The Effect of Correlated Failure on the Reliability of HPC Systems

High Performance Computing (HPC) system utilization can be maximized and sustained if one understands the failure behavior. In general, Time to Failure (TTF) of HPC systems has been long studied and showed that the Wei bull distribution gives the best fit. In addition, in many cases, TTF of such systems exhibit correlations. In our previous study, we developed a reliability model of an HPC system where failures among nodes are independent. However, some studies have clearly shown that in some cases nodes do not fail independently of one another. Therefore, it is of importance to develop a reliability model for an HPC system based on the occurrence of simultaneous failures. In this paper, we develop such a model and derive expressions for the probability density function of time to failure, system reliability, system failure rate, and mean time to failure (MTTF). Results show that if the failure of the components (nodes) in the system possesses a degree of dependency, the system reliability decreases.