Battery Reliability

Reliability, Failure rate and MTBF

Each cell in today's VRLA batteries can have a reliability of 0.995, or 99.5% over its useful lifetime, which could be for example 10 years.

Reliability simply means; probability for the unit to be functional without faults over a specified time. If the reliability is 1.0 then the unit will work for the whole specified time with absolute certainty.

Failure rate is the probability for the unit to have a fault within a specified time;
Failure rate = (1 - Reliability)
The VRLA cells mentioned above have a Failure rate of 0.005, or 0.5%, over 10 years.

For electronic components and whole systems, such as a small DC/DC converter or a complete UPS, the term MTBF is more commonly used to describe reliability.
A high quality DC/DC converter can have a specified MTBF of 46 years.
A typical high end UPS system can have a specified MTBF of 17 years.

MTBF is NOT the expected life time. It is the Mean Time Between Failure during its useful lifetime. Assuming the UPS have a useful lifetime of 20 years, in average one will fail each year if you would have 17 UPS:s.

The reliability (R) over a 10 year period (t) of a UPS with a MTBF of 17 years is;
R = e^(-t/MTBF) = e^(-10/17) = 0.56, or 56%
There is a 44% chance that the UPS will fail during the useful life of the VRLA cell.

While the likelihood of that one particular cell will survive its whole useful life is 99.5%, since a battery string may comprise 200 cells in series, the reliability of a whole battery string is only 0.995^200 = 0.37, or 37%.
There is a 63% chance that the battery will fail during its useful lifetime of 10 years.

Despite the fact that the MTBF of each individual VRLA cell can be calculated as;
MTBF.cell = (-10) / ln(0.995) = 1995 years (!),
the MTBF of a whole battery string is only;
MTBF.string = (-10) / ln(0.995^200) = 10 years.

Paralleling cells with electronic components

Assuming one would like to connect some electronic device, such as voltmeter, equalizer etc., to each cell in a battery, and thereby making the reliability of the cell dependent of the connected device, and that this new device has a specified MTBF of 10 years;

The reliability over a 10 year period for each device is; e^(-10/MTBF) = 0.37. This means that the chance for a device to survive for 10 years is 37%.
The failure rate for a device is (1 - 0.37) = 0.63, or 67% per 10 year.

In this example, the MTBF of each connected device is the same as the MTBF of a whole battery string with 200 cells.

The reliability, or the probability, for a battery string to work without failure for 10 years, will be determined by a number of connected electronic devices as followed.

Conclusion

• The MTBF of a normal battery cell is 2000 years.
• The MTBF of a high quality electronic device is 10 years.
• Making the reliability of the battery cells depending on any electronic device would be devastating.

References

1. Wikipedia − Mean time between failures
2. Pro-face America − MTBF vs. Reliability
3. Vicor − Reliability and MTBF Overview
4. McDowall, Jim, (2005), Lies, damned lies and statistics: the statistical treatment of battery failures, Battcon 2005, McDowallPaper2005.pdf