Keywords: dynamic reliability, theory of stimulated dynamics, probabilistic safety analysis, exceedance frequency, Monte Carlo.

This paper presents an algorithm that solves the dynamic reliability theory of stimulated dynamics (TSD) integral equations in order to compute the exceedance frequency of a given accident sequence in a facility. The algorithm is then applied to a benchmark example and provides numerical results obtained from the TSD methodology.

The safety of a facility can be defined as the limitation in magnitude and frequency of the damage that the facility can potentially generate. Damage is any undesired consequence of the operation of the facility. The appropriate magnitude to characterize the plant safety is the expected frequency of generation of some amount of damage or a larger one, called the exceedance frequency of that damage. Classical probabilistic safety assessment (PSA) techniques for the exceedance frequency computation make use of event trees (ET) and fault trees (FT) as probabilistic tools. However, the protection actions or stochastic phenomena are naturally linked to the dynamic evolution of the accident progression, links that classical PSA does not reflect explicitly.

The stimulus-driven theory of probabilistic dynamics (SDTPD) [1] tries to better link the dynamic variables of an accident sequence to the computation of the damage exceedance frequency, introducing the concept of stimuli. A so-called stimulus is either an order for action (often given by an electronic device or corresponding to an operator diagnosis), or the fulfillment of conditions triggering a stochastic phenomenon. Human-driven actions or stochastic phenomena, may occur with given stochastic delays after the activation of the corresponding stimulus, and are therefore susceptible to stochastic sampling within the sequence set of soyourn time duration intervals in each of the header states representing a sequence. Therefore, the combination of a sequence of events in the sense of the PSA and a vector of occurrence times for each of those dynamic events constitutes a so-called path, and all the possible combinations of times provide all the paths belonging to the same sequence, leading to the "path and sequences" version of the SDTPD [1].

The dynamic reliability integral equations of the exceedance frequency may be further restricted by limiting the stimuli activation probability density function to just the times at crossing specified regions partitioning the process variables multidimensional domain. This restriction in the possible type of stimuli yields to strong additional simplification of the path and sequence SDTPD equations, called here the ingoing density TSD equations, that are now numerically tractable leading to the associated TSD methodology.

Essential in the TSD method is the selection of a specific integration algorithm that is able to both search the damage domain (paths leading to damage) within the sequence sampling domain and integrate the ingoing frequency density inside this domain. The way we perform the sampling strategy and the accurate computation of the incremental volume associated to each path are key points for an accurate exceedance frequency computation. The article describes the algorithm designed to perform these computations and solve the integral equations, and presents the results obtained from the application to a particular example of accident progression.

1

P.E. Labeau, J.M. Izquierdo, "Modeling PSA problems. I The stimulus driven theory of probabilistic dynamics. II A cell-to-cell transport theory approach", NSE, 150, 115-154, 2005.

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