An Apparent Flaw in Geomechanical Analysis of Rock Structures is the Application of Single Value Parameters as Input to Numerical Models. a Known But Often overlooked Characteristic of the Rock Mass is its Inherent Strong Property Variability. in Conventional Reliability Analysis of Rock Mechanics, Subjective Assumptions Are Often Made on the Probability Density Function of Parameters Because, in Many Cases, the Results of Geotechnical Investigations Are Set-Valued Rather Than Being Precise and Point-Valued. on the Other Hand, Imprecise Probability Theories Such as the Random Set Theory Could Be Considered a Possible Attractive Candidate to Employ in These Analyses. in This Study, the Random Set Theory in Combination with the Bonded Block Modeling (RS-BBM) Approach is Employed to Demonstrate its Practical Applicability in Determining Coal Rib Stability and Support Requirements. Sensitivity Analysis of the BBM Input Parameters is Conducted. the Uncertainties of the Geomechanical Parameters of the BBM Contacts, Which Control Model Behavior, Are Considered in the Reliability Analysis Model. the Analyses Were Performed in UDEC, and the Strength Reduction Method Was Used to Evaluate Rib Stability. It is Shown that RS-BBM is an Efficient Tool to Determine the Most Likely Bounds of Coal Rib Performance. a Method Combining the RS-BBM Approach with Empirical Methods is Also Described to Illustrate its Practical Application.