Diagnostics of lithium-ion batteries are frequently performed in battery management systems for optimized operation of lithium-ion batteries or for second-life usage. However, attempting to extract dominant degradation information requires long rest times between diagnostic pulses, which compete with the need for efficient diagnostics. Here, we design a set of efficient optimal hybrid pulse power characterization (HPPC) diagnostics using model-based design of experiment (DOE) methods, applying knowledge of degradation effects on pulse kinetics and cell properties. We validate that these protocols are effective through minimization of uncertainty, and robust with Markov Chain Monte Carlo (MCMC) simulations. Contrary to traditional HPPC diagnostics which use fixed pulse magnitudes at uniformly distributed state of charges (SOC), we find that well-designed HPPC protocols using our framework outperform traditional protocols in terms of minimizing both parametric uncertainties and diagnostic time. Trade-offs between minimizing parametric uncertainty and total diagnostic time can be made based on different diagnostics needs.