The point estimation method can be applied to the safety factor (SF) equation for any specified rock slope failure mode (such as plane shear, step path, or wedge) to obtain reliable estimates of the mean and standard deviation of the SF probability distribution. A gamma probability density function is recommended for modeling this probability distribution, because it allows only for positive values and is flexible enough to provide symmetrical shapes and right-skewed, exponential-type shapes for the SF distribution. The mean and standard deviation define this distribution, which then can be integrated numerically from 0 to 1 to obtain the probability of sliding, PS (portion of the SF distribution where SF<1.0). The overall probability of failure, PF, for the potential slope failure mass is the joint probability that the rock discontinuities are long enough to allow kinematic failure (PL) and that sliding occurs along the rock discontinuities (PS); that is, PF = PSPL. This method for estimating the probability of sliding is extremely efficient computationally, and thus, expedites slope stability simulation routines used by NIOSH software to stochastically describe rock slope behavior and assist the engineer in designing catch benches for large rock slopes. Enhanced bench design translates into increased operational efficiency and safer working conditions in open pit mines and quarries.
Stochastic simulations of fractured rock masses can provide valuable information for the engineering design of rock slopes, particularly when the natural geologic discontinuities may form potential slope failure modes. An essential component of such engineering simulations is being able to compute the probability of sliding for a given potential failure mass once the geometry of that failure mass has been identified through spatial rock-fracture simulations. In cases where several thousand (or ore) simulations of possible failure geometries are needed to provide a realistic representation of the rock slope, computational efficiency is essential for the repetitious protocol used to calculate the probability of sliding.
An example of applying this type of geotechnical approach to rock slope design was presented by Miller and others  in a paper focused on the design of catch benches for open pit mines and quarries. This issue is important to NIOSH (National Institute for Occupational Safety and Health) as part of its research mission to improve safety and health in the mining industry. Between 1995 and 2003 there were 42 reported fatalities dueto slope failure accidents at surface mines in the United States, at least one and as many as eleven each year. Additional accident statistics collected by the Mine Safety and Health Administration (MSHA) have shown that loose material from slope and bench failures can pose significant safety hazards to miners. To address these concerns the NIOSH Spokane Research Laboratory has been developing and testing rock slope stability software ver the past few years to provide advanced technical tools for analyzing bench stability. A key element of this software is a module used to compute the probability of sliding for a given viable failure geometry that has been simulated for the bench under study.