A Spatially Correlated Competing Risks Time-to-Event Model for Supercomputer GPU Failure Data

Graphics processing units (GPUs) are widely used in many high-performance computing (HPC) applications such as imaging/video processing and training deep-learning models in artificial intelligence. GPUs installed in HPC systems are often heavily used, and GPU failures occur during HPC system operations. Thus, the reliability of GPUs is of interest for the overall reliability of HPC systems. The Cray XK7 Titan supercomputer was one of the top ten supercomputers in the world. The failure event times of more than 30,000 GPUs in Titan were recorded and previous data analysis suggested that the failure time of a GPU may be affected by the GPU's connectivity location inside the supercomputer among other factors. In this paper, we conduct in-depth statistical modeling of GPU failure times to study the effect of location on GPU failures under competing risks with covariates and spatially correlated random effects. In particular, two major failure types of GPUs in Titan are considered. The connectivity locations of cabinets are modeled as spatially correlated random effects, and the positions of GPUs inside each cabinet are treated as covariates. A Bayesian framework is used for statistical inference. We also compare different methods of estimation such as the maximum likelihood, which is implemented via an expectation-maximization algorithm. Our results provide interesting insights into GPU failures in HPC systems.