A Physics Space and Deterministic Modeling of Battery Lifetimes

This paper uses a case study involving sixteen electric batteries to introduce a novel, new approach for analyzing the results from a well-planned experimental design, in this case a split-plot with no replicates. This particular study collected information on several “ancillary” variables throughout the discharge cycle for each battery. The information from these variables describes the cycle life up through the final life degradation. This paper recognizes that the data are actually deterministic and not stochastic. The fundamental aims are (1) to demonstrate how the ancillary data can reduce the variability of the proper predictive model for the data, (2) to show how standard hypothesis tests based on the battery means fail with respect to the observed degradation of the battery's life, (3) to introduce a modification of Mallow's 𝐶𝑝, designed specifically for evaluating deterministic systems, (4) to illustrate how plots of residuals from the predictive models demonstrate the stable and predictable system, and (5) to demonstrate relationships between proper predictive modeling and statistical process control.