MTBF: the formula, and the assumption inside it

MTBF is mean time between failures: operating hours divided by the number of failures in that period. A pump that ran 4,000 hours and failed 5 times has an MTBF of 800 hours. It is a measure of reliability, and it is routinely misread as a lifespan.

The formula

MTBF equals total operating time divided by the number of failures. Use operating time, not calendar time. A machine that sat idle for six months did not accumulate reliability data during those months.

A worked example

Three identical air handling units ran 6,000 hours each last year, so 18,000 operating hours in total. Between them they failed 12 times. MTBF is 1,500 hours, or roughly once every ten weeks of running per unit.

That last translation is the useful part. Hours mean nothing to most people. "Each unit fails about every ten weeks of running" starts a conversation.

MTBF is not how long it will last

An MTBF of 100,000 hours does not mean the equipment lasts eleven years. It means that across a population, over the period measured, failures occurred at that rate. A component with a five-year design life can honestly carry a six-figure MTBF.

The assumption inside it

MTBF as a single number assumes a constant failure rate: that a machine is no more likely to fail today than it was last year. Real equipment does not behave that way. New equipment fails early from installation faults, then settles, then fails increasingly as it wears out.

Practical consequence: MTBF is most useful in the flat middle of an asset’s life. On brand new equipment and on equipment past its design life, the number will mislead you, and the direction of the error is different at each end.

MTBF and MTTF are not the same

MTBF is for things you repair and return to service. MTTF, mean time to failure, is for things you replace: bearings, lamps, sensors. Using MTBF for consumables is a common and harmless-looking error that makes replacement planning wrong.

What to do with it

Compare the same asset with itself over time, and compare identical assets with each other. A rising MTBF after an interval change is evidence the change worked. One unit with an MTBF a third of its three identical siblings is a bad actor and deserves an afternoon of somebody’s attention.