POF Darts is a new algorithm for the QMU problem of estimating device or system probability of failure (POF), e.g., of critical infrastructures in the face of a potentially disruptive event.
POF Darts wraps around a computational simulation of a device, evaluating it at particular parameter values, such as uncertain environmental conditions and varying as-manufactured device characteristics. These evaluations are interpolated to build an estimate of the conditions under which the device fails, and their likelihood of occurrence (i.e., the POF).
Reducing the number of simulations required is important because each may be an expensive supercomputer run. Initial experiments indicate that POF Darts offers at least an order of magnitude improvement over the common alternative, Latin Hypercube Sampling, in terms of the number of simulations needed to obtain the same relative accuracy. The advantage grows for small failure probabilities and large sample budgets.
How POF Darts reduces the expense so dramatically comes from two innovations, borrowed from the field of computational geometry and applied to POF for the first time.
- The first innovation is to model failure or not-failure neighborhoods as spheres around evaluation points. Spheres cover wide swaths of the domain that need no further exploration. The remaining exploration is efficiently guided toward the critical failure boundary. The volume of the union of spheres estimates the POF.
- The second innovation is to gain more information about the union-volume per sample, by evaluating the set of spheres analytically along lines, rather than just at single points as in standard Monte Carlo sampling.