Emanuele Borgonovo

A new uncertainty importance measure

Abstract Uncertainty in parameters is present in many risk assessment problems and leads to uncertainty in model predictions. In this work, we introduce a global sensitivity indicator which looks at the influence of input uncertainty on the entire output distribution without reference to a specific moment of the output (moment independence) and which can be defined also in the presence of correlations among the parameters. We discuss its mathematical properties and highlight the differences between the present indicator, variance-based uncertainty importance measures and a moment independent sensitivity indicator previously introduced in the literature. Numerical results are discussed with application to the probabilistic risk assessment model on which Iman [A matrix-based approach to uncertainty and sensitivity analysis for fault trees. Risk Anal 1987;7(1):22–33] first introduced uncertainty importance measures.

A new importance measure for risk-informed decision making

Abstract In this paper, we introduce a new importance measure, the differential importance measure (DIM), for probabilistic safety assessment (PSA). DIM responds to the need of the analyst/decision maker to get information about the importance of proposed changes that affect component properties and multiple basic events. DIM is directly applicable to both the basic events and the parameters of the PSA model. Unlike the Fussell–Vesely (FV), risk achievement worth (RAW), Birnbaum, and criticality importance measures, DIM is additive, i.e. the DIM of groups of basic events or parameters is the sum of the individual DIMs. We discuss the difference between DIM and other local sensitivity measures that are based on normalized partial derivatives. An example is used to demonstrate the evaluation of DIM at both the basic event and the parameter level. To compare the results obtained with DIM at the parameter level, an extension of the definitions of FV and RAW is necessary. We discuss possible extensions and compare the results of the three measures for a more realistic example.

Sensitivity analysis: A review of recent advances

The solution of several operations research problems requires the creation of a quantitative model. Sensitivity analysis is a crucial step in the model building and result communication process. Through sensitivity analysis we gain essential insights on model behavior, on its structure and on its response to changes in the model inputs. Several interrogations are possible and several sensitivity analysis methods have been developed, giving rise to a vast and growing literature. We present an overview of available methods, structuring them into local and global methods. For local methods, we discuss Tornado diagrams, one way sensitivity functions, differentiation-based methods and scenario decomposition through finite change sensitivity indices, providing a unified view of the associated sensitivity measures. We then analyze global sensitivity methods, first discussing screening methods such as sequential bifurcation and the Morris method. We then address variance-based, moment-independent and value of information-based sensitivity methods. We discuss their formalization in a common rationale and present recent results that permit the estimation of global sensitivity measures by post-processing the sample generated by a traditional Monte Carlo simulation. We then investigate in detail the methodological issues concerning the crucial step of correctly interpreting the results of a sensitivity analysis. A classical example is worked out to illustrate some of the approaches.

Global Sensitivity Measures from Given Data

Simulation models support managers in the solution of complex problems. International agencies recommend uncertainty and global sensitivity methods as best practice in the audit, validation and application of scientific codes. However, numerical complexity, especially in the presence of a high number of factors, induces analysts to employ less informative but numerically cheaper methods. This work introduces a design for estimating global sensitivity indices from given data (including simulation input–output data), at the minimum computational cost. We address the problem starting with a statistic based on the L1-norm. A formal definition of the estimators is provided and corresponding consistency theorems are proved. The determination of confidence intervals through a bias-reducing bootstrap estimator is investigated. The strategy is applied in the identification of the key drivers of uncertainty for the complex computer code developed at the National Aeronautics and Space Administration (NASA) assessing the risk of lunar space missions. We also introduce a symmetry result that enables the estimation of global sensitivity measures to datasets produced outside a conventional input–output functional framework.

A Monte Carlo methodological approach to plant availability modeling with maintenance, aging and obsolescence

Abstract In this paper we present a Monte Carlo approach for the evaluation of plant maintenance strategies and operating procedures under economic constraints. The proposed Monte Carlo simulation model provides a flexible tool which enables one to describe many of the relevant aspects for plant management and operation such as aging, repair, obsolescence, renovation, which are not easily captured by analytical models. The maintenance periods are varied with the age of the components. Aging is described by means of a modified Brown–Proschan model of imperfect (deteriorating) repair which accounts for the increased proneness to failure of a component after it has been repaired. A model of obsolescence is introduced to evaluate the convenience of substituting a failed component with a new, improved one. The economic constraint is formalized in terms of an energy, or cost, function; optimization studies are then performed using the maintenance period as the control parameter.

Moment Independent Importance Measures: New Results and Analytical Test Cases

Moment independent methods for the sensitivity analysis of model output are attracting growing attention among both academics and practitioners. However, the lack of benchmarks against which to compare numerical strategies forces one to rely on ad hoc experiments in estimating the sensitivity measures. This article introduces a methodology that allows one to obtain moment independent sensitivity measures analytically. We illustrate the procedure by implementing four test cases with different model structures and model input distributions. Numerical experiments are performed at increasing sample size to check convergence of the sensitivity estimates to the analytical values.

Comparison of global sensitivity analysis techniques and importance measures in PSA

This paper discusses application and results of global sensitivity analysis techniques to probabilistic safety assessment (PSA) models, and their comparison to importance measures. This comparison allows one to understand whether PSA elements that are important to the risk, as revealed by importance measures, are also important contributors to the model uncertainty, as revealed by global sensitivity analysis. We show that, due to epistemic dependence, uncertainty and global sensitivity analysis of PSA models must be performed at the parameter level. A difficulty arises, since standard codes produce the calculations at the basic event level. We discuss both the indirect comparison through importance measures computed for basic events, and the direct comparison performed using the differential importance measure and the Fussell ‐ Vesely importance at the parameter level. Results are discussed for the large LLOCA sequence of the advanced test reactor PSA. q 2002 Elsevier Science Ltd. All rights reserved.

Sensitivity analysis in investment project evaluation

Abstract This paper discusses the sensitivity analysis of valuation equations used in investment decisions. Since financial decision are commonly supported via a point value of some criterion of economic relevance (net present value, economic value added, internal rate of return, etc.), we focus on local sensitivity analysis. In particular, we present the differential importance measure (DIM) and discuss its relation to elasticity and other local sensitivity analysis techniques in the context of discounted cash flow valuation models. We present general results of the net present value and internal rate of return sensitivity on changes in the cash flows. Specific results are obtained for a valuation model of projects under severe survival risk used in the industry sector of power generation.

The reliability importance of components and prime implicants in coherent and non-coherent systems including total-order interactions

In the management of complex systems, knowledge of how components contribute to system performance is essential to the correct allocation of resources. Recent works have renewed interest in the properties of the joint (J) and differential (D) reliability importance measures. However, a common background for these importance measures has not been developed yet. In this work, we build a unified framework for the utilization of J and D in both coherent and non-coherent systems. We show that the reliability function of any system is multilinear and its Taylor expansion is exact at an order T. We then introduce a total order importance measure (DT) that coincides with the exact portion of the change in system reliability associated with any (finite or infinitesimal) change in component reliabilities. We show that DT synthesizes the Birnbaum, joint and differential importance of all orders in one unique indicator. We propose an algorithm that enables the numerical estimation of DT by varying one probability at a time, making it suitable in the analysis of complex systems. Findings demonstrate that the simultaneous utilization of DT and J provides reliability analysts with a complete dissection of system performance.

Differential, criticality and Birnbaum importance measures: An application to basic event, groups and SSCs in event trees and binary decision diagrams

Recent works [Epstein S, Rauzy A. Can we trust PRA? Reliab Eng Syst Safety 2005; 88:195–205] have questioned the validity of traditional fault tree/event tree (FTET) representation of probabilistic risk assessment problems. In spite of whether the risk model is solved through FTET or binary decision diagrams (BDDs), importance measures need to be calculated to provide risk managers with information on the risk/safety significance of system structures and components (SSCs). In this work, we discuss the computation of the Fussel–Vesely (FV), criticality, Birnbaum, risk achievement worth (RAW) and differential importance measure (DIM) for individual basic events, basic event groups and components. For individual basic events, we show that these importance measures are linked by simple relations and that this enables to compute basic event DIMs both for FTET and BDD codes without additional model runs. We then investigate whether/how importance measures can be extended to basic event groups and components. Findings show that the estimation of a group Birnbaum or criticality importance is not possible. On the other hand, we show that the DIM of a group or of a component is exactly equal to the sum of the DIMs of the corresponding basic events and can therefore be found with no additional model runs. The above findings hold for both the FTET and the BDD methods.