Statistical Dependence of Input Variables in Doproc Method / Statistická Závislost Vstupních Veličin V Metodě Popv

2012 ◽  
Vol 12 (2) ◽  
pp. 48-58 ◽  
Author(s):  
Petr Janas ◽  
Krejsa Martin
Keyword(s):  
Reliability Assessment ◽  
Random Variables ◽  
Statistical Dependence ◽  
Software System ◽  
Dependent Variables ◽  
Computational Procedures ◽  
Input Variables

Abstract In probabilistic tasks, input random variables are often statistically dependent. This fact should be considered in correct computational procedures. In case of the newly developed Direct Optimized Probabilistic Calculation (DOProC), the statistically dependent variables can be expressed by the socalled multidimensional histograms, which can be used e.g. for probabilistic calculations and reliability assessment in the software system ProbCalc.

scholarly journals Risk Assessment of Large-Scale Infrastructure Projects—Assumptions and Context

2020 ◽  
Vol 11 (1) ◽  
pp. 109
Author(s):  
Jana Korytárová ◽  
Vít Hromádka
Keyword(s):  
Risk Assessment ◽  
Economic Efficiency ◽  
Large Scale ◽  
Cash Flows ◽  
Statistical Characteristics ◽  
Individual Risk ◽  
Dependent Variables ◽  
Research Findings ◽  
Input Variables ◽  
Individual Risk Factors

This article deals with the partial outputs of large-scale infrastructure project risk assessment, specifically in the field of road and motorway construction. The Department of Transport spends a large amount of funds on project preparation and implementation, which however, must be allocated effectively, and with knowledge of the risks that may accompany them. Therefore, documentation for decision-making on project financing also includes their analysis. This article monitors the frequency of occurrence of individual risk factors within the qualitative risk analysis, with the support of the national risk register, and identifies dependent variables that represent part of the economic cash flows for determining project economic efficiency. At the same time, it compares these dependent variables identified by sensitivity analysis with critical variables, followed by testing the interaction of the critical variables’ effect on the project efficiency using the Monte Carlo method. A partial section of the research was focused on the analysis of the probability distribution of input variables, especially “the investment costs” and “time savings of infrastructure users” variables. The research findings conclude that it is necessary to pay attention to the setting of statistical characteristics of variables entering the economic efficiency indicator calculations, as the decision of whether or not to accept projects for funding is based on them.

scholarly journals Dealing with Dependent Uncertainty in Modelling: A Comparative Study Case through the Airy Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
J.-C. Cortés ◽  
J.-V. Romero ◽  
M.-D. Roselló ◽  
R.-J. Villanueva
Keyword(s):  
Differential Equations ◽  
Random Variables ◽  
Monte Carlo Sampling ◽  
Statistical Dependence ◽  
Mathematical Treatment ◽  
Multivariate Gaussian Distribution ◽  
Random Differential Equations ◽  
Highly Oscillatory ◽  
Airy Equation ◽  
Study Case

The consideration of uncertainty in differential equations leads to the emergent area of random differential equations. Under this approach, inputs become random variables and/or stochastic processes. Often one assumes that inputs are independent, a hypothesis that simplifies the mathematical treatment although it could not be met in applications. In this paper, we analyse, through the Airy equation, the influence of statistical dependence of inputs on the output, computing its expectation and standard deviation by Fröbenius and Polynomial Chaos methods. The results are compared with Monte Carlo sampling. The analysis is conducted by the Airy equation since, as in the deterministic scenario its solutions are highly oscillatory, it is expected that differences will be better highlighted. To illustrate our study, and motivated by the ubiquity of Gaussian random variables in numerous practical problems, we assume that inputs follow a multivariate Gaussian distribution throughout the paper. The application of Fröbenius method to solve Airy equation is based on an extension of the method to the case where inputs are dependent. The numerical results show that the existence of statistical dependence among the inputs and its magnitude entails changes on the variability of the output.

scholarly journals Shapley effects for sensitivity analysis with dependent inputs: bootstrap and kriging-based algorithms

2019 ◽  
Vol 65 ◽  
pp. 266-293 ◽  
Author(s):  
Nazih Benoumechiara ◽  
Kevin Elie-Dit-Cosaque
Keyword(s):  
Sensitivity Analysis ◽  
Confidence Intervals ◽  
Global Sensitivity Analysis ◽  
Estimation Error ◽  
Random Variables ◽  
Monte Carlo Sampling ◽  
Estimation Methods ◽  
Statistical Dependence ◽  
Global Sensitivity ◽  
Sensitivity Indices

In global sensitivity analysis, the well-known Sobol’ sensitivity indices aim to quantify how the variance in the output of a mathematical model can be apportioned to the different variances of its input random variables. These indices are based on the functional variance decomposition and their interpretation becomes difficult in the presence of statistical dependence between the inputs. However, as there are dependencies in many application studies, this drawback enhances the development of interpretable sensitivity indices. Recently, the Shapley values that were developed in the field of cooperative games theory have been connected to global sensitivity analysis and present good properties in the presence of dependencies. Nevertheless, the available estimation methods do not always provide confidence intervals and require a large number of model evaluations. In this paper, a bootstrap resampling is implemented in existing algorithms to assess confidence intervals. We also propose to consider a metamodel in substitution of a costly numerical model. The estimation error from the Monte-Carlo sampling is combined with the metamodel error in order to have confidence intervals on the Shapley effects. Furthermore, we compare the Shapley effects with existing extensions of the Sobol’ indices in different examples of dependent random variables.

Reliability Assessment of Software System Using IFS and OWA-Tree Analysis

2020 ◽  
Vol 27 (05) ◽  
pp. 2040013
Author(s):  
Abhishek Tandon ◽  
Neha ◽  
Anu G. Aggarwal ◽  
Ajay Jaiswal
Keyword(s):  
Failure Rate ◽  
Failure Probability ◽  
Intuitionistic Fuzzy Set ◽  
Reliability Assessment ◽  
Weighted Averaging ◽  
Software System ◽  
Tree Analysis ◽  
Software Product ◽  
To Come ◽  
Theory Failure

To address the software design and development, reliability assessment is considered as crucial and most important task. Several studies have been directed towards reliability assessment approaches for obtaining highly reliable software product. In conventional reliability theory, failure probability of any component is assumed as an exact value but in actuality it’s not possible to get failure probability precisely. In this study, we have proposed an approach to assess the reliability of a software system with vague failure rate of the components as the given information might be incomplete or uncertain. It is a bottom–top methodology which includes the combination of intuitionistic fuzzy set (IFS) theory and ordered weighted averaging (OWA) tree analysis. Using IFS, we are able to come over the vagueness in the failure rate data and by using OWA-tree, we incorporate the subjectivity in the opinion of software developers with respect to selection of module. Further, for the illustration of the proposed approach one numerical example has been discussed and software reliability is assessed based upon different orness level.

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