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Statistical modelling and prediction of lifetime of batteries based on aging tests
Life cycle analysis (LCA)

Accurate assertions on the lifetimes of battery cells via an end-of-life (EoL) criterion within a reasonably short time period are of major interest. These are possible through data obtained from accelerated aging tests. Under such tests, in order to speed up aging and to study the influence of stress factors (such as temperature, voltage, range of state of charge), the design of experiments is varied. In general, accelerated life testing (ALT) is widely employed to determine the lifetime distributions of highly reliable products under increased stress conditions. Then, an associated life-stress relationship is needed to predict the product’s reliability under normal operating conditions. We consider common battery aging tests such as cyclic aging, review some ALT aspects and propose an advanced ALT-method, namely step-stress tests, where the level of some stress factor is increased at intermediate, pre-specified time points of the test (cf. Balakrishnan et al. 2009, 2012, Bedbur et al. 2015, Kateri, Kamps 2017).
Particular statistical methods are illustrated by a data set of Baumhöfer et al. (2014). Capacity degradation of lithium-ion batteries under long-term cyclic aging is modelled via a flexible regression set-up, which can also be applied in second-life scenarios of batteries. Resulting statistical procedures, such as parameter estimation, confidence and prediction intervals are highlighted. Using some prior information or training data on the complete degradation path, the model can be fitted satisfactorily even if only short-term degradation data is available (Johnen et al. 2021). Moreover, the fitting of two popular lifetime distributions, namely Weibull and lognormal, is examined with respect to the EoL criterion by means of residual capacity. The impact of an improper distributional assumption on confidence intervals for the mean lifetime and certain quantiles is studied. Since data of capacity decline is commonly not continuously observed but interval-censored, the effect of interval monitoring on the quality of the estimation is examined in a simulation study by comparing results under full and interval-censored information (Johnen et al. 2020, cf. Harris et al. 2017, Wang et al. 2019).

Balakrishnan N, Beutner E, Kateri M (2009) IEEE Trans Reliability 58:132-142
Balakrishnan N, Kamps U, Kateri M (2012) Ann Inst Statist Math 64:303-318
Baumhöfer T, Brühl M, Rothgang S, Sauer DU (2014) J Power Sources 247:332-338
Bedbur S, Kamps U, Kateri M (2015) Appl Math Modelling 39:2261-2275
Harris SJ, Harris DJ, and Li C (2017) J Power Sources 342:589-597
Johnen M, Pitzen S, Kamps U, Kateri M, Sauer DU (2021) Journal of Energy Storage 34 102011:1-10
Johnen M, Schmitz C, Kateri M, Kamps U (2020) Computers & Industrial Engineering, 143 106418:1-11
Kateri M, Kamps U (2017) Ann Review Statistics Appl 4:147-168
Wang YF, Tseng ST, Lindqvist BH, Tsui KL (2019) J Quality Technology 51:198-213

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