Yang and Xiao [6] introduced the propagation time in SDGs, based on which the problem has been defined protein inhibitor and solved, and some applicable Inhibitors,Modulators,Libraries rules have been presented to obtain a reasonable sensor location. Bhushan and Rengaswamy [7] studied the reliability problem of fault detection and proposed some algorithms to choose sensor location to improve reliability. Bhushan et al. [8] also studied the robustness of the network to uncertainties/errors in the underlying model and probability data. However, only missed alarm probability has been considered in their work. On the other hand, the false alarm probability should also have been taken into account because adding sensors increases the number of false alarms that is undesirable.

The reliability optimization problem of false alarms is discussed in this paper as a complementary criterion to the optimization problem of undetectability.This paper is structured as follows: The criteria of fault detection, especially Inhibitors,Modulators,Libraries the reliability criterion regarding false and missed alarms in sensor readings, are presented in Section 2. Section 3 explains how to use graph theory to obtain the reachability measure between faults and process variables measured by sensors, which is needed in the optimization criteria. In Section 4, the optimization algorithm for the sensor location is proposed to improve the reliability of fault detection, followed by a case study to illustrate the application in Section 5. Finally some concluding remarks are given in the last section.2.

?Sensor Location Criteria for Fault DetectionThere are basic criteria that should be met under all fault detection issues, and also optimization criteria in consideration of faulty sensors or unreliability of sensor Inhibitors,Modulators,Libraries measurements.2.1. Detectability and IdentifiabilityThe nodes in the SDG are classified into two types�Cvariables and fault origin actors, which Inhibitors,Modulators,Libraries are denoted as ni’s and fj’s respectively. When a fault occurs, it is propagated along consistent paths as designed in the SDG convention.Definition 1Starting from the fault node f, the set of nodes affected by f is R(f) = m : l (f m) where l(f m) means a path from fault f to node m. If n R(f), then we say that node n is reachable from fault f.Regarding detectability, each fault should be detected by at least one sensor.

The definition of detectability appears below:Definition 2If there exists at least one sensor placed in the nodes Brefeldin_A of R(f) (measuring the corresponding variables), then we say that fault f is detectable.Because the propagation time selleck chemicals is ignored here, only leaf nodes are needed to consider whether or not to place sensors [2]. Then we have the following theorem from Yang and Xiao [6].Theorem 1Based on the SDG, disregarding the cases that some variables cannot be measured, sensors need to be placed only on the leaf nodes.ProofAccording to the weak connection condition (i.e.