An External Shock -- Internal Barrier Degradation Model to Account for Operational Loads

Abstract

Modelling the reliability of safety instrumented systems requires a proper understanding of the failure model and how operational loads influence the degradation. Many authors propose models where a proof test will affect the failure rate of a component negatively. The very simple models assume a binary situation where the component has two states, i.e., functioning or failed. More refined models assume a transition between several states representing physical degradation of the component. Common to most models are that transition times are assumed to be exponentially distributed, i.e., that the process has Markovian properties. The assumption of degradation caused by the proof test and usage will generally compromise the Markovian assumption if there is some internal degradation in between the tests. It is therefore hard to defend an approach assuming exponentially distributed transition times. This paper presents a conceptual model which will allow modelling with Markovian assumptions, i.e., the external shock, internal barrier degradation model (ESIBD). We assume that the component is exposed to external shocks. Such a shock might be for example a kick in the well, a sudden pressure surge in a pipeline or a condensate plug in a safety valve. The shocks are assumed to follow a Homogeneous Poisson process. The component is assumed to have some inherent resistance to withstand the external chocks. This resistance is denoted the internal barrier performance. We allow the component to have two or more performance states. The internal barrier performance in the various states is influenced by usage and/or proof tests. The assumption of external shocks will ensure the Markovian properties of the model provided we have knowledge regarding the usage and proof-test regime of the component. Examples are given both for the binary situation and for the multi-state situation. We demonstrate the use of Markov chain modelling and give examples of regimes for an optimized proof test regime. In case of non Markovian transitions phase type distributions are used to simplify the modelling.