A class of linear models for describing the capacity paths of lithium-ion batteries (LIB) is proposed in case of sparse data from a calendar aging experiment. This way the reliability of LIB is monitored and modeled based on degradation data. The introduced family of models allows for random effects and includes tuning parameters, both of which make it a powerful tool for modeling LIB capacities. Because of sparsity of data, a procedure for simulating degradation data based on the model fitted on the sampled data is discussed and illustrated. The robustness of such models against misspecification in terms of tuning parameters is assessed by a simulation study.

In lifetime analysis of lithium-ion batteries, the failure of a battery is commonly defined as the time point at which the battery holds only a certain percentage of its initial storage capacity. Usually, lifetime experiments are carried out to record degradation up to a certain level, and thus do not offer an appropriate data base for fitting lifetime distributions to different end-of-life (EoL) criteria by means of residual capacity. However, for a second use of batteries, e.g. in a home energy storage system, lifetime modeling for long-term usage is of specific interest. Based on real data from long-term cyclic aging experiments with lithium-ion batteries, the fitting of three of the most popular lifetime distributions, namely Weibull, lognormal and inverse Gaussian distributions, is examined with respect to some particular EoL criteria. The impact of chosen lifetime distributions on confidence intervals (CIs) for the mean lifetime and certain quantiles is studied. Moreover, since data of capacity decline are commonly interval-censored, comparisons of resulting CIs under full and interval-censored information are made by means of simulations.