# Evaluation of Present Accelerated Temperature Testing and Modeling of Batteries
## 1 Introduction
[PERSON] et al. [15] employed the Arrhenius model in the cycle aging modeling of lithium-ion batteries, and [PERSON] et al. [16; 17; 18; 19] assumed that the effect of temperature on calendar degradation of lithium-ion batteries followed this model. NASA's Aerospace Flight Battery Program [20] proposed the standard approach for lithium-ion batteries where they established the correlation between the capacity fade and cycles by conducting tests at various temperatures and analyzing the data to get the Arrhenius coefficient. [PERSON] et al. [21] and [PERSON] et al. [22] expressed the resistance growth and capacity fade for lithium-ion batteries as a product of cycles and degradation rates expressed by the Arrhenius model, then implemented battery-oriented optimization control during its lifetime. All the studies described above assume that the Arrhenius model works for the temperature-dependent degradation behavior of lithium-ion batteries without rigorous verification. However, a battery is a complex nonlinear system with far more than one chemical reaction taking place. [PERSON] and [PERSON] [23] proved that the coefficients in this model for a certain chemical reaction can change with temperature. [PERSON] et al. [24] pointed out that while the Arrhenius model indicates that the degradation rate increases with temperature, it does not hold true for low temperature in a lithium-ion battery case study. The derived activation energy in this model is shown to change with temperature [14]. To further simplify modeling of the temperature effect, a rule of thumb commonly used by some researchers [10] and companies [25] is that the aging rate doubles for every 10 \({}^{\circ}\)C that a battery is operated above the rated temperature. This rule of thumb is then used to calculate the acceleration factor (AF), which is defined as the ratio between the times necessary to obtain a stated proportion of failures for two different sets of stress conditions involving the same failure modes and/or mechanisms. However, this rough approximation can result in wildly inaccurate estimation of battery lifetime, thus misleading battery manufacturers and device companies. Comprehensively planning the accelerated testing and correctly modeling the aging effect of stress factors is essential to the accurate lifetime prediction of batteries. This paper presents issues encountered when conducting accelerated temperature testing of batteries using the Arrhenius model and the decade rule. Two case studies with actual experimental results demonstrate the problemswith the current temperature testing and modeling methods. Case study 1 illustrates how a company conducted accelerated temperature testing and applied the Arrhenius model to storage life prediction of primary zinc-based batteries. In case study 2, testing data of lithium-ion batteries are used to demonstrate the impropriety of these approaches. Proper approaches for reliability testing and modeling are then provided. The remaining sections of this paper are as follows. Section 2 introduces the Arrhenius model and the \(Q_{10}\) factor as well as its characteristics. Section 3 presents the two case studies, discusses the issues from the case studies and proposes recommendations. Section 4 concludes the main findings of this paper.