A failure probability for a system having multi-fail regions is computed by generating failure directions in a space whose dimensions are the system parameters under consideration. The failure directions are preferably uniform, forming radial slices. The failure directions may be weighted. The radial slices have fail boundaries defining fail regions comparable to broken shells. The distribution of the system parameters is integrated across the broken shell regions to derive a failure contribution for each failure direction. The failure probability is the sum of products of each failure contribution and its weight. Failure contributions are computed using equivalent expressions dependent on the number of dimensions, which can be used to build lookup tables for normalized fail boundary radii. The entire process can be iteratively repeated with successively increasing failure directions until the failure probability converges. The method is particularly useful in analyzing failure probability of electrical circuits such as memory cells.