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Component Reliability Analysis
Published in Mohammad Modarres, Mark P. Kaminskiy, Vasiliy Krivtsov, Reliability Engineering and Risk Analysis, 2016
Mohammad Modarres, Mark P. Kaminskiy, Vasiliy Krivtsov
3.7 For the following Rayleigh distribution, f(t)=tα2exp(−t22α2),t≥0,α>0.Find the hazard rate h (t) corresponding to this distribution.Find the reliability function R (t).Find the MTTF. Note that ∫0∞e−ax2=12πa.For which part of the bathtub curve is this distribution adequate?
Properties of Random Variables
Published in Shaila Dinkar Apte, Random Signal Processing, 2017
For a Rayleigh distribution, skew is positive as expected from the graph of the Rayleigh distribution pdf. Now, let us find the skew and kurtosis for a segment of the speech signal. A MATLAB program for this is given as follows.
Random Vibrations
Published in William T. Thomson, Theory of Vibration with Applications, 2018
The mean and mean square values for the Rayleigh distribution can be found from the first and second moments to be () A¯=∫0∞Ap(A)dA=∫0∞A2σ2e−A2/2σ2dA=π2σA¯2=∫0∞A2p(A)dA=∫0∞A3σ2e−A2/2σ2dA=2σ2The variance associated with the Rayleigh distribution is () σA2=A2¯−(A¯)2=(4−π2)σ2∴σA≅23σ
ℋ2 state-feedback control for continuous semi-Markov jump linear systems with rational transition rates
Published in International Journal of Control, 2023
M. de Almeida, M. Souza, A. R. Fioravanti, O. L. V. Costa
The Rayleigh Distribution normally appears in two-dimensional (or complex) problems, whenever we are interested in the magnitude (or the absolute value) when each component is uncorrelated, normally distributed with equal variance, and zero mean. It presents one scale parameter , and probability density function and the cumulative distribution function which implies that, for this case, transition rates (21) are of the form . Thus, the transition rate, from mode i to mode j, for a Rayleigh distributed sojourn time is not timer-independent, but linearly increasing with slope .