A Bayesian nonlinear random effects model for identification of defective batteries from lot samples

Numerous materials and processes go into the manufacture of lithium-ion batteries, resulting in variations across batteries' capacity fade measurements. Accounting for this variability is essential when determining whether batteries are performing satisfactorily. Motivated by a real manufacturing problem, this article presents an approach to assess whether lithium-ion batteries from a production lot are not representative of a healthy population of batteries from earlier production lots, and to determine, based on capacity fade data, the earliest stage (in terms of cycles) that battery anomalies can be identified. The approach involves the use of a double exponential function to describe nonlinear capacity fade data. To capture the variability of repeated measurements on a number of individual batteries, the double exponential function is then embedded as the individual batteries' trajectories in a Bayesian random effects model. The model allows for probabilistic predictions of capacity fading not only at the underlying mean process level but also at the individual battery level. The results show good predictive coverage for individual batteries and demonstrate that, for our data, non-healthy lithium-ion batteries can be identified in as few as 50 cycles.