Probability of detection

Depending on the requirements and costs, one method may be chosen over another provided it registers sufficient reliability. For example, whereas visual inspection is unreliable for small defects compared to an instrument inspection, in some aerospace in-service applications, it can be more cost-effective or practical to use visual inspection on a frequent basis than to conduct a more sensitive and costly instrument inspection less frequently to achieve the same service reliability of a component. It is common to specify that inspections require a signal-to-noise ratio (SNR) of 2.5 for the system sensitivity to the detection criteria of designated features in a calibration standard. Under a normal curve distribution, this would provide better than 98.7% detectability. 

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It can be concluded, that indications with lengths of more than about 1.5 mm can be detected with high probability (100%). This confirms with the recommended smallest acceptance level (optimum conditions) of 1.5 mm (registration level) in various product standards (e g. as [10]). It is self evident that smaller indications (1 = 0.6 mm) will be detected too, but the correlations explained above, clearely indicates a decreasing probability of detection with decreasing length of indications. 

Naturally, such a high probability of detection of theoretically 100% never can be realized in practice. The inspector will not recognize all good visible indications at any time because he cannot always be fiilly concentrated on his task, which is called "human factor". This human factor appears in any visual inspection and may be reduced only by a second redundant inspection or extreme signals as a light flash or an acustic signal. 

Suppose that P[/(se)] is the probability of detecting the object when it is in fact at x. 

At PicArsn (Ref 19), the fast neutron activation approach for detection of expls in suitcases was extended to the activation of both nitrogen and oxygen using two 7-ray detector stations in sequence. After 14 MeV neutron irradiation, the baggage is first monitored for 6.1 MeV 7-rays from the l60(n,p),6N reaction (7.5 sec half-life), followed by measurement of the 10 min 13N. Because expls are also rich in oxygen and have characteristic ratios of N/O, it was felt that this approach would increase the probability of detection with a corresponding decrease in the false alarm rate... 

I will present here the properties of various sources when the random variable considered is the field intensity. In this case, one has access to the mean and variance via a simple photodetector. The autocorrelation function can be interpreted as the probability of detecting one photon at time t + t when one photon has been detected at time t. The measurement is done using a pair of photodetectors in a start stop arrangement (Kimble et al., 1977). The system is usually considered stationary so that the autocorrelation function, which is denoted depends only on r and is defined by ... 

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... 

All detection systems feature a trade-off between the probability of detection (POD) of the target substance and the probability of false (positive) alarms (PFA). POD refers to the probability that the instrument will detect a threat material that is present PFA refers to the probability that the instrument will alarm when a threat material is not present at a given threshold level. The overall concentration of the target substance affects this trade-off higher concentrations are easier to detect, resulting in performance closer to the optimum operating point (perfect detection with zero false alarms). In addition, where data are accumulated over time, one can increase POD and decrease PFA by increasing the accumulation time. 

The problem with defining criteria for such a test is that it depends on the j8 probability, which is difficult to determine (although we could arbitrarily specify a value, such as 95%). It also depends on the smallest difference you need to detect, the number of samples, the variability of the data (which at least can be determined from the data, the same way it is done for determining a), and the probability of detecting the given difference at a specified alpha- significance level. 

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. 

Too few Prior to approval, most drugs are administered to 2,000 to 3,000 patients. (To obtain an 80% probability of detecting an adverse drug event that occurs in one out of every 10,000 recipients, 16,000 patients must receive the drug). 

Prequency and size of broth fills must be clearly defined. The size of fill is usually based upon the statistical probability of detecting an acceptably low incidence of microbial contamination. Tables have been published to this effect [4], but the BPS operator has to decide both size and frequency of broth fills based upon their speeifie facility, routine product batch sizes, and operation. Por high speed BPS maehines used for filling routine produet batehes in excess of 100,000 units, broth fill batehes larger than traditional aseptic filling lines are both feasible and appropriate. 

Use of Composited Samples To Increase the Precision and Probability of Detection of Toxic Chemicals... 

Table V. Probability of Detecting a Difference Between a Single Mean and a Standard Level, Given Sample Size J...

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... 

Level 1 sampling provides a single set of samples acquired to represent the average composition of each stream. This sample set is separated, either in the field or in the laboratory, into solid, liquid, and gas-phase components. Each fraction is evaluated with survey techniques which define its basic physical, chemical, and biological characteristics. The survey methods selected are compatible with a very broad spectrum of materials and have sufficient sensitivity to ensure a high probability of detecting environmental problems. Analytical techniques and instrumentation have been kept as simple as possible in order to provide an effective level of information at minimum cost. Each individual piece of data developed adds a relevant point to the overall evaluation. Conversely, since the information from a given analysis is limited, all the tests must be performed to provide a valid assessment of the sample. 

The power or desired probability of detecting the treatment difference with a defined significance level - for most controlled trials, a power of 80% or 90% (0.8-0.9) is frequently chosen as adequate, although higher power is chosen for some studies. 

The aim of any clinical trial is to have low risk of Type I and II errors and sufficient power to detect a difference between treatments, if it exists. Of the three factors in determining sample size, the power (probability of detecting a true difference) is arbitrarily chosen. The magnitude of the drug s effect can be estimated with more or less accuracy from previous experience with drugs of the same or similar action, and the variability of the measurements is often known from published experiments on the primary endpoint, with or without the drug. These data will, however, not be available for novel substances in a new class and frequently the sample size in the early phase of development has to be chosen on an arbitrary basis. 

We see that in contrast to the type-1 error, the type-11 error is defined as occurring when accepting the null hypothesis if it is false. The power of a test is defined to be the probability of detecting a true difference and is equal to 1 — probability (type-11 error). The type-11 error and power depend upon the type-1 error, the sample size, the clinically relevant difference (CRD) that we are interested in detecting and the expected variability. Where do these values come from ... 

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