# EMANUELE BORGONOVO

## Publications

Author of more than 100 works. See the full list in the "Full publication list" folder.

W. Castaings, E. Borgonovo, M.D. Morris, S. Tarantola

Environmental Modelling&Software

Decision and policy-makers benefit from the utilization of computer codes in an increasing number of areas and applications. Several authorities and agencies recommend the utilization of proper sensitivity analysis methods in order to confidently entrust model results. In this respect, density-based techniques have recently attracted interest among academicians and practitioners, for their property to characterize uncertainty in terms of the entire distribution of an output variable. However, their estimation is a challenging task and, without a proper methodical approach, errors in the estimates can lead to misleading conclusions. In this work, we propose sampling plans for reducing the computational burden of sensitivity estimates while improving and controlling the accuracy in the estimation. We compare designs based on column substitutions and designs based on permutations. We investigate their behaviour in terms of type I and type II errors. We apply the methods to the Level E model, a computational tool developed by the Nuclear Energy Agency of the OECD for the assessment of nuclear waste disposal sites. Results show that application of the proposed sampling plans allows one to obtain confidence in the sensitivity estimates at a number of model runs several orders of magnitude lower than a brute-force approach. This assessment, based upon the entire distribution of the model output, provides us with ways to effectively reduce uncertainty in the model output, either by prioritizing the model factors that need to be better known or by prioritizing the areas where additional modelling efforts are needed.

- pdf (610 Kb)

Composite Multilinearity, Epistemic Uncertainty and Risk Achievement Worth (03/05/2012)

Borgonovo E. and Smith C.L.

European Journal of Operational Research, forthcoming.

- Pdf (448 Kb)

A Study of Interactions in the Risk Assessment of Complex Engineering Systems: An Application to Space PSA (10/12/2011)

E. Borgonovo and C.L. Smith

Operations Research

- A Study of Interactions_Full_Text (366 Kb)

Emulators in Moment Independent Sensitivity Analysis: An Application to Environmental Modelling (01/03/2012)

E. Borgonovo, W. Castaings and S. Tarantola

Environmental Modelling and Software

Sensitivity Analysis with Finite Changes: an Application to Modified EOQ Models (01/06/2010)

E. Borgonovo

European Journal of Operational Research

*European Journal of Operational Research*, 200, pp. 127–138.

- FiniteChanges_pdf (236 Kb)

Function decomposition, monotonicity and ultramodularity: applications to multi-attribute utility theory (01/09/2011)

Beccacece F. and Borgonovo E.

European Journal of Operational Research

*European Journal of Operational Research*, 210, 326-335.

- FunctionalANOVAMultiattribute_pdf (218 Kb)

The Reliability Importance of Components and Prime Implicants in Coherent and Non-Coherent Systems Including Total-Order Interactions (01/09/2010)

E. Borgonovo

European Journal of Operational Research

*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 ($D^{T}$) 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 $D^{T}$ synthesizes the Birnbaum, joint and differential importance of all orders in one unique indicator. We propose an algorithm that enables the numerical estimation of $D^{T}$ by varying one probability at a time, making it suitable in the analysis of complex systems. Findings demonstrate that the simultaneous utilization of $D^{T}$ and $J$ provides reliability analysts with a complete dissection of system performance.*

*European Journal of Operational Research*, 204, pp. 485–495.

- TotalOrder_pdf (233 Kb)

Finite Change Comparative Statics for Risk Coherent Inventories (01/01/2011)

Borgonovo E. and Peccati L., 2011

International Journal of Production Economics, 2011, 131(1), 52-62

This work introduces a comprehensive approach to the sensitivity analysis (SA) of risk-coherent inventory models. We address the issues posed by i) the piecewise-defined nature of risk-coherent objective functions and ii) by the need of multiple model evaluations. The solutions of these issues is found by introducing the extended finite change sensitivity indices (FCSI's). We obtain properties and invariance conditions for the sensitivity

of risk-coherent optimization problems. An inventory management case study involving risk-neutral and conditional value-at-risk (CVaR) objective function illustrates our methodology. Three SA settings are formulated to obtain managerial insights. Numerical findings show that risk-neutral decision-makers are more exposed to variations in exogenous variables than CVaR decision-makers.

- Pdf (294 Kb)

Moment Independent Importance Measures: New Results and Analytical Test Cases (05/06/2010)

Borgonovo E., Castaings W. and Tarantola S.

Risk Analysis

*Risk Analysis*, 2010, 31 (3), pp. 404-428.

- MomentIndependentAnalytical_pdf (497 Kb)

A Methodology for Determining Interactions in PSA models by Varying One Parameter At-a-Time (01/06/2010)

E. Borgonovo

Risk Analysis

knowledge, analysts and decision-maker are able to understand whether risk is apportioned by individual factor contributions or by their joint action. However, models are oftentimes large, requiring a high number of input

parameters, and complex, with individual model runs being time consuming. Computational complexity leads analysts to utilize one-parameter-at-a-time sensitivity methods, which prevent one from assessing interactions. In this work, we illustrate a methodology to quantify interactions in probabilistic safety assessment (PSA) models by varying one-parameter-at-a-time. The method is based on a property of the functional ANOVA decomposition of a finite change that allows to exactly determine the relevance of factors when considered individually or together with their interactions with all other factors. A set of test cases illustrates the technique. We apply the

methodology to the analysis of the Core Damage Frequency of the Large Loss of Coolant Accident of a nuclear reactor. Numerical results reveal the non-additive model structure, allow to quantify the relevance of interactions and to identify the direction of change (increase or decrease in risk) implied by individual factor variations and by their cooperation.

*Risk Analysis*, 2010, 30 (3), pp. 385

- MethodologyInteractionsPSA_pdf (295 Kb)

What Drives Value Creation? An Application of Sensitivity Analysis to Project Finance Transactions (05/05/2010)

E. Borgonovo, S. Gatti and L. Peccati

European Journal of Operational Research

suboptimal exploitation of the modelling efforts. We propose a methodology based on the so-called "differential importance measure ($D$)" to enhance the managerial insights obtained from financial models. We illustrate our

methodology by applying it to a project finance case study. We show that the additivity property of $D$ grants analysts and managers full flexibility in combining parameters into any group and at the desired aggregation level. We analyze investment criteria related to both the investors's and lenders' perspectives. Results indicate that exogenous factors affect investors (sponsors and lenders) in different ways, whether exogenous variables are considered individually or by groups.

*European Journal of Operational Research*, 205 (1), pp. 227-236

- Sensitivity_Project_Finance_pdf (218 Kb)

Moment Calculations for Piecewise-Defined Functions: An Application to Stochastic Optimization with Coherent Risk Measures (05/08/2010)

Borgonovo E. and Peccati L.

Annals of Operations Research

- PiecewiseRiskCoherent_pdf (256 Kb)

Managerial Insights from Service Industry Models: a new scenario decomposition method (03/06/2011)

Borgonovo E. and Peccati L.

Annals of Operations Research

analysts to quantify the effects of factors, their synergies and to identify the key drivers of scenario results. The method is applied to the scenario analysis of the workforce allocation model by Corominas et al 2004.

Annals of Operations Research, 2011, 185(1), pp. 161-179.

- ServiceIndustry_pdf (215 Kb)

Cancer cell reprogramming: stem cell differentiation stage factors and an agent based model to optimize cancer treatment (01/01/2011)

Biava P.M., Basevi M., Biggiero L., Borgonovo A., Borgonovo E. and Burigana F.

Current Pharmaceutical Biotechnology, 2011, 12(2), pp. 231-242

- Pdf (300 Kb)

Sensitivity Analysis of Model Output with Input Constraints: A Generalized Rationale for Local Methods (01/06/2008)

Borgonovo E., 2008: , .

Risk Analysis, 28 (3) (June 2008), pp. 667-680

effects is found by proposing a result that leads to a natural extension of the local sensitivity analysis rationale introduced in Helton (1993). We then extend the definitions of the Birnbaum, Criticality and the Differential importance measures to the constrained case. In addition, it is introduced a procedure that allows to obtain constrained sensitivity results at the same cost as in the absence of constraints. The application to a non-binary event tree concludes the paper providing a numerical illustration of the above findings.

- Pdf (217 Kb)

A note on the sensitivity analysis of the internal rate of return (forthcoming)

M. Percoco and E. Borgonovo

International Journal of Production Economics, forthcoming

Epistemic Uncertainty in the Ranking and Categorization of Probabilistic Safety Assessment Model Elements: Issues and Findings (06/06/2008)

Borgonovo E.

Risk Analysis, 2008, 28 (4), pp. 983 - 1001.

- Pdf (268 Kb)

Financial Management in Inventory Problems: Risk Averse vs Risk Neutral Policies (01/01/2009)

Borgonovo E. and L. Peccati

International Journal of Production Economics, 2009, 118 (1), pp. 233-242.

- Pdf (258 Kb)

Differential Importance and Comparative Statics: An Application to Inventory Management (01/01/2008)

Borgonovo E.

International Journal of Production Economics, 111 (1) (January 2008), pp. 170-179

In this work the framework for establishing which of the input parameters influences an inventory management policy the most is developed. To do so, a new sensitivity measure ($Gamma $) is introduced by relating the

differential importance ($D$) and comparative statics (CS) techniques. We discuss the properties of the new indicator, and show that it shares the additivity property. We provide the expression of $Gamma $ for inventory

management models both in the form of unconstrained and constrained optimization. Numerical results are offered for the sensitivity analysis of the Luciano and Peccati (1999) inventory management model.

- Pdf (179 Kb)

Decision Making During Nuclear Power Plant Incidents gco A New Approach to the Evaluation of Precursor Events (01/01/2007)

C. Smith and Borgonovo E.

Risk Analysis, 2007, 27 (4), pp.1027-1042.

- Pdf (241 Kb)

A New Uncertainty Importance Measure (06/06/2007)

Borgonovo E., 2007

Reliability Engineering and System Saftey, 2007, 92, pp. 771-784

- Pdf (283 Kb)

Measuring Uncertainty Importance: Investigation and Comparison of Alternative Approaches (06/06/2006)

Borgonovo E.

Risk Analysis, 2006, 26 (5), pp. 1349-1362

- Pdf (292 Kb)

Global Sensitivity Analysis in Inventory Management (07/07/2007)

Borgonovo E. and Peccati L.

International Journal of Production Economics, 2007, 108 (1-2), pp. 302-313.

- Pdf (217 Kb)

Differential, Criticality and Birnbaum Importance Measures: an Application to Basic Event, Groups and SSCs in Event Trees and Binary Decision Diagrams (10/10/2007)

Borgonovo E.

Reliability Engineering & System Safety, 2007, 92,10, pp. 1458-1467

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 investgate 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.

- Pdf (202 Kb)

Uncertainty and Global Sensitivity Analysis in the Evaluation of Investment Projects (06/06/1006)

Borgonovo E. and L. Peccati

International Journal of Production Economics, 2006, 104 (1), pp. 62-73

- Pdf (203 Kb)

The Importance of Assumptions in Investment Evaluation (06/06/2006)

Borgonovo E. and L. Peccati

International Journal of Production Economics, 2006, 101 (2), pp. 298-311.

- Pdf (259 Kb)

Sensitivity Analysis in Investment Project Evaluation (04/04/2004)

Borgonovo E. and L. Peccati

International Journal of Production Economics, 2004, 70, p.17-25

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.

Link to Pdf

Comparison of Global Sensitivity Analysis Techniques and Importance Measures in PSA (03/03/2003)

Borgonovo E., G.E. Apostolakis, S. Tarantola and A. Saltelli

Reliability Engineering and System Safety, 2003, 79, pp. 175-185.

Link to pdf

A new importance measure for risk-informed decision making (01/01/2001)

Borgonovo E. and G.E. Apostolakis

Reliability Engineering & System Safety, 2001, 72 (2), pp. 193-212

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.

Link to pdf

A Monte Carlo methodological approach to plant availability modeling with maintenance, aging and obsolescence (01/01/2000)

Borgonovo E. , M. Marseguerra, and E. Zio

Reliability Engineering & System Safety, 2000, 67 (1), 2000, pp. 6173

Link to pdf