Efficient statistical analysis for correlated rare failure events via asymptotic probability approximation

Correlated Rare Failure Analysis via Asymptotic Probability Evaluation

“…Such an error refinement process is particularly important when there exist a large number of replicated cells in the system and, therefore, the impact of numerical error can be significant. Compared to the traditional APA method [1], our proposed APE method can reduce the estimation error by up to 45× without increasing the computational cost, as will be demonstrated by the numerical results in Section 4.…”

“…If any cell fails, the SRAM system fails. Hence, the systemlevel failure event FN U can be defined as a union of all cell-level failure events [1], i.e., FN U = c1 ∪ c2 ∪ ⋅⋅⋅ ∪ cN. The system-level failure rate PN can be defined as:…”

“…A large body of works have been proposed in the literature to efficiently estimate rare cell-level failure rate [1] (i.e., the failure probability of a single cell). Most of them are based on Important Sampling (IS) [2]- [4] or Boundary Searching (BS) [5].…”

“…Even though the problem of estimating cell-level rare failure rate has been extensively studied, it remains an open question how we could efficiently estimate the rare failure rate for an entire system (i.e., system-level failure rate [1]) containing a large number of replicated cells. The system-level failure events depend on a large number of cell-level failures.…”

“…To address this correlation issue, Asymptotic Probability Approximation (APA) has been recently proposed [1]. It captures the correlation among cell-level failures by exploring a series of partial failure events (i.e., the probability for a small number of cells to fail).…”