MTBF Definition

[Anonymous]

The definition of MTBF is often misunderstood in the technical community. I frequently have to do a self review to clear my understanding. This is one of those times.

My current confusion is regarding MTBF and the use of the 66 2/3% failures figure. I interpret MTBF as the average operating time between failures for a unit. This number will almost always surpass useful life of the product, and is a general measure of reliability pertaining to random failures only. I have heard people use the 66 2/3% figure to say that the MTBF number is the time it takes for two-thirds of the population to fail. I disagree. I say 66 2/3% of the units must fail to have an accurate MTBF number. This is generally for demonstrated testing, but could be used for actual field data as well.

Is this correct?

[RS Support]

You are right the term MTBF can be misleading and it is a lousy metric when it comes to reliability (see the Reliability Edge newsletter article at http://www.reliasoft.com/newsletter/2Q2000/mttf.htm ). Having said that let me try to answer your question.

The misunderstanding and misuse comes from years of using the exponential distribution in reliability analysis. The exponential distribution is easy to work with (thus it has been widely used), however it is rarely appropriate for most situations since it assumes a constant failure rate.
Now if you can assume a constant failure rate (i.e. use an exponential distribution) you will find out that regardless of the definition you use for the MTBF (i.e. Mean Time Between Failures, Mean Time Before Failures, Mean Time To Failure) the meaning is identical (since again your rate is constant). In this case you will find out that for the exponential case (ONLY) this number corresponds to the time by which 63.2% of the units will fail (or are expected to fail if making predictions).

Now, if you assume any other distribution (with a non-constant failure rate, i.e. Weibull, Lognormal, Gen-Gamma etc.) – which you should in most cases if you want your analysis to be right – none of the above is valid. In these cases we refer to the mean life (see http://www.weibull.com/LifeDataWeb/mean_life_function.htm), and the percentages can vary widely depending on parameter values.

[Krasin]

Is it true that 66 2/3% of the units must fail to have an accurate MTBF number? And how many units we have at the beginning?

[RS Support]

First: Where are you getting the 66 2/3 number. See http://www.weibull.com/LifeDataWeb/probability_plotting_example_exp.htm for derivation of 63.2%.
Second: Confidence intervals can be utilized to quantify the ‘accuracy’ of the number (whether that is the MTBF, B10 etc). Thus, depending on the desired confidence different sample sizes can be used and multiple censoring schemes utilized. In other words there are many options on what the sample size can be and how long you want to run the test as well as how many units to run to failure
ReliaSoft’s Weibull++ ( see http://www.reliasoft.com/Weibull/features.htm )includes a utility (DRT) that can me utilized to answer these questions. Additionally ReliaSoft’s SimuMatic (see http://www.weibull.com/freetools/index.htm ) tool can be used to simulate test plans and provide answers as to the accuracy.

[Karl Martin]

L10 compared to MTBF

Please help me understand why L10 numbers are more often used than MTBF numbers in the fan industry (using ball bearings, from a statistical perspective. Secondly since MTBF is so predominant in the electronics industry how do one convert the L10 data to an MTBF number (wich is usually required), using what distribution? Appreciate any help I can get to understand this.

[RS Support]

I assume L10 numbers are the same as B10 numbers, which are the time by which 10% of the units will fail. This number is based and computed from an assumed distribution. When using Weibull one computes time by which 10% of the units will fail.

On the MTBF question this usually refers to the mean-time-to-failure. If one uses a distribution such as the Weibull distribution, this value is not sufficient in describing the distribution – and by itself is often a poor metric. In other words under a Weibull assumption B10 gives me the time by which 10% of the units will fail. The mean time alone does not tell me the percent of units that will fail by what time.
So on your last question, as to “how to convert between the two” the answer is that you cannot convert if you assume a distribution with a non-constant failure rate, and the only knowledge that you have is of the mean. If you assume a constant failure rate (a poor assumption) then the exponential distribution can be used. In doing so then, and ONLY under the exponential assumption, B(10)=(-ln(90)*Mean)

[donald a miller]

12 years on the Minuteman weapon system; 10 years on AWAC and other programs involving failure rate predictions. (reired boeing areospace eng.)There is no evidence that hardware has any generic failure characteristic. In my 36 years I have never witness a single "random failure". I have dozens of stories which show conclusively that there is no intelligence in so called component failure rate. Prediction at the module level are always unrelated to reality. This dimension of reliability analysis (failure rate predictions) should be eliminate from the engineering communkity

[Pantelis]

Agree …
Using “so called generic component failure rates” for predictions is a poor way to do reliability analysis.

[Paul Booth]

I understand that the L-10 life refers to the lubrication life of the bearing. The rational is that the lubricant life is now the dominant life limiting mechanism. The B10 life, the inherent life of the bearing itself, has been so extended by elimination of nitride inclusions (vacuum processing of the steels) that lubricants are the major issue. This was all word-of-mouth from some bearing engineers. Of course, dirt, misapplication, and mishandling are usually (by far) the principle culprits in killing bearings.