# MTBF and MTTF Definition(s)

Recently Glenn S. asked if I had a reference for clear definitions of MTBF and MTTF. After a bit of a search I sent him a definition or two, meanwhile he gathered a few more.

They are all basically the same, with some slight differences. What is interesting to me is the amount of variability in the interpretation and understanding.

Here’s the list Glenn collected:

This is what I’ve compiled thus far on definitions for MTTF and MTBF. There seems to be some variations in the definitions.

From a 1974 paper on DTIC.

Mean Time Between Failures (MTBF): The average operating time expected between failures in a population of identical components. This measure has meaning only when we are discussing a population where there is repair or replacement.

Mean Time To Failure (MTTF): The average operating time expected before failure of a component which is not repaired or replaced. This is simply the average time to failure of “n” units, i. e., the sum of “n” individual unit times to failure divided by “n” units.

MIL-HDBK-721 and MIL-STD-109 (Both Rescinded)

MEAN-TIME-TO-FAILURE (MTTF): A basic measure of reliability for non-repairable items: The total number of life units of an item divided by the total number of failures within that population, during a particular measurement interval under stated conditions.

MEAN-TIME-BETWEEN-FAILURE (MTBF): A basic measure of reliability for repairable items: The mean number of life units during which all parts of the item perform within their specified limits, during a particular measurement interval under stated conditions.

Internet PDF File of definitions

Mean Time to Failure. MTTF is the expected value (mean) of an item’s failure-free operating time. It is obtained from the reliability function R(t) as MTTF = ò R(t) dt, with TL as the upper limit of the integral if the life time is limited to TL (R(t) = 0 for t > TL ). MTTF applies to both non repairable and repairable items if one assumes that after a repair the item is as-good-as-new. If this is not the case, a new MTTF (MTTFsi starting from state Zj) can be considered (Table 6.2). An unbiased (empirical) estimate for MTTF is MTTF = (tl + … + tn )/n, where tl + … + tn are observed failure-free operating times of statistically identical, independent items.

MTBF= 1/l. MTBF should be reserved for items with constant failure rate A. In this case, MTBF = 1/ l is the expected value (mean) of the exponentially distributed item’s failure-free operating time, as expressed by Eqs. (1.9) and (A6.84). The definition given here agrees with the statistical methods generally used to estimate or demonstrate an MTBF. In particular MTBF= T/ k, where T is the given, fixed cumulative operating time (cumulated over an arbitrary number of statistically identical and independent items) and k the total number of failures (failed items) during T. The use of MTBF for mean operating time between failures (or, as formerly, for mean time between failures) has caused misuses (see the remarks on pp. 7, 318, 327,416) and should be dropped. The distinction often made between repairable and non-repairable items should also be avoided (see MTTF).

Electropedia (http://www.electropedia.org/)

Mean Operating Time Between Failures – MTBF the expectation of the operating time between failures

Mean Time to Failure – MTTF the expectation of the time to failure

If you know other references with clear definitions I sure would like to know about them.

I am an experienced reliability engineering and management consultant with my firm FMS Reliability. My passion is working with teams to create cost-effective reliability programs that solve problems, create durable and reliable products, increase customer satisfaction, and reduce warranty costs.

## 4 thoughts on “MTBF and MTTF Definition(s)”

1. Thanks Fred for that post. Normally I would skip over a post on definitions if I already knew. But the contradictions peaked my interest, and I am glad you did. Because I learn something new, MTBFc. Which is basically what my article http://bin95.com/plc-controller-failure-rate.htm was calling for, a Cyclic MTBF, wich is defined as “MTBFc”. Too bad the vendors don’t use MTBFc more.

1. Hi Don,

Sure, we can use time in hours or other units, cycles, pages printed, whatever to denote the passage of time.

Be careful what you wish for though. The current use of MTBF and similar measures is so poorly understood and used it is not something we should encourage. Rather use percent surviving a some period of time (or cycles). For example, 90% of motors survived 2 years with our failure.

Cheers,

Fred

2. basant kukreti says:

best learning experience to novice like me

3. Grace says:

Thanks fred very useful article