Probability of false alarm

PFA POD PROACT PROTECT probability of false alarms probability of detection Protective and Response Options for Airport Counter-Terrorism Program for Response Options and Technology Enhancements for Chemical/Biological Terrorism... 

The probability of detection (Pd) performance versus SNR, of a nonfluctuating target with a probability of false alarm (Pfa) of 10-6, for a single look or CPI is shown by the red (dashed) curve in figure 16. For an SNR of 12 dB, the single look Pd is 0.7. The cumulative Pd for an M hits of N looks scheme, with M=2 and N=3 and a cumulative Pfa of 10-6, is shown by the blue (solid) curve. This shows that the same 12 dB SNR provides a cumulative Pd of 0.99. The TMT detection processing will likely employ such schemes to improve detection performance. 

Automatic tank gauging equipment may be used if it can detect a leak of two-tenths (0.2) of a gallon per hour or larger with a probability of detection of 95% and probability of false alarm of 5% or less. Monitoring must be carried out once per week or... 

Figures 6.5 and 6.6 are referred to a slow drift of the output of sensor Sj, i.e., a linearly increasing signal, with a 10-3 K s 1 rate of change, is added to the measured variable for t >t = 9000 s. It can be recognized that the fault is detected a few time instants after the occurrence, while it is isolated about 2000 s after tf. This is due to the slow time evolution of the fault it can be argued that, in the first 2000 s after the occurrence of the fault, its effect is quite negligible and/or almost totally compensated by the observers. In order to reduce the isolation time, the normalization factors could be reduced, at the expense of an increased probability of false alarms. Moreover, Fig. 6.5 shows that the voted measure is the mean value of the measured and estimated data until the isolation is performed, and then it switches to the value of the healthy sensor (5), i).

To provide a method for the evaluation, or at least comparison between two analyzers probabilities of false alarms, a model for the prediction of FAR was devised, which is based on relating the total number of the analyzer s orthogonal measurement channels and the analyzer s signal-to-noise ratio (R, ) tio to the probability of analysis errors obtained imder specific test conditions, which also corresponds to errors predicted by ROC curves [8], as illustrated by the example in Fig. 9.3.14. The area above the ROC curve, 1-Az, represents the total instrumental error of the involved analyzer, and may be plotted by simply using the result of tests yielding values of FPF (False Positive Fraction) and FNF [16]. One set of specific test conditions assumed in early model computations consisted of a simple symmetry for FPF and FNF, leading to the symmetrical Decision Matrix and Proportions shown in Fig. 9.3.14. 

Table 2.9 Probabilities of false alarms by tbe TVAREX and ANN models...

In which and are the values of the normalized random variable for the standard normal distribution at the probabilities of a and For example, if the correct prediction probability of slope failure is 99.99%, prediction probability of missing the slope failure is 0.01% (= 100% 99.99%). Similarly, the correct rejection probability is 90%, if the probability of false-alarm prediction is 10% (= 100%-90%). If random variables are assumed to have a normal distribution, for = 2 as mentioned before equation (9), referring to the standard normal distribution table, we have a= 0.0001 = 3.675 and z =o.io = -1.2825. Assuming l M - 0.0001 and fip = 0.001, we can find the value of L that equals 7.67 x lO ". The value is considered as the acceptable probability of slope failure in the paper. 

The performance requirements given by the user are usually in terms of the probability that the sensor will perform a given task (e.g. for probabihty of detection) and the probability that a false action will take place (e.g., Pfa for probability of false alarm on noise). It is not easy to express these parameters Pj and Pfa) in terms of the radar characteristics, and so usually an intermediate calculation is performed. 

Probability of detection Pn measures the HkeHhood of detecting an event or object when the event does occur. Probability of false alarm is a measure of the likelihood of saying something happened when... 

Receiver operating characteristics (ROC) curves Plots of the probability of detection (likelihood of detecting the object when the object is present) vs. the probability of false alarm (likelihood of detecting the object when the object is not present) for a particular processing system. 

For normal distribution, 3false alarm. However, with the control limits showed above using Weibull distribution, the probability of false alarm a = P T UCL = 0.000754573. This false alarm probability is much less than the desired value of 0.0027. Also, the in-control average run length value will be ARLq = j = 1325.25 which is much greater than the normal value of 370. This control chart is, hence, needed to be adjusted. 

With the above control limit, the probability of false alarm is 0.0183, which is still much higher than 0.0027. Hence, the Cornish-Fisher expansion will be considered to help adjust the control limits. 

In this research, control chart for monitoring the time elapsed between two consecutive defectives in high-quality processes, which is assumed to follow exponential distribution, is developed. To deal with skewness of the exponential distribution, two approaches have been considered, the first one uses Weibull transformation, and the second one uses cumulants by employing Comish-Fisher expansion. Correction factors are determined in order to ensure that the revised control charts satisfy the basic requirements, i.e., the probability of false alarm is about 0.0027 and the average mn length is maximized when the process is in control. It is interesting to note that the two revised control charts are equivalent. They have the same detection power, and the main difference is in the value plotted... 

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