  Large-scale computing systems today are assembled by numerous computing units
for massive computational capability needed to solve problems at scale, which
enables failures common events in supercomputing scenarios. Considering the
demanding resilience requirements of supercomputers today, we present a
quantitative study on fine-grained failure modeling for contemporary and future
large-scale computing systems. We integrate various types of failures from
different system hierarchical levels and system components, and summarize the
overall system failure rates formally. Given that nowadays system-wise failure
rate needs to be capped under a threshold value for reliability and
cost-efficiency purposes, we quantitatively discuss different scenarios of
system resilience, and analyze the impacts of resilience to different error
types on the variation of system failure rates, and the correlation of
hierarchical failure rates. Moreover, we formalize and showcase the resilience
efficiency of failure-bounded supercomputers today.
