Lifetime distributions of components enables us to compute the reliability of a system that consists of these components. Generally, lifetime distribution is determined from accelerated life testing of the components, but this cannot be applied for the case of Lithium-Ion battery (LiB). Consequently, industry is using state of health to indicate the reliability of LiB and its associated system, and this cannot provide prediction to the LiB pack reliability according to the system reliability theory that has long been established. This work derives statistical time to failure distribution of LiBs from their experimental discharge degradation paths using a statistical capacity fading (SCF) model with fixed and random coefficients (mixed effect), and our method demonstrated that less than 50% of their entire life cycle data is sufficient for the distribution determination. In contrast to the statistical methods in literatures, our model was based on a simplification of the electrochemistry-based electrical (ECBE) model which had a strong support from electrochemistry theory. With the time to failure distribution of LiBs determined, the reliability and life span of LiB pack with various structure connections can now be computed as shown with examples here. The important of having the LiBs to degrade at similar rate is also demonstrated with the life time distribution of the LiBs, and the optimal connection for a given set of LiBs where the pack reliability is the highest is derived.
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