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Reliability forecasting of components/systems in automobile applications by using two-dimensional stress functions
Published in Stein Haugen, Anne Barros, Coen van Gulijk, Trond Kongsvik, Jan Erik Vinnem, Safety and Reliability – Safe Societies in a Changing World, 2018
Abderrahim Krini, Josef Börcsök
The empirical probability of failure is defined as: () F˜(x1,x2)=na(x1,x2)n0
SINGULAR CONDITIONING OF PROCESSES AND THE RANDOM DECREMENT METHOD
Published in W. Q. Zhu, G.Q. Cai, R.C. Zhang, Advances in Stochastic Structural Dynamics, 2003
Now, another approach to the conditional law is also possible, which can be seen as a statistical approach. Observe the value of the derivative A(ifc) at all times t* such that X(tk) = a. Then compute the empirical probability distribution of these observations. This empirical probability distribution is well defined, and one can try to determine its limit as the number of l s go to infinity. If such a limit exists, it can be interpreted as the conditional probability distribution of A( ) when X(t) = a. One more way to define a conditional probability distribution with respect to a nul event.
Introduction to Coefficient of Variation
Published in K. Hima Bindu, M Raghava, Nilanjan Dey, C. Raghavendra Rao, Coefficient of Variation and Machine Learning Applications, 2019
K. Hima Bindu, M Raghava, Nilanjan Dey, C. Raghavendra Rao
Compute empirical probability of the event X≤mean×(1+p*CV/100)
Development and comparison of seismic fragility curves for bridges based on empirical and analytical approaches
Published in Structure and Infrastructure Engineering, 2023
Eduardo Allen, Teodoro Amaya, Alondra Chamorro, Hernán Santa María, Felipe Baratta, Hernán de Solminihac, Tomás Echaveguren
The third step is the calibration process, which starts with the estimation of the empirical probability of exceedance for each damage state and for each intensity measure, i.e. the probability that a bridge exceeds a damage state given that the intensity measure is equal to im. The empirical probability is given by where dsi is the target damage state, im is the seismic intensity measure or an intensity measure range; nim is the total number of bridges exposed to the intensity measure im or its range; is the number of bridges that exceed the analyzed damage state Dsi given the intensity measure im (or a range). Following this calculation, in order to fit a probability density function, the square error minimization method is applied, where the objective is to minimize the sum of the square difference between the empirical value (vemp) and the expected value from a certain distribution (vdist) as Equation (2) indicates. The selected parameters (usually mean and standard deviation) are those that minimize the square error:
Informative index for investment based on Kelly criterion
Published in Enterprise Information Systems, 2021
Mu-En Wu, Jia-Hao Syu, Gautam Srivastava, Jerry Chun-Wei Lin
The Kelly criterion is meant to optimise long term expected log-returns, and is therefore inapplicable only to short-term investments and volatile investment environments. The Kelly criterion is based on the assumption that the empirical probability of the th outcome will approach the theoretical probability () over the long term (). For example, when tossing a coin, the theoretical probability of flipping heads is ; however, the empirical probability of flipping heads on the first flip (short-term) is 0 or 1. Thus, the Kelly criterion is suitable only for games (or investment situations) that involve numerous iterations over extended durations, during which the empirical probability would revert to the mean (theoretical probability).
Modeling the cybersecurity of hospitals in natural and man-made hazards
Published in Sustainable and Resilient Infrastructure, 2019
Xilei Zhao, Ian Miers, Matthew Green, Judith Mitrani-Reiser
In this paper, we apply FTA to model the Medical Records Services in hazards, and combine self-protecting EMR technique with the fault tree to build a more comprehensive model. This approach helps policy-makers, stakeholders, emergency managers, and researchers to identify failure mechanism after hazards and make better decisions and emergency plans. FTA gives us a framework to carry out both qualitative and quantitative assessment of the top event (Vesely, 2002). Although the model and results discussed in this paper are deterministic, it can be extended to a probabilistic FTA. To do so first requires us to identify the probability distributions for all the basic work, as well as the empirical probability distribution of this basic event. After populating the lowest level of the fault tree, we could use Monte Carlo simulations to combine the uncertain basic events in each simulation and ultimately obtain the probability distribution of the top event, namely, the failure probability distribution of Medical Records Services. Furthermore, it is possible to extend this analysis to dynamic FTA, as discussed in Dugan et al. (1992). In addition, the methodology discussed in this paper can also be applied to other departments/services in the hospital to facilitate a more comprehensive emergency planning and decision-making.