# MTBF Calculation & Product Reliability

MTBF is commonly confused with a component’s useful life, even though the two principles are not related in any way. For example, a battery may have a useful life of four hours and an MTBF of 100,000 hours. These statistics indicate that in a amount of 100,000 batteries, there will be approximately one battery failure every hour during a single battery’s four-hour life span. By contrast, a 64-processor server may last 50,000 hours before it goes into its wear-out period, while its MTBF value may only be 2,000 hours.

## How to calculate Mean Time Between Failures (Basic)

Actual or historic Mean Time Between Failures is calculated using observations in the real world. Calculating actual Mean Time Between Failures requires a set of observations; each observation is:

- Uptime: the moment at which a device or component began operating (initially or after a repair)
- Downtime: the moment at which the chip or semiconductor failed after operating since the previous uptime-moment

So each Time Between Failure (TBF) is the difference between one Uptime_moment observation and the subsequent Downtime_moment.

**Three basic values are required:**

- n = Number of observations.
- uT = This is the Uptime of the device
- dT = This is the dT Downtime of the devic follwoing the Uptime

**Calculation:**

MTBF = Sum (dT– uT) / n

More simply, it is the total working time divided by the number of failures. This is the most basic sense of MTBF. However, when calculating MTBF for semiconductors, a more advanced method is required.

## Advanced formula for calculating the MTBF

MTBF= T/R where T = total time and R = number of failures

MTTF stands for Mean Time To Failure. To separate between the two, the approach of suspensions must first be understood. In reliability calculations, a suspension occurs when a destructive test or observation has been completed without observing a failure.

Whereas MTBF calculations do not consider suspensions whereas MTTF does. MTTF is the number of total hours of service of all devices divided by the number of devices. It is only when all the components fail with the same failure mode that MTBF converges to MTTF.

MTTF= T/N where T = total time and N = Number of units under test.

Example: 10 laser diode devices are tested for 500 hours. During the test 2 failures occur.

The estimate of the MTBF is:

MTBF= (10*500)/2 = 2,500 hours / failure.

Whereas for MTTF

MTTF= (10*500)/10 = 500 hours / failure.

If the MTBF is known, one can calculate the failure rate as the reverse of the MTBF.

The formula for failure rate is:

failure rate= 1/MTBF = R/T where R is the number of failures and T is total time.

Once an MTBF is calculated, what is the possibility that any one selected device will be operational at time equal to the MTBF?

An MTBF of a semiconductor of 1.4 million hours, determined in say, six weeks of lab testing, doesn’t mean we can expect an individual device to operate for 159 years before failing. MTBF is a statistical measure, it can’t forecast anything for a single device. We can use that MTBF rating more correctly to calculate that if we have 1,000 photodiode devices operating continuously in the field, we can expect one to fail every 58 days for a total of perhaps 19 photodiode failures in three years.

So, in summary:

MTBF is an abbreviation for Mean Time Between Failures.

MTBF is a measure of how reliable a product is. MTBF is usually given in units of hours; the higher the MTBF, the more reliable the product is.