*3.1. Field Data of Batteries*

The BCI collected a total sample of 1454 batteries from different locations in the USA and presented the results in [13]. The batteries were collected within five months between August and December 2014 and analysed using a teardown analysis to find the dominant failure mode that led to the battery failure. Although several ageing mechanisms can occur in parallel and in total can affect the performance of the battery, there is one failure mode that is most pronounced and has thus been identified as the dominant failure mode for this battery failure. If this dominant ageing mechanism did not occur to the same extent, the battery would possibly still be functional at this time.

The sample reflects the different influences of temperature on batteries because of the different climatic conditions of the sample locations. Due to the large climatic differences in the USA between the North and the South, the sample can be divided into North and South accordingly. In the North with lower mean temperatures 857 batteries were collected; in the South with higher mean temperatures 597 batteries were collected.

In addition to climatic differences due to the locations where the batteries were collected, the sample contains batteries of varying quality and from a wide variety of cars. With an age of up to 12 years, the oldest batteries date back to 2002 and thus come from vehicles that rarely had energy management or start-stop function. Furthermore, besides the manufacturing quality of the batteries, nothing is known about the type, so the sample contains few or no advanced lead batteries such as absorbent glass mat or enhanced flood batteries but mainly older flood batteries.

Furthermore, the design of the batteries differs. For example, the sample includes battery housings according to the European standard with a protective terminal niche [20]. However, this type of housing represents a maximum of about 20% of the sample, most batteries are built according to the US standard or the Japanese Industrial Standards (JIS) [21]. This means that the majority of the batteries in the sample have a battery housing without terminal niche and the battery terminals are exposed. This makes mechanical impacts on the battery housing, e.g., during installation or removal or even during transportation when stacked, much more critical. Due to improper handling, the battery terminals are prone to mechanical damage. This can cause fractures between the battery terminal and the cell, which partially or directly destroys the battery.

All in all the lead batteries investigated in this sample are no longer relevant for today's driving applications with high safety requirements. Since the operational demands on the battery were different back then, energy management was rarely implemented and a wide variety of qualities and types of lead batteries can be found in the sample. For future driving applications, however, only high-quality lead batteries of the latest generation will be used in combination with a powerful battery sensor and energy management.

In addition to the failure probability *F(t)* for the total sample, those of the sample parts North and South over a time period of 12 years are also published. In this study, the data of the total sample is used for the evaluation, because it covers locations from all over the USA. In combination with batteries surviving up to 12 years, this sample can be recognised as a representative sample of lead batteries in the field in 2014. These batteries represent the various stress levels, qualities and types used at that time. To perform the statistical approach the graphs are digitised again and converted into individual lifetime values of the batteries. The total sample used for this analysis is shown in Figure 1 as probability of failure *F(t)* for all failure modes including exchanged but functional batteries in one curve. The failure probability *F(t)* always starts for *t* = 0 with *F(t=0) =* 0% failed parts and always results after *t=n* until all parts of the sample failed in *F(t=n) =* 100%.

**Figure 1.** The total sample as a sum of all failures modes is shown in this graph for a time period of 12 years. On the left side the empirical probability of failure *F(t)* is shown [13].

Besides the failure probability *F(t)* of all failures modes as a sum, the failure probabilities *F(t)* of the major five failure modes found by BCI while examining the batteries are published as well. The probability of failures *F(t)* of each failure mode is separately presented for a time period of 4 years for the sample parts North and South by BCI. The failure probabilities *F(t)* of these five failure modes are shown for the total sample in Figure 2.

Figure 2 shows the major failure modes. For a better differentiation of the individual curves, they are mentioned in relation to the time of 4 years. Starting from the top, *Serviceable*, *Short Circuit*, *Plates and Grids*, *Worn out and Abused* and *Open Circuit* are displayed.

Both Figures 1 and 2 are based on single lifetime values derived from the *Report on Battery Failure Modes* by BCI in 2015 [13]. In particular, the data of the five major failure modes in Figure 2 are the basis to present the methodology for determining time-dependent failure rates *λ*(*t*) in Section 2.

In order to discuss the time-dependent failure rates of the individual failure modes in relation to their ageing behaviour, the five major failure modes are presented in the following sections.

**Figure 2.** The major five failure modes found by BCI are shown for the total sample. The individual probability of failures *F(t)* is displayed for a time period of 4 years [13].
