisions occasionally... 

Decision levels and detection limits are relatively easy to define and evaluate for simple" (zero dimensional) measurements. The transition to higher dimensions and multiple components introduces a number of complications and added assumptions related to the number and identity of components, shapes and parameters of calibration functions and spectra, and distributional consequences of non-linear estimation. 

In online fault detection, ARR residuals are close to zero for a healthy system. Generally, they are not identical to zero for various reasons such as modelling uncertainties, uncertain parameters, noise, or numerical inaccuracies. For correct online fault detection it is important that true faults are reliably detected and false alarms are avoided. To that end, residuals are fed into a fault decision procedure. The result is a coherence vector. If this vector is a null vector, then the system is healthy, no fault has happened. If some of its entries are non-zero, then the coherence vector is compared with the rows of the structural FSM. Given a single fault hypothesis, the fault is isolated if there is a match with one row of the FSM. If there is more than one match then the detected fault cannot be isolated. Also, if the number of fault candidates exceeds the number of sensors, not all faults can be isolated. Isolation of multiple simultaneous faults by means of parameter estimation is considered in Chap. 6. 

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