Reliability assessment of stochastic networks with ER connectivity and ER dependency

2021 ◽  
pp. 1748006X2110019
Author(s):  
Heping Jia ◽  
Rui Peng ◽  
Dunnan Liu ◽  
Yanbin Li ◽  
Yi Ding
Keyword(s):  
Monte Carlo Simulation ◽  
Probability Distributions ◽  
Reliability Assessment ◽  
Reliability Evaluation ◽  
Stochastic Networks ◽  
Evaluation Framework ◽  
Stochastic Network ◽  
Time To Failure ◽  
Numerical Examples ◽  
Mdd Method

In stochastic networks, nodes usually function dependently and interact with other nodes through connectivity links or dependency links. In this paper, the model for stochastic networks considering sub-networks with connectivity and dependency links of Erdös-Rényi (ER) topology is proposed, which is defined as networks with arbitrary pair of nodes randomly connected/depended by a constant probability. The reliability evaluation framework for the proposed networks is developed, where both of the extended multi-valued decision diagram (MDD) method and Monte Carlo simulation (MCS) are involved. The MDD method is proposed to assess the reliability of deterministic stochastic networks with ER connectivity and dependency, where arbitrary time to failure distributions of nodes are allowed. Based on the reliability evaluation for a stochastic network with a deterministic structure, the MCS is employed to achieve the reliability analysis of corresponding stochastic networks. Numerical examples are presented to demonstrate the proposed stochastic network model and reliability evaluation framework, where the probability distributions for the reliability of stochastic networks are provided.

scholarly journals A New Approach to Determine the Critical Path in Stochastic Activity Network

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Weng-Ming Chu ◽  
Koan-Yuh Chang ◽  
Chien-Yu Lu ◽  
Chang-Hung Hsu ◽  
Chien-Hung Liu ◽  
...  
Keyword(s):  
Monte Carlo Simulation ◽  
Path Dependence ◽  
Critical Path ◽  
Stochastic Networks ◽  
Stochastic Network ◽  
New Approach ◽  
Path Index ◽  
Tracing Algorithm ◽  
Selection Of

The determination of the critical path (CP) in stochastic networks is difficult. It is partly due to the randomness of path durations and partly due to the probability issue of the selection of the critical path in the network. What we are confronted with is not only the complexity among random variables but also the problem of path dependence of the network. Besides, we found that CP is not necessarily the longest (or shortest) path in the network, which was a conventional assumption in use. The Program Evaluation and Review Technique (PERT) and Critical Path Index (CPI) approaches are not able to deal with this problem efficiently. In this study, we give a new definition on the CP in stochastic network and propose a modified label-correcting tracing algorithm (M-LCTA) to solve it. Based on the numerical results, compared with Monte Carlo simulation (MCS), the proposed approach can accurately determine the CP in stochastic networks.

Approximating the Stochastic Network by its M Shortest Paths

1989 ◽  
Vol 3 (3) ◽  
pp. 435-451
Author(s):  
Bajis Dodin
Keyword(s):  
Monte Carlo ◽  
Shortest Path ◽  
Probability Distributions ◽  
Shortest Paths ◽  
Monte Carlo Sampling ◽  
Stochastic Networks ◽  
Mean Value ◽  
Stochastic Network ◽  
Distributional Properties ◽  
Deterministic Methods

Given a stochastic activity network in which the length of some or all of the arcs are random variables with known probability distributions. This paper concentrates on identifying the shortest path and the M shortest paths in the network and on using the M paths to identify surrogate stochastic networks which are amenable for deriving analytical solutions. First, it identifies the M shortest paths using a certain form of stochastic dominance. Second, it identifies the M shortest paths by applying the deterministic methods to the network resulting from replacing the random length of every arc by its mean value. The two sets of the M paths are compared with those obtained by Monte Carlo sampling. Finally, the paper investigates how the distributional properties of the shortest path in the surrogate network compare with those of the shortest path in the original stochastic network.

Adaptive Reliable Shortest Path in Discrete Stochastic Networks

2014 ◽  
Vol 587-589 ◽  
pp. 1854-1857
Author(s):  
Yi Yong Pan
Keyword(s):  
Shortest Path ◽  
Stochastic Networks ◽  
Shortest Path Problem ◽  
Successive Approximations ◽  
Stochastic Network ◽  
Route Guidance ◽  
Travel Times ◽  
Routing Policy ◽  
The Face ◽  
Stochastic Travel Times

This paper addresses adaptive reliable shortest path problem which aims to find adaptive en-route guidance to maximize the reliability of arriving on time in stochastic networks. Such routing policy helps travelers better plan their trips to prepare for the risk of running late in the face of stochastic travel times. In order to reflect the stochastic characteristic of travel times, a traffic network is modeled as a discrete stochastic network. Adaptive reliable shortest path problem is uniformly defined in a stochastic network. Bellman’s Principle that is the core of dynamic programming is showed to be valid if the adaptive reliable shortest path is defined by optimal-reliable routing policy. A successive approximations algorithm is developed to solve adaptive reliable shortest path problem. Numerical results show that the proposed algorithm is valid using typical transportation networks.

scholarly journals The Sum and Difference of Two Lognormal Random Variables

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
C. F. Lo
Keyword(s):  
Stochastic Process ◽  
Probability Distributions ◽  
Operator Splitting ◽  
Splitting Method ◽  
Unified Approach ◽  
New Approach ◽  
Numerical Examples ◽  
Operator Splitting Method ◽  
Approximate Probability ◽  
Analytical Series

We have presented a new unified approach to model the dynamics of both the sum and difference of two correlated lognormal stochastic variables. By the Lie-Trotter operator splitting method, both the sum and difference are shown to follow a shifted lognormal stochastic process, and approximate probability distributions are determined in closed form. Illustrative numerical examples are presented to demonstrate the validity and accuracy of these approximate distributions. In terms of the approximate probability distributions, we have also obtained an analytical series expansion of the exact solutions, which can allow us to improve the approximation in a systematic manner. Moreover, we believe that this new approach can be extended to study both (1) the algebraic sum ofNlognormals, and (2) the sum and difference of other correlated stochastic processes, for example, two correlated CEV processes, two correlated CIR processes, and two correlated lognormal processes with mean-reversion.

scholarly journals Technical-Economic Analysis of Grapple Saw

2020 ◽  
Vol 41 (2) ◽  
pp. 219-229 ◽  
Author(s):  
Ricardo Hideaki Miyajima ◽  
Paulo Torres Fenner ◽  
Gislaine Cristina Batistela ◽  
Danilo Simões
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Probability Distributions ◽  
Simulation Method ◽  
Forest Harvesting ◽  
Production Costs ◽  
Wood Harvesting ◽  
Food And Agriculture ◽  
The Monte Carlo Method

The processing of Eucalyptus logs is a stage that follows the full tree system in mechanized forest harvesting, commonly performed by grapple saw. Therefore, this activity presents some associated uncertainties, especially regarding technical and silvicultural factors that can affect productivity and production costs. To get around this problem, Monte Carlo simulation can be applied, or rather a technique that allows to measure the probabilities of values from factors that are under conditions of uncertainties, to which probability distributions are attributed. The objective of this study was to apply the Monte Carlo method for determining the probabilistic technical-economical coefficients of log processing using two different grapple saw models. Field data were obtained from an area of forest planted with Eucalyptus, located in the State of São Paulo, Brazil. For the technical analysis, the time study protocol was applied by the method of continuous reading of the operational cycle elements, which resulted in production. As for the estimated cost of programmed hour, the applied methods were recommended by the Food and Agriculture Organization of the United Nations. The incorporation of the uncertainties was carried out by applying the Monte Carlo simulation method, by which 100,000 random values were generated. The results showed that the crane empty movement is the operational element that most impacts the total time for processing the logs; the variables that most influence the productivity are specific to each grapple saw model; the difference of USD 0.04 m3 in production costs was observed between processors with gripping area of 0.58 m2 and 0.85 m2. The Monte Carlo method proved to be an applicable tool for mechanized wood harvesting for presenting a range of probability of occurrences for the operational elements and for the production cost.

scholarly journals PROBABILISTIC DURABILITY PREDICTION OF EXISTING BUILDING ELEMENTS

2004 ◽  
Vol 10 (2) ◽  
pp. 107-112 ◽  
Author(s):  
Romualdas Kliukas ◽  
Antanas Kudzys
Keyword(s):  
Reliability Index ◽  
Probability Distributions ◽  
Reliability Assessment ◽  
Reliability Prediction ◽  
Existing Building ◽  
Reliability Indices ◽  
Latent Defects ◽  
Durability Prediction ◽  
Building Elements

An effect of service and proof actions on probabilistic reliability (serviceability, safety and durability) of building elements (components and members) of existing enclosure and bearing structures is under consideration. Time‐dependent models for reliability assessment of elements under sustained variable and multicycle actions are presented. Revised reliability indices of existing elements exposed to service permanent and variable actions are discussed. It is recommended to assess the long‐term reliability index of elements taking into account the effect of latent defects. Truncated probability distributions of physical‐mechanical resistances of elements and an effect of their latent defects on reliability index assessment are taken into account. Methodological peculiarities of durability prediction of elements and avoiding unfounded premature repairs or replacements are analysed. The applied illustration of the presented method on the probabilistic reliability prediction of deteriorating concrete covers is demonstrated.

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