Which formula do you use to calculate MTBF?

a) MTBF = operating time / no. of failures in between,

where operating time = current date - date of first production. Of course, running hour is better if available.

b) MTBF = (start date of last failure - start date of first failure)/(No. of failures - 1). This leaves out the running time before the first failure and final failure from the caculation. Any advantage in doing this?

This message has been edited. Last edited by: Josh,

MTBF is usually applied to a group of similar equipment, for example all the pumps in a refinery. The formula for this is (NUMBER OF PIECES OF EQUIPMENT X TIME PERIOD) / NUMBER OF FAILURES DURING THAT TIME
Example:
1200 Pumps over one year with a total of 387 failures during the year.

(1200 X 12(months))/ 387 = 37 months MTBF

For a single item, it is just the time period / number of failures.
Example: Pump failed twice in one year, the MTBF would be 12(months)/2 = 6 months MTBF

Yes, Cheddar, that's what I think but somebody said the second formula above should be used because we cannot find the exact start and end dates. Also it's time between Failures, not between the start point and end point.

So I just want to confirm what formula others used to calculate their MTBF especially the published MTBF for pumps which can be increased from 1 year to 3 to 4 years.

speech to employee: You see those pumps out there. I expect 7 yrs service and will accept 5 and iffen you can't do it plan on traveling and meeting new people. One approach; training could be another.

Sam, how do calculate your 7 and 5 years? Do you calculate operating time by subtracting the running time before the first failure and running time after the last failure?

quote:

Originally posted by cheddar-caveman:
MTBF is usually applied to a group of similar equipment, for example all the pumps in a refinery.

How much similar is similar?

In your example, any pump at the facility gets in regardless:
* type: reciprocating, centrifugal, diaphragm, etc,
* size,
* or other characteristics?

Despite there is some controversy among peers with regard to what is understood by the acronyms MTTF and MTBF, the attached simple example illustrates the way I treat operating data since long with satisfaction from users and no misunderstandings along the way. From a management perspective, the data accommodates any failure mode. The method can be easily implemented in software and the indicators made available on a timely basis. Of course, many more indicators can be developed at the equipment level to reflect progress in the pursuit of objectives set by management.

Regards

This message has been edited. Last edited by: <Rui Assis>,

Indicators.xls (32 Kb, 198 downloads)

I wasn't being all that serious before. Wearing out the end of one's boot by kicking a_- may not be exactly correct.

Machines are like people, people are like snowflakes - no two alike. You may take an exact model pump and subject it to different environments and industries and come up with different failure rates. Sitting in an office coming up with statistical data doesn't do anything and I've never seen a computer pull a wrench although I have seen it done remotely.

Generally the weakest link is the equipments bearing. It is the first thing to fail usually. Rotors are generally rugged and up to the task as is the shaft and other components. What's the L10 life of the bearing? Do you realize it? You should! If not roll up your sleeves and get to work: why isn't it lasting longer? Maximum is 7 years and has L10 of 12 then its environment may be that 7 years MTBF is max life?????? But by getting out there and interacting with people and training on alignment and machinery setup will get you to max MTBF which will be reflected by smiling faces. It has to go beyond compiling data to get an attaboy. You'll know the MTBF when the machine has reached its max life maybe L10 +20%. Also your paycheck should increase.

Are your machines running longer now than they were two years ago?

I personally had first hand knowledge of a PdM program where a guy got a $15,000 bonus for a successfull program - he didn't have a program. In 6 years he had written 2 reports totalling 3 pages and no improvements but he had attaboys and pull or draft as the case may be.

I recently retained a contract where the head guy wanted to go with a cheaper service vendor. The techs said, don't screw with what works, we have planned scheduled maintenance and no call-outs and it's good that way. Still there. When I started failures were ~1.5 yrs and now ~6-9 on all. Of course lightning is hard to predict.

We've got so many acronyms now they are hard to keep up with. Seems there's 5-10 acronyms for every icon and it's growing. My soapbox is getting shaky about now!

L10 rating is largely... inadequate... even when just considering the fatigue question. Forget not the effect of contaminants, lubrication, etc, etc.

In the paper I presented at the CMVA last year (Canadian equivalent to VI), the early portion deals with fatigue. See the ugly red thumbnail in the last segment of http://vibra-k.com/?cat=15

To make a long story short: bearing fatigue life has more to do with contaminant inclusions within the steel than load and cycling. That is the principal reason why so many bearings which should fail from fatigue keep going well beyond the life estimate: low contaminant contents in the load zone.

As a rule, the design target is 50,000 or 100,000 hours for many machines. It can be higher for electric motors since the bearing size tends to be relative to shaft dimensions, and that last size will be based on force couple and torque issues rather than the very light rotor loads.

It doesn't mean that you would not cases with a more extensive life: they abound. But the previous values of 50K hours (standard) and 100k hours (by request) are good estimates.

Rui

Clarifications:

What do you mean by Constant time window? How is it equal to 6*25*8?

Why do you get no. of failures is 5? I thought the no. of failures is 7.

What do you mean by moving constant time window?

This message has been edited. Last edited by: Josh,

First we need to understand how do you plant to use MTBF in the first place, in my training the formula can be quite confusing and depending on your application : MTBF can be use for

MTBF by critical component (usually called mttf)

MTBF by sub-assembly - so we can pinpoint the worst sub assembly for a particular machine

MTBF by Machine - to determine the MTBF of a particular machine irregardless what part will fail

MTBF by process - so we can determine the part in the process that fail frequently

MTBF by group of machines - so we can determine the total MTBF

In the formula, MTBF = operating time / BDO
where BDO is Breakdown occurence or frequency of failure, Operating time is loading time - machine downtime

Hence machine downtime can vary a lot and is not only attributed to failures or breakdowns hence if your equipment is being converted to another product it is also a machine downtime.

Hence I would like to clarify and add to the
forumula

MTBF = (Loading Time - Machine DT attributed to
failures ) / Frequency of Breakdown

My Warm Regards,


Rolly Angeles
Teacher

I'm looking at MTBF of a machine and a group of similar machines.

From when do you start and finish calculating the loading time? From the first production date and to today if the machine is still runing ie not decommissioned yet?

MTBF is an indicator as to the reliability of a machine/group of machines. Where you "start" your recording is up to you, however, the longer the time period you can use, the more accurate the result will be. Go back to the beginning of your reliable breakdown data.
MTBF will also indicate the effectiveness of your maintenance practices and also any steps you might take to improve reliability.
For example, in a refinery where I was the Machinery Engineer, we had around 1200 pumps of one sort or another. It was an old refinery, around 1936, and their failure rate was horrific, with an MTBF of around 6 months.
I looked back over the failures and identified several key failures that kept repeating across the group. The most significant was that most of the pumps had grease lubricated, gear couplings. Another was that many of the pumps still had packing, leading to expensive shaft replacements etc. Another was poor alignment and there were many premature bearing failures.
Over the next couple of years I replaced all the gear couplings with membranes, upgraded all pumps to mechanical seals and bought a couple of laser alignment kits and trained the guys to use them properly. I also looked at the workshop practices for bearing changes and yes, they were "drifting" the new bearings onto the shafts. This to me is criminal! I bought a couple of oil baths and some heavy duty gloves.
The result of all this hard work, and yes expense, was that after four years the MTBF was at a very healthy 37 months!
At the same time I introduced a vibration monitoring programme along with lube oil analysis and thermography.
The most important result from all this was that Operations could plan long runs and we could schedule our maintenance to suite. Needless to say, there was no war between Operations and Maintenance in this refinery (Rolly!).

quote:

Originally posted by cheddar-caveman:
MTBF is usually applied to a group of similar equipment, for example all the pumps in a refinery. The formula for this is (NUMBER OF PIECES OF EQUIPMENT X TIME PERIOD) / NUMBER OF FAILURES DURING THAT TIME
Example:
1200 Pumps over one year with a total of 387 failures during the year.

(1200 X 12(months))/ 387 = 37 months MTBF

For a single item, it is just the time period / number of failures.
Example: Pump failed twice in one year, the MTBF would be 12(months)/2 = 6 months MTBF

I would like to know Time Period are only running pump (duty) if we have standby pump, that are including in number of piece of equipment?

Hi Aromatics Thailand.
Yes, you include the "total population" of your pumps. Your goal is that ALL pumps fail less often.
Our "standby" units were invariably steam-turbine driven, auto cut-in units so that, in the event of a power failure, we could keep running and these need to be just as reliable as the main units.
To take this discussion to the extreme, if ALL your equipment was only ever on stand-by, your MTBF would be "infinity", they'd never fail!

Josh,

The moving time window is just a convention or a rule to set the time span within which performance indicators (PI) are to be calculated. Its use is quite common in management performance control at large. It is set arbitrarily though it should be sufficiently long to accommodate several episodes (failures in the instance of MTTF or MTBF) – the more episodes the higher the accuracy.

I forgot to erase the product 6*25*8 in cell D21 but the product "6 month, 25 days per month and 8 hours per day" was in my mind at the time I created the example in Excel. I should simply have entered 1,200 hours straight in that cell. In this example, only the latest 5 failure matter because the other 2 are already out of the time window, being consequently omitted (or discarded).

Suppose you are using a time interval of 6 weeks (your time window). If you calculate PI´s, say, weekly, then the time window is said to move (or slide) one week at a time. As time advances, data pertaining to the seventh week back in time are abandoned and new data, this time pertaining to the very last week, are now considered in calculations.

When an equipment is under a process of change, it is common practice to give different weights to data – the older the lesser the weight (the weights must sum up to 1) – in order to get a picture that anticipates, in a certain way, the changes that are currently on the way. PI´s are, in this particular circumstance, calculated by a weighted average. By doing this, you attribute more importance (weight) to more recent events and less importance (weight) to older ones. In the end, if you plot the PI´s collected over time on a graph, you get a trend which might be quite informative on whether you are going the right way or not.

There is another method which was baptized "exponential smoothing" that automatically attributes less weight to older data, never "forgetting" any data, regardless of how old they might be. This method doesn't use the constant time window like the simpler methods I referred above and is less popular among practitioners.

Regards

This message has been edited. Last edited by: <Rui Assis>,

Rui

What is the purpose of arbitrarily setting the time span and moving the time span forward as time goes by? Is this idea of constant time window the same as constant moving average? Why not just calculate the mtbf since the first failure to today becasue you said the more the episode the higher the accuracy? I need to compare our mtbf values with similar industrial values and also for trending, so I need standard methods of calculating the mtbf.

Why do you we need to apply weightage to the data set for equipment under process of change? WHat change do you mean here? Is it modification, operational mode change, operating parameter change, etc?

This message has been edited. Last edited by: Josh,

Cheddar

Good job for increasing the mtbf for your refinery pumps.

Yes, we could just take the straight forward approach that you used i.e. by summing up operating time for all pumps (rgdless of pump types) divided by no. of failures in between (rgdless of failure modes). This composite or overall mtbf allows us to see the improvement from its trending.

For further simplication, did you take the operating time period to start from the year of the refinery being built which is 1936, rgdless whether any pumps being replaced over the years? Also look like you did not mentioned whether you subtracted any downtime from the operating time period.

However, I would like to follow a standard method to calculate the mtbf so that I can compare my figures with published mtbf data such as those for HP Bloch's book.

One more question, did you track the mtbf of the pump components individually such as bearings, seals, impellers, etc?

This message has been edited. Last edited by: Josh,

When I arrived at the refinery I realised that they had a reliability problem, particularly with the pumps. I took a long time and looked at the pump failures just for the previous five years, and came up with the 6 months. I then analysed the failures and started by addressing the biggest problem, the coulpings, then the next, the sealing and so on.
If you are looking at MTBF to help analyse the effectiveness of your maintenance practices, then you just need sufficient data to make your readings realistic. Obviously, the more data you have, the further back you can go with GOOD DATA, the more reliable your initial MTBF calculation will be.
So look at your records and see how far back you can go with a good degree of accuracy. Even if it's only a couple of years, it's a good starting point.
Then look at "what were the most common failures", and possibly ask !why were these failures happening (as I did with the bearings).
There's nothing management like better than seeing an improving MTBF.

Hello All,

I worked in a semiconductor before and we have a machine called a wirebond where it placed the goldwire in the circuit. One wirebond machine (my estimate) will compose of around 500,000 parts and most of them are electronic parts, (this machine is full of boards), and one station can have around 100 or more wirebonds.

We use to trend MTBF on a monthly basis for all machines total and a perfect MTBF for a month is 168 hrs.

Let me give you an example : (MTBF for 100 WB)

Jan. 49 hrs / mo
Feb. 63 hrs / mo
Mar. 46 hrs / mo
Apr. 31 hrs / mo

Note the trend is getting low, MTBF is not good

Level 1 : MTBF = 49 hrs / month for Jan.

Now we want to prepare an MTBF analysis

Level 2 : What particular Wirebond machines
contribute to the low MTBF

Level 3 : Once we pinpointed what particular
machines with low MTBF we go on to
what particular sub-assembly are
always failing

Level 4 : Then we identify the components
that usually fail

If you are just hired in your plant today, and you have no records of your failures for example then as suggested by some, you start calculating your MTBF today and wait till something fails.

So the start time is where you start to actually compute your MTBF. Now in our case where we compute the MTBF monthly so we can see the trend of our line/station. What if there are no failures, then the denominator for frequency of failures is zero which gives an MTBF of infinity. We have 2 options.

In case where we achieve perfect MTBF of 168 hours a month, then we assume a denominator of one, since anything you divide by 1 will give you the numerator.

Another option is prolong the duration of MTBF until 1 machine will fail, however using this option you cannot trend MTBF on a monthly basis.

Now for a group of machines you have 3 options to get the total MTBF :

1st Add the total MTBF

MTBF = (36 + 45 + 74 + 90) hrs

2nd You may get the average MTBF

MTBF = (36 + 45 + 74 + 90) / 4

3rd you may get the percentage MTBF

MTBF = (36 + 45 + 74 + 90) / 4 x 168 hrs

what is important will be the trend of the MTBF if this would be monthly, quarterly, semi-annually or yearly and it must be increasing.

My Warm Regards,


Rolly Angeles
Teacher