In large-scale systems, the components are interconnected and so the variables are correlated, which constitutes information on system topology with causality. After a fault occurs, it not only shows up as local phenomenon but also propagates to some other components or variables. Hence we should consider the sensor location problem to find the root cause of the fault origin and type from the viewpoint of the whole system.In order to measure the fault detection quality related to sensor location, some criteria are defined in Kawabata et al.’s paper . Firstly, all the faults should be detected when they occur. Secondly, different faults should be identified from each other so that one can differentiate them based on the sensor readings.
The criteria of detectability and identifiability are basic requirements for fault detection .
In this reference all the sensors are assumed to be effective, that is, they show exactly whether the process variables are normal or abnormal.In engineering practice, sensors may often be faulty, meaning that they may fail to give adequate readings. For example, the reading may remain unchanged when the true value should be a deviation, which is called a missed alarm; or the sensor may give an alarm for a normal operation state, known as a false alarm. We should therefore allow for some redundancy in sensors in case of failures. More commonly, the measurements may show Drug_discovery these two kinds of sensor faults because of the choice of the threshold.
Often due to noise there are no real Entinostat sensor faults but deviations due to measurement noise, which is inevitable.
If the threshold setting is strict in order to suppress the missed alarm probability, the reading will be sensitive to random noise and temporary deviations, resulting in a high probability of false alarm. If we relax the threshold and accept larger region to be considered as normal, then the number of false alarms will decrease with more missed alarms. Therefore, missed alarms and false alarms are two aspects of reliability and we have to make a trade-off between them. This can be clearly illustrated via a receiver operating characteristics (ROC) curve [3,4].
Sensors in this present paper also include soft sensors that measure some specific variables by soft sensing techniques .With increasing complexity in process industrial systems, traditional mathematical models are difficult to obtain. Hence, graph-based models are proposed in the modeling analysis. Based on the signed directed graph (SDG) model, Raghuraj, et al.  have discussed the problems of detectability and identifiability in sensor location and presented the corresponding algorithm for locating each sensor.