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Communication Dans Un Congrès Année : 2015

Technical tools for the use of extended gamma processes in reliability

Résumé

Standard gamma processes are widely used to model the phenomena of cumulative degradation. However, a notable restriction of a standard gamma process is that its variance-to-mean ratio is constant over time. To overcome this restriction (among others), the use of an extended gamma process is proposed, which is defined as a stochastic integral with respect to a standard gamma process. Contrary to its standard version, the scale parameter of an Extended Gamma Process (EGP) may vary over time. This allows for more flexibility for modelling purpose. However, there is a cost and the use of an EGP presents technical difficulties which have to be dealt with, before EGPs to be used in a practical reliability context: as a first step, the probability distribution of an EGP is not known in full form and it has to be numerically assessed; as a second step, no exact simulation procedure is available, so that approximate simulation procedures have to be developed. The presentation deals with these two issues: an approximate EGP with a piecewise constant scale function is first constructed, which allows both to compute the cumulative distribution function of a general EGP at a known precision and to simulate approximate paths. The quality of the approximation is studied and compared to other possible methods from the literature, both from a theoretical and numerical point of view.
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Dates et versions

hal-01355162 , version 1 (22-08-2016)

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  • HAL Id : hal-01355162 , version 1

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Sophie Mercier, Zeina Al Masry, Ghislain Verdier. Technical tools for the use of extended gamma processes in reliability. CMStatistics 2015 (8th International Conference of the ERCIM WG on Computational and Methodological Statistics), 2015, London, France. ⟨hal-01355162⟩
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