Probability of loss of assured safety in systems with weak and strong links subject to dependent failures and random shocks

2021 ◽  
Vol 209 ◽  
pp. 107483
Author(s):  
Shiqiang Pi ◽  
Ying Liu ◽  
Haiyan Chen ◽  
Yan Deng ◽  
Longyuan Xiao
1994 ◽  
Vol 33 (4II) ◽  
pp. 1417-1429 ◽  
Author(s):  
Nasir M. Khiui

Recently there has been an increased interest in the theory of chaos by macroeconomists and fmancial economists. Originating in the natural sciences, applications of the theory have spread through various fields including brain research, optics, metereology, and economics. The attractiveness of chaotic dynamics is its ability to generate large movements which appear to be random, with greater frequency than linear models. Two of the most striking features of any macro-economic data are its random-like appearance and its seemingly cyclical character. Cycles in economic data have often been noticed, from short-run business cycles, to 50 years Kodratiev waves. There have been many attempts to explain them, e.g. Lucas (1975), who argues that random shocks combined with various lags can give rise to phenomena which have the appearance of cycles, and Samuelson (1939) who uses the familiar multiplier accelerator model. The advantage of using non-linear difference (or differential) equation models to explain the business cycle is that it does not have to rely on ad hoc unexplained exogenous random shocks.


2021 ◽  
Author(s):  
Jialin Ma ◽  
Guo Xie ◽  
Lingxia Mu ◽  
Jing Xin ◽  
Wenbin Chen ◽  
...  

2018 ◽  
Vol 33 (4) ◽  
pp. 592-602
Author(s):  
Amanda Mattsson ◽  
Tetsu Uesaka

Abstract In end-use, containerboard is subjected to a variety of loading histories, such as seconds of loading/unloading, hours of vibration, days of creep load. The fundamental question is whether the commonly measured static strength represents “strength” under these conditions. Another question is, since those time-dependent failures are notoriously variable, how to describe the probabilistic aspect. This study concerns the characterisation of these different facets of “strength”. In our earlier work, we have investigated the theoretical framework for time-dependent, probabilistic failures, and identified three material parameters: (1) characteristic strength, {S_{c}}, representing short-term strength, (2) brittleness/durability parameter, ρ, and (3) reliability parameter, β. We have also developed a new method that allows us to determine all these parameters much faster than typical creep tests. Using the new method, we have started investigating effects of basic papermaking variables on the new material parameters. Among the samples tested, the parameter ρ varied from 20 to 50, and β from 0.5 to 1.0. This suggests that, even within the current papermaking practice, there is a wide operating window to tune these new material parameters. The future work is, therefore, to find specific manufacturing variables that can systematically change these new material parameters.


1991 ◽  
Vol 34 (3) ◽  
pp. 417-427 ◽  
Author(s):  
P. Humphreys ◽  
A.M. Jenkins
Keyword(s):  

1993 ◽  
Vol 30 (4) ◽  
pp. 979-984 ◽  
Author(s):  
Eui Yong Lee ◽  
Jiyeon Lee

A Markovian stochastic model for a system subject to random shocks is introduced. It is assumed that the shock arriving according to a Poisson process decreases the state of the system by a random amount. It is further assumed that the system is repaired by a repairman arriving according to another Poisson process if the state when he arrives is below a threshold α. Explicit expressions are deduced for the characteristic function of the distribution function of X(t), the state of the system at time t, and for the distribution function of X(t), if . The stationary case is also discussed.


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