Variance-Importance of System Components

Nakashima, Kyoichi; Yamato, K.

doi:10.1109/tr.1982.5221247

Cited by 26 publications

(7 citation statements)

References 3 publications

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“…Vesely [5] and Fussell [6] put forward the FussellVesely importance based on the fault tree analysis. Nakashima and Yamato [7] raised the uncertainty importance for the component to discriminate the component which affected the system reliability significantly. Hong and Lie [8] proposed the joint importance to evaluate the effect on system reliability which is caused by the interaction of the components.…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

Reliability Optimization and Importance Analysis of Circular‐Consecutive k‐out‐of‐n System

Zhang

Zhao

et al. 2017

Mathematical Problems in Engineering

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The circular-consecutive -out-of-: ( ) system (Cir/Con/ / : ( ) system) usually consists of components arranged in a circle where the system fails (works) if consecutive components fail (work). The optimization of the Cir/Con/ / system is a typical case in the component assignment problem. In this paper, the Birnbaum importance-based genetic algorithm (BIGA), which takes the advantages of genetic algorithm and Birnbaum importance, is introduced to deal with the reliability optimization for Cir/Con/ / system. The detailed process and property of BIGA are put forward at first. Then, some numerical experiments are implemented, whose results are compared with two classic Birnbaum importance-based search algorithms, to evaluate the effectiveness and efficiency of BIGA in Cir/Con/ / system. Finally, three typical cases of Cir/Con/ / systems are introduced to demonstrate the relationships among the component reliability, optimal permutation, and component importance.

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Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

Reliability Optimization and Importance Analysis of Circular‐Consecutive k‐out‐of‐n System

Zhang

Zhao

et al. 2017

Mathematical Problems in Engineering

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“…After the works of Sobol (1993Sobol ( , 2001Sobol ( , 2003, Rabitz and Alis (1999), Alis and Rabitz (2001), Saltelli et al (2000), Saltelli et al (1999), and Saltelli (2002), variance-based techniques have been recognized as the preferred methods for assessing uncertainty importance. Before these works, uncertainty importance measures based on output variance were introduced in the works of Nakashima and Yamato (1982), Bier (1983), Iman (1987), and Iman and Hora (1990).…”

Section: Measuring Uncertainty Importance Using Variancementioning

confidence: 99%

Measuring Uncertainty Importance: Investigation and Comparison of Alternative Approaches

Borgonovo¹

2006

Risk Analysis

223

169

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Uncertainty importance measures are quantitative tools aiming at identifying the contribution of uncertain inputs to output uncertainty. Their application ranges from food safety (Frey & Patil (2002)) to hurricane losses (Iman et al. (2005a, 2005b)). Results and indications an analyst derives depend on the method selected for the study. In this work, we investigate the assumptions at the basis of various indicator families to discuss the information they convey to the analyst/decisionmaker. We start with nonparametric techniques, and then present variance-based methods. By means of an example we show that output variance does not always reflect a decisionmaker state of knowledge of the inputs. We then examine the use of moment-independent approaches to global sensitivity analysis, i.e., techniques that look at the entire output distribution without a specific reference to its moments. Numerical results demonstrate that both moment-independent and variance-based indicators agree in identifying noninfluential parameters. However, differences in the ranking of the most relevant factors show that inputs that influence variance the most are not necessarily the ones that influence the output uncertainty distribution the most.

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“…Since regression provides an estimate of E(log FFj), the variance of E(log FIX,) from Eq. (6) where n is the number of observations, SS, is the residual sum of squares for the model with a total of K terms on the right side, including the intercept, and SS,, is the residual sum of squares for the model havingp terms on the right side.…”

Section: A Regresssion-based Measure Of Uncertainty Importancementioning

confidence: 99%

A Robust Measure of Uncertainty Importance for Use in Fault Tree System Analysis

1990

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The analysis of probabilistic fault trees often involves the investigation of events that contribute both to the frequency of the top event and to the uncertainty in this frequency. This paper provides a discussion of three measures of the contribution of an event to the total uncertainty in the top event. These measures are known as uncertainty importance measures. Two of these measures are new developments. Each of the measures is shown to have unique advantages and disadvantages. The three measures are based on, respectively, the expected reduction in the variance of the topevent frequency should the uncertainty in an event be resolved, the same measure based on the log frequency, and a measure based on shifts in the quantiles of the distribution of top-event frequency.

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Variance-Importance of System Components

Cited by 26 publications

References 3 publications

Reliability Optimization and Importance Analysis of Circular‐Consecutive k‐out‐of‐n System

Reliability Optimization and Importance Analysis of Circular‐Consecutive k‐out‐of‐n System

Measuring Uncertainty Importance: Investigation and Comparison of Alternative Approaches

A Robust Measure of Uncertainty Importance for Use in Fault Tree System Analysis

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