Estimating a failure probability using a combination of variance-reduction techniques

Abstract

Consider a system that is subjected to a random load and having a corresponding random capacity to withstand the load. The system fails when the load exceeds capacity, and we consider efficient simulation methods for estimating the failure probability. Our approaches employ various combinations of stratified sampling, Latin hypercube sampling, and conditional Monte Carlo. We construct asymptotically valid upper confidence bounds for the failure probability for each method considered. We present numerical results to evaluate the proposed techniques on a safety-analysis problem for nuclear power plants, and the simulation experiments show that some of our combined methods can greatly reduce variance.

Quantile Estimation Via a Combination of Conditional Monte Carlo and Randomized Quasi-Monte Carlo

“…We now present numerical results from a stylized version of the model in Example 1, where the goal is to estimate the 0.05-quantile ξ of the system's safety margin Y = C − L. We first describe the model, which is also considered in Nakayama (2015), Alban et al (2017), and Kaplan et al (2019). As in some actual NPP PSA studies (e.g., Dube et al 2014), the CDF G C of the capacity C is assumed triangular with support [1800,2600] and mode 2200, with L and C independent.…”

Randomized Quasi-Monte Carlo for Quantile Estimation

“…,t, let G L, s be the CDF of L s = exp(µ s + σ s Z s ), where Z s ∼ N(0, 1), and µ s and σ s > 0 are given constants, so L s has a lognormal distribution. Our experiments set µ s = 7.4 + 0.1s and σ s = 0.01 + 0.01s, which are as in [18]. Then define G L as a mixture of G L, s , 1 ≤ s ≤ t; i.e., G L (y) = ∑ t s=1 λ s G L, s (y) for given positive constants λ s , 1 ≤ s ≤ t, summing to 1.…”

“…, r, we will shift (modulo 1) each point in the original set P m by S k to obtain P m may no longer be a digital net. In this latter case, we instead can apply scrambling to obtain each P (k) m satisfying (17) and (18), where the scrambled point set still possesses the desirable properties of the original point set; see [21,22].…”