Instantaneous failure probability

Figure 2 shows an ECSPN version of the anonymous PN model from Fig. 1, the system RBD model in the upper right comer and the ECSPN component model below. In the upper left comer the declarations of the ECSPN model can be seen. The token within the model contains the pre-age of the component which is considered when calculating the component s stochastic lifetime. This can be seen by the depiction of the arc inscription AgeEn = a. The age of a component is equivalent to its instantaneous failure probability. The... 

Table 5.4 Mechanical properties and instantaneous failure probability for a carbon fiber-reinforced polymer...

The instantaneous failure probabilities at time T = 0, of a fully deteriorated pipe rehabilitated with carbon-FRP (CFRP) and glass-FRP (GFRP) composites versus... 

The behavior of the failure rate as a function of time can be gaged from a hazard plot. If data are plotted on exponential hazard paper, the derivative of the cumulative hazard function at some time is the instantaneous failure rate at that time. Since time to failure is plotted as a function of the cumulative hazard, the instantaneous failure rate is actually the reciprocal of the slope of the plotted data, and the slope of the plotted data corresponds to the instantaneous mean time to failure. For the data that are plotted on one of the other hazard papers and that give a curved plot, one can determine from examining the changing slope of the plot whether the tme failure rate is increasing or decreasing relative to the failure rate of the theoretical distribution for the paper. Such information on the behavior of the failure rate cannot be obtained from probability plots. 

Availability and reliability are different metrics. Reliability is always a function of failure rates and operating time interval. Availability is a function of failure rates and repair rates. While instantaneous availability will vary during the operating time interval, this is due to changes in failure probabilities and repair situations. Availability is often calculated as an average over a long operating time interval. This is referred to as "steady state availability."... 

According to the concept of Transformed Conditional Probabilities (TCP) (Kudzys et al. 2009, 2010, 2013), the instantaneous failure... 

Hazard rate. The probability of failure (usually instantaneous) given survival to date for example, the probability that you will stop reading this book this instant having got so far. This is obviously greater than the unconditional probability of failure that you will stop this instant since you may not have got this far. (However, since you are reading this, it is the hazard rate and not the unconditional failure which is important.) An important concept in survival analysis. Like a probability density (see below), a hazard rate has to be defined with respect to some unit interval (in this case of time). 

Owing to tank failure there is a puff (instantaneous) release of 10,000 kg of CO. A building stands at a distance of 100 m in the direction of the wind. Determine the time-dependent concentrations and probabilities of death. 

Let us define the instantaneous probability of failure of the mechanical products at time t by ... 

Knowing the initial instantaneous probability of failure and the up-crossing rate v(t), it is possible to compute an upper bound of the cumulative probability of failure of mechanical products within the time interval [0, 7 by (Mejri et al. 2010) ... 

Systems definition It is supposed that a redundant system contains n units. The instantaneous availability of which are independent but follow the same exponential distribution A(t) = e where t = the failure rate of each unit. Note that the probability that a unit or system without maintenance is able to perform its mission at time t equals to the probability that it is able to perform its mission for a stated period of time [0, t]—that is the instantaneous availability equals to the reliability). The system is workable when at least k units are in operation without failures. Maintenance interval is constant Tq. And fault detection rate is supposed to be FDR fault isolation rate equals FIR repair rate equals RR. Maintenance time is negligible. 

Willard Libby discussed with the Joint Committee what could happen in the "worst possible case" reactor accident that would totally release its fission products. But he differentiated between maxumun possible damage and the more likely probable damage in the event of a reactor failure. He also testified that estimates of consequences were necessarily theoretical because, fortunately, "practical experience with reactor failure has been minimal." The danger arose from the fission products accumulated during the operating period, and not just from the additional fission products generated instantaneously in a runaway accident. ... 

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