Importance and Sensitivity Analysis in Dynamic Reliability

  • Robert Eymard
  • Sophie MercierEmail author
  • Michel Roussignol


In dynamic reliability, the evolution of a system is governed by a piecewise deterministic Markov process, which is characterized by different input data. Assuming such data to depend on some parameter p ∈ P, our aim is to compute the first-order derivative with respect to each p ∈ P of some functionals of the process, which may help to rank input data according to their relative importance, in view of sensitivity analysis. The functionals of interest are expected values of some function of the process, cumulated on some finite time interval [0,t], and their asymptotic values per unit time. Typical quantities of interest hence are cumulated (production) availability, or mean number of failures on some finite time interval and similar asymptotic quantities. The computation of the first-order derivative with respect to p ∈ P is made through a probabilistic counterpart of the adjoint state method, from the numerical analysis field. Examples are provided, showing the good efficiency of this method, especially in case of a large P.


Dynamic reliability Sensitivity analysis Importance factor Piecewise deterministic Markov process Chapman–Kolmogorov equation 

AMS 2000 Subject Classification

60K20 90B25 74S10 


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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Robert Eymard
    • 1
  • Sophie Mercier
    • 1
    Email author
  • Michel Roussignol
    • 1
  1. 1.Laboratoire d’Analyse et de Mathématiques Appliquées (CNRS UMR 8050)Université Paris-EstMarne-la-ValléeFrance

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