^{1}and Marco Torbol

^{2}

^{1}Department of Nuclear Engineering, Ulsan National institute of Science and Technology/UNIST, 50 UNIST-GIL, Eonyang-eup, Ulju-gun, Ulsan, South Korea

^{2}Reliability and Risk Assessment laboratory, Ulsan National institute of Science and Technology/UNIST50 UNIST-GIL, Eonyang-eup, Ulju-gun, Ulsan, South Korea

Finding the probability of failures of complex engineering systems is a never-ending challenge, because with the increase in computational power, we either require better accuracy of the results or want to compute additional information. Different methods have been developed throughout the years to address such problems: fault tree analysis, event tree analysis, binary decision diagram, Markov Chain Monte Carlo among others. This study focuses on the development of a new algorithm that solves Markov Chain Monte Carlo problems using General Purpose Graphic Processing Units (GPGPU). The algorithm takes advantage of the innate parallelism of this new technology to handle large Markov Chain that a typical CPU could not solve or store in a reasonable amount of time without resorting to supercomputers. While a first inception of this algorithm solved only static Markov Chains, the algorithm presented in this study considers different issues and features that an analyst encounter in his daily practice. The transition matrix is stored in a new compact form. The probability of failure of each component can be expressed as a function of time. The correlation between different components can be considered. Because of its parallelism and the used data structure, the GPU runs through the entire chain in a single pass carrying with it hundreds of simulations simultaneously. Different examples are presented to demonstrate and validate the algorithm.