Publication Date

Spring 5-2021


Issues linked to abnormal environments (like high-consequence systems safety, e.g., nuclear weapon components, bridges, apartment buildings, etc.) may have insufficient information to use either classical statistical methods or Bayesian approaches for calculating associated probabilistic risks, so there is often a requirement for another method that can deal with a low-information situation to obtain a risk assessment. Belief/plausibility measures of uncertainty from A. P. Dempster and G. Shafer’s Evidence Theory is one such method. This thesis has two goals. First, a brief discussion on belief/plausibility measures as an application of Evidence Theory will familiarize the audience with its history and how it can be applied as a general framework for managing problem spaces with significant epistemic uncertainty – this introduction will be followed by a series of examples which will build in mathematical rigor to finally reach the level of complexity of the problem of interest. Second, the application involves the puncture of three layers of material by a probe to simulate a common safety issue with high- consequence system components – specifically, what is the minimum energy needed to penetrate through all three layers of material with a 0.10 probability of not exceeding that lowest energy? This thesis shows that a convolution of three non-interactive belief/plausibility intervals can be used to solve the triple-layer puncture problem, and a sample, step-by-step analysis using simulated expert elicitation data is provided to demonstrate that process.

Degree Name


Level of Degree


Department Name

Mathematics & Statistics

First Committee Member (Chair)

Erik Barry Erhardt

Second Committee Member

Fletcher G. W. Christensen

Third Committee Member

Walter Gilmore




Belief, Plausibility, Evidence Theory, High-consequence systems safety, Dempster-Shafer Theory, Dempster, Shafer, Belief/plausibility measures

Document Type