Probability Distributions in Complex Systems

2009 ◽  
pp. 7009-7024 ◽  
Author(s):  
Didier Sornette
Keyword(s):  
Complex Systems ◽  
Probability Distributions

Star-shaped order for distributions characterized by several parameters and some applications

2021 ◽  
pp. 1-11
Author(s):  
Idir Arab ◽  
Milto Hadjikyriakou ◽  
Paulo Eduardo Oliveira ◽  
Beatriz Santos
Keyword(s):  
Complex Systems ◽  
Probability Distributions ◽  
Real Parameter ◽  
Applied Probability ◽  
Aging Properties ◽  
Multidimensional Parameter ◽  
Complex Models

Abstract The star-shaped ordering between probability distributions is a common way to express aging properties. A well-known criterion was proposed by Saunders and Moran [(1978). On the quantiles of the gamma and F distributions. Journal of Applied Probability 15(2): 426–432], to order families of distributions depending on one real parameter. However, the lifetime of complex systems usually depends on several parameters, especially when considering heterogeneous components. We extend the Saunders and Moran criterion characterizing the star-shaped order when the multidimensional parameter moves along a given direction. A few applications to the lifetime of complex models, namely parallel and series models assuming different individual components behavior, are discussed.

Reliability analysis for complex systems subject to competing failure processes in an uncertain environment

2020 ◽  
Vol 39 (3) ◽  
pp. 4331-4339
Author(s):  
Baoliang Liu ◽  
Zhiqiang Zhang ◽  
Yanqing Wen ◽  
Shugui Kang ◽  
Yanxin Guo ◽  
...  
Keyword(s):  
Complex Systems ◽  
Reliability Analysis ◽  
Uncertainty Theory ◽  
Probability Distributions ◽  
External Shocks ◽  
Process Reliability ◽  
Degradation Models ◽  
Renewal Reward Process ◽  
Internal Degradation

Reliability analysis of complex systems subject to competing failure processes based on probability theory has received increasing attention. However, in many situations, the observed data is too limited to estimate the parameters and probability distributions of the system by statistic methods. To address this problem, an uncertain degradation models is proposed in this paper under the framework of uncertainty theory. Based on this model, a complex system which is subject to both continuous internal degradation and external shocks is introduced. The continuous internal degradation of the system is controlled by some uncertain factors, and the external shocks are deemed to an uncertain renewal reward process. Reliability for the complex systems is obtained by employing the uncertainty theory. Finally, a case study is presented to demonstrate the effectiveness of the results obtained in the paper.

Asteroid and Comet Impact Speeds upon Mars: Significance for Panspermia and the Supply of Organics

1997 ◽  
Vol 161 ◽  
pp. 197-201 ◽  
Author(s):  
Duncan Steel
Keyword(s):  
Probability Distributions ◽  
Regions Of Interest ◽  
Significant Fraction ◽  
Organic Chemicals ◽  
Impact Speed ◽  
The Mean ◽  
The Impact

AbstractWhilst lithopanspermia depends upon massive impacts occurring at a speed above some limit, the intact delivery of organic chemicals or other volatiles to a planet requires the impact speed to be below some other limit such that a significant fraction of that material escapes destruction. Thus the two opposite ends of the impact speed distributions are the regions of interest in the bioastronomical context, whereas much modelling work on impacts delivers, or makes use of, only the mean speed. Here the probability distributions of impact speeds upon Mars are calculated for (i) the orbital distribution of known asteroids; and (ii) the expected distribution of near-parabolic cometary orbits. It is found that cometary impacts are far more likely to eject rocks from Mars (over 99 percent of the cometary impacts are at speeds above 20 km/sec, but at most 5 percent of the asteroidal impacts); paradoxically, the objects impacting at speeds low enough to make organic/volatile survival possible (the asteroids) are those which are depleted in such species.

HUMAN FACTORS IN COMPLEX SYSTEMS.

1967 ◽  
Author(s):  
FRANCIS H. THOMAS
Keyword(s):  
Complex Systems ◽  
Human Factors
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