: In chip design, one of the main objectives is to decrease its clock cycle; however, the existing approaches to timing analysis under uncertainty are based on fundamentally restrictive assumptions. Statistical timing analysis techniques assume that the full probabilistic distribution of timing uncertainty is available; in reality, the complete probabilistic distribution information is often unavailable. Additionally, the existing alternative of treating uncertainty as interval-based, or affine, is limited since it cannot handle probabilistic information in principle. In this paper, a fundamentally new paradigm for timing uncertainty description is proposed as a way to consistently and rigorously handle partially available descriptions of timing uncertainty. The paradigm is based on a formal theory of interval probabilistic models that permit handling parameter uncertainty that is described in a distribution-free mode - just via the range, the mean, and the variance. This strategy perm...