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The MTBF calculation is widely used to evaluate the reliability of parts and equipment, in the industry is usually defined as one of the key performance indicators. This short article is intended to demonstrate in practice how we can fool ourselves by evaluating this indicator in isolation. [Read more…]
Guest post by Msc Teofilo Cortizo
The term MTBF (Mean Time Between Failures) within maintenance management, it is the most important KPI after Physical Availability. Unlike MTTF (Mean Time To Failure), which relates directly to available equipment time, MTBF also adds up the time spent inside a repair. That is, it starts its count from a certain failure and only stops its counter when this fault was remedied, started and repeated itself again. According to ISO 12849: 2013, this indicator can only be used for repairable equipment, and MTTF is the equivalent of non-repairable equipment.
The graphic below illustrates these occurrences:
Calculating the MTBF in the Figure 01, we have added the times T1 and T2 and divided by two. That is, the average of all times between one failure and another and its return is calculated. It is, therefore, a simple arithmetical calculation. But what does it mean?
Generally speaking, this indicator is associated with a reliability quality of assets or asset systems, and may even reach a repairable item, although it is rarer to have data available to that detail. Maintenance managers set some benchmark numbers and track performance on a chart over time. In general, the higher the MTBF the better, or fewer times of breaks and repairs over the analyzed period.
Once we have fixed the concepts, some particularities need to be answered:
1. Can we establish periodicity of a maintenance plan based on MTBF time?
2. Can I calculate my failure rates based on my MTBF?
3. Can I calculate my probability of failure based on my MTBF?
4. If the MTBF of my asset or system is 200 hours, after that time will it fail?
It is interesting to answer these questions separately:
The MTBF is an average number calculated from a set of values. That is, these values can be grouped into a histogram to generate a data distribution where the average value is its MTBF, or the average of the data. Imagine that this distribution follows the Gaussian law and we have a Normal curve that was modeled based on the failure data. The chart below shows that the MTBF is positioned in the middle of the chart.
In a modeled PDF curve (Probability Density of Failure) the mean value, or the MTBF, will occur after 50% of the failure frequencies have occurred. If we implement the preventive plan with a frequency equal to the MTBF time, it will already have a 50% probability of failing. Therefore, the MTBF is not a number that indicates the optimal time for a scheduled intervention.
Considering the modeling of the failure data to calculate the MTBF, it´s only possible in the exponential distribution fix a value where the failure rate is the inverse of the MTBF:
MTBF = 1 / ʎ
In this distribution, the MTBF time already corresponds to 63.2% probability of failure.
Any modeling other than exponential, the failure rate will be variable and time dependent, so its calculation will also depend on factors such as the probability density function f(t) and the reliability function R(t).
ʎ(t) = h(t) = f(t) / R(t)
Although the exponential distribution is the most adopted in reliability projects, which would generate a constant failure rate over time, most of the assets have variations within their “bathtub curve”, as exemplified by Moubray:
This means that the exponential expression is not best suited to reflect the behavior of most assets in an industrial plant.
As seen above, only in the exponential distribution has a constant failure rate that can be calculated as the inverse of the MTBF. In this case, yes, we can calculate the probability of failure of an asset using the formula below:
f(t) = ʎˑexp(-ʎt)
For other models where the failure rate depends on the time, it is only possible to calculate the probability of failure through a data modeling and determination of a parametric statistical curve.
The question is, what exactly does that number mean? It was shown that MTBF isn´t used as a maintenance plan frequency. According to the items explained above, this time means nothing as it is not comparable to its history over the months. If the parametric model governing the behavior of the assets in a reliability study is not determined, the time of 200 hours has no meaning for a probability of failure. In the case of the MTBF provided by equipment manufacturers is different, through life tests they determine exponential curves and thus calculate the time in which there will be 63.2% of sample failures.
I hope the article has helped us to reflect on the definitions of an indicator that is both used but also so misunderstood within industrial maintenance management.
Msc Teofilo Cortizo
Reliability Engineer
An Elusive Product Life Time DefinitionThe following note and question appear in my email the other day. I had given the definition of reliability quite a bit of thought, yet have not really thought too much about a definition of ‘product life time’.
So after answering Najib’s question I thought it may make a good conversation starter here. Give it a quite read, and add how you would answer the questions Najib poses. [Read more…]
Let’s think of this as a crowdsourced project. The first version of this book is a compilation of NoMTBF.com articles. It lays out why we do not want to use MTBF and what to do instead (to some extent).
With your input of success stories, how to make progress using better metrics, and input of examples, stories, case studies, etc. the next version of the book will be much better and much more practical. [Read more…]
The Army Memo to Stop Using Mil HDBK 217Over 20 years ago the Assistant Secretary of the Army directed the Army to not use MIL HBK 217 in a request for proposals, even for guidance. Exceptions, by waiver only.
217 is still around and routinely called out. That is a lot of waivers.
Why is 217 and other parts count database prediction packages still in use? Let’s explore the memo a bit more, plus ponder what is maintaining the popularity of 217 and ilk. [Read more…]
The Damage Done by Drenick’s TheoremHave you ever wondered by we use the assumption of a constant failure rate? Or considered why we assume our system is ‘in the flat part of the curve [bathtub curve]’?
Where did this silliness first arise?
In part, I lay blame on Mil Hdbk 217 and parts count prediction practices. Yet, there is a theoretical support for the notion that for large, complex systems the overall system time to failure will approach an exponential distribution.
Thanks go to Wally Tubell Jr., a professor of systems engineering and test. He recently sent me his analysis of Drenick’s theorem and it’s connection to the notion of a flat section of a bathtub curve.
Wally did a little research and found the theorem lacking for practical use. I agree and will explain below. [Read more…]
The Importance of the Discussions around MTBF QuestionsThe best way to help others understand and stop using MTBF is to engage them in a discussion. I get questions concerning MTBF or reliability a few times a week. I attempt to answer each and every one, plus adding a follow up question or two.
In person or online, ask and answer MTBF questions. You not only improve your understanding of MTBF and reliability, you improve your still at tell stories to help affect change across your industry. [Read more…]
The MTBF Stories You Tell Can Cause ChangeStories communicate well. We have been telling stories long before the invention of writing, or the internet. The MTBF stories we tell communicate our ideas, suggestions, and recommendations.
There are a differences between good and poor stories. How you tell a story matters as well as the subject of the story. Now, MTBF stories may not be the most thrilling or entertaining, yet there are stories on MTBF topics that matter.
Let’s explore using the power of story to cause those around us to better understand and avoid the use of MTBF. [Read more…]
Trying to Respond to All Questions and Comments Concerning MTBFOver the past couple of days, like most days, have received questions and comments concerning MTBF. I do try to respond to all questions and acknowledge the comments.
Glad to help in anyway I can, so please feel free to send me your questions. Certainly do appreciate the supporting comments, or any comments for that matter.
Let’s take a look a few such discussion that occurred over the past two days. [Read more…]
When Asking for Reliability Information Do You Ask for MTBF?Our customers, suppliers, and peers seem to confuse reliability information with MTBF. Why is that?
Is it a convenient shorthand? Maybe I’m the one confused, may those asking or expecting MTBF really want to use an inverse of a failure rate. Maybe they are not interested in reliability.
MTBF is in military standards. It is in textbooks and journals and component data sheets. MTBF is prevalent.
If one wants to use an inverse simple average to represent the information desired, maybe I have been asking for the wrong information. Given the number of references and formulas using MTBF, from availability to spares stocking, maybe asking for MTBF is because it is necessary for all these other uses. [Read more…]
What Price Providing MTBF?If your livelihood consists of providing MTBF upon request, what good is your service?
Sure you earn some money, yet did the customer receive value in the transaction? As you know, or should know, MTBF is so commonly misunderstood that it is likely the customer confused what they want, reliability, with MTBF. Providing them MTBF does not answer their question.
Worse the customer thinks they got something of value and blithely heads off with rather meaningless information.
My contention is by providing MTBF because customer’s request it is wrong. We know better. Those performing predictions, doing data analysis, and other reliability engineering work know that MTBF is a faulty and rather meaningless metric often confused with reliability, R(t). (probability of success over a duration). [Read more…]
How Do You Judge a Reliability Book?By it’s cover no doubt. The title and cover are important, this is true. When you judge a reliability book we often first see and evaluate the cover.
The author? Do you buy the book based on who wrote or edited it?
Do you have a quick scan or check for key features before you add the book to your library? I’m curious how you select a book to use a reference for your work. The books we read and use for work shape our work, thus it’s important to have the right works at our disposal. [Read more…]
Accelerated Testing: Statistical Models, Test Plans, and Data Analyses by Wayne NelsonPublished by John Wiley & Sons in 1990 this 601 page book started my career in reliability engineering.
I didn’t know it at the time in the early ‘90s, yet my assigned task to create an accelerated test for a new product would spark an interest in cheating time. Wayne’s book helped make that first accelerated test successful.
The Accelerated Testing book is a compendium of different ways to conduct accelerate tests with a focus on the planning the test and analyzing the data. Wayne is a reliability statistician, and as he will tell you, not an engineer. Thus the book tends to focus on the math.
What I enjoy about the book is the math is not the dry academic derivation driven material, it is full of examples and immediately useful formulas. There is just enough explanation to help the math wonks pursue their interest, and enough practical information to allow engineers to develop and conduct meaningful experiments. [Read more…]
Can You Have a High MTBF and Low Reliability?As regular readers know, MTBF by itself is misleading. When representing actual data it can be deceptive as well. Just because you have a high MTBF value doesn’t mean it is reliable.
In a previous article, 10 Reasons to Avoid MTBF, I mentioned that it is possible to have a relatively high MTBF value when the actual reliability is low. Ashley sent me the following note:
Hi Fred, i love reading your articles they are very informative. I have a question about something you said in a comment which i am hoping you will be able to clarify for me. You said products with higher MTBF can actually be less reliable than products with a lower MTBF
I have tried to find information on how this is possible online, and tried to do the maths myself to make this happen but i have to admit i am struggling.
No worries, Ashley, let’s work out an example to illustrate what I meant. [Read more…]
Here is a Challenge: Life Data AnalysisSome years ago a few colleagues compared notes on results of a Weibull analysis. Interesting we all started with the same data and got different results.
After a recent article on the many ways to accomplish data analysis, Larry mentioned that all one needs is shipments and returns to perform field data analysis.
This got me thinking: What are our common methods and sets of results when we perform life data analysis? [Read more…]