Markov Chain method in dynamic fault tree with reparable components

Abstract

Markov Chain method for Dynamic Fault Tree with reparable components is discussed. The complexity of the problem and definition of dynamic gates is considered. Significant simplification of the method is suggested based on joining and truncation of Markov Chain states. The accuracy of approximation is based on assumption that Mean Time to Repair is much less than Mean Time to Failure. Several examples are studied.The second, joining approach is based on combining together states with the same set of failure events but with different order of their failures. We studied when the second approach is possible to apply without significant loss of accuracy of the calculation result. It is shown that both approximations are applicable if the Mean Time between Failure (MTBF) of the system is much less than Mean Time to Repair (MTTR). Obviously, this is the most important practical case. We illustrated the accuracy and efficiency of the approximate method with several examples. DYNAMIC GATES DEFINITION AND COMPLEXITY OF THE PROBLEMWe use MC method to define DGs with reparable components developing definition introduced earlier for DTF without reparable components (Dugan et al. 1992). We recognize that this approach has its limitations, compared, for example, to Monte Carlo method. In this paper we will be focused mostly on considering several significant simplifications of MC method under reasonable assumptions. Priority and gate (PAND)

Quantification of Highly Coupled Dynamic Fault Tree Using IRVPM and SBDD

“…However, for a medium‐scale or large‐scale DFT, its quantitative analysis turns out to be a very challengeable job. Initially, the researchers adopted a Markov state space‐based method to quantify systems modeled by DFT. This method requires the whole DFT converted into a Markov chain model completely, which would suffer from the notorious problem of ‘state space explosion’.…”