Negative bias temperature instability (NBTI) is a leading aging mechanism in modern digital and analog circuits. Recent NBTI data exhibits an excessive amount of randomness and fast recovery, which are difficult to be handled by conventional power-law model (tn). Such discrepancies further pose the challenge on long-term reliability prediction under statistical variations and Dynamic Voltage Scaling (DVS) in real circuit operation. To overcome these barriers, the modeling effort in this work (1) practically explains the aging statistics due to randomness in number of traps with log(t) model, accurately predicting the mean and variance shift; (2) proposes cycle-to-cycle model (from the first-principle of trapping) to handle aging under multiple supply voltages, predicting the non-monotonic behavior under DVS (3) presents a long-term model to estimate a tight upper bound of dynamic aging over multiple cycles, and (4) comprehensively validates the new set of aging models with 65nm statistical silicon data. Compared to previous models, the new set of aging models capture the aging variability and the essential role of the recovery phase under DVS, reducing unnecessary guard-banding during the design stage. With CMOS technology scaling, design for reliability has become an important step in the design cycle, and increased the need for efficient and accurate aging simulation methods during the design stage. NBTI induced delay shifts in logic paths are asymmetric in nature, as opposed to averaging effect due to recovery assumed in traditional aging analysis. Timing violations due to aging, in particular, are very sensitive to the standby operation regime of a digital circuit. In this report, by identifying the critical moments in circuit operation and considering the asymmetric aging effects, timing violations under NBTI effect are correctly predicted. The unique contributions of the simulation flow include: (1) accurate modeling of aging induced delay shift due to threshold voltage (Vth) shift using only the delay dependence on supply voltage from cell library; (2) simulation flow for asymmetric aging analysis is proposed and conducted at critical points in circuit operation; (3) setup and hold timing violations due to NBTI aging in logic and clock buffer are investigated in sequential circuits and (4) proposed framework is tested in VLSI applications such DDR memory circuits. This methodology is comprehensively demonstrated with ISCAS89 benchmark circuits using a 45nm Nangate standard cell library characterized using predictive technology models. Our proposed design margin assessment provides design insights and enables resilient techniques for mitigating digital circuit aging.