# The MTBF Calculation: What It Really Is and Why You Should Care

You struggle to find the right solution for your business. You pore over spec sheets, slice the features, weigh the costs, and try to make the most correct purchase that will be a trouble-free value-add for your restaurant roll-out.

In most cases, the haste to absorb all of this data causes some to gloss over the Mean-Time-Between-Failure (MTBF) numbers. The MTBF calculation can be defined as a measurement of how reliable a hardware product or component is. Some may make the assumption that this represents the typical life of the product they are considering to buy. Others may even think these numbers are not useful in their decision making at all.

There may be some logic in each way of thinking, but both are missing the most useful part of these numbers.

The MTBF formula is typically given in hours and represents either real-world analysis of actual failures in a population of repairable products over a period of time. Or it can be derived from empirical data derived from accelerated life testing in a lab environment. Either way, it provides a statistical metric that doesn’t pertain to one particular unit but, instead, to the universe of like products. A simple way we look at this number is as an indicator of reliability. That is something pretty useful that we can see with relatively simple math.

We look at MTBF as a tool used to understand the probability that a particular device will operate without needing repair for a particular period of time.

So, it’s fairly simple. The reliability is R(t) = e ^{–t/mtbf. }So, ‘t’ is the time period you are interested in (in hours) and MTBF is that number of hours derived and reported by the manufacturer.

If your restaurant hardware provider tells you their keypad has an MTBF of 100,000 hours, that doesn’t mean you can count on it lasting that long. If the metric is a good one, it will mean that the probability that it will last 3 years will be R(3) = e ^{-26280/100000 }= 0.7689 or 76.9%. Any one particular keypad from that manufacturer would have a @77% of lasting 3 years before it needed repair.

That provides something more meaningful to consider. You can have cool, innovative, or inexpensive technology roll out to your restaurants, but if it’s not supportable and too much of your time is being spent keeping it operational, it will be a failure for both your operations and support teams.

An interesting point to make is that (and you can do this math) if the time ‘t’ is equal to the MTBF itself, then the probability that ANY product reaches its MTBF will be only 36.8%!

Keep in mind that this isn’t a linear measure. What that means is that a keypad with a 100,000 hour MTBF will have a one year survival reliability of 91.6% and a keypad with a 2.5M hour MTBF would have a reliability of 99.7% over the same period of time. Though the MTBF is 25X, the reliability increased by only 8 points. Over time, the difference will become more apparent. The probability of survival at 5 years would be 64.5% and 98.3%, respectively.

**Don’t mistake MTBF for a warranty!** A warranty is a promise by the manufacturer. The MTBF calculation is a statistical measure not pertaining to any one particular unit but can useful in understanding the odds of a piece of hardware lasting for your desired period of time.

Obviously, environmental considerations and ‘uptime’ come into play when determining the life you can expect from any particular product. But using the MTBF as a reliability indicator instead of life cycle promise will help you gain a clearer understanding of what you can expect from the technology in your deployments.

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