# MTTR, MTBR, Failure Rate, Availability and Reliability

The objective of this post is to bring clarity in understanding the two often confused terms viz, Availability and Reliability, by explaining in simple perspective for the purpose of understanding by a common maintenance man.

Let’s try to understand through this picture.

This is the time-line of a particular Equipment where U is Operating time (Uptime in Hrs), D is Repair time (Downtime in Hrs). A total period of 6 weeks has been taken for analysis.

Two cases have been depicted here .

Case1:

No. of Failures  = 6 (Denominator for MTTR, MTBR Calculations)

Total Uptime  = U1 + U2 +U3 + U4 + U5 + U6 + U7.  = Say 900 Hrs.

Total Downtime = D1 + D2 + D3 + D4 + D5 + D6.     = Say 108 Hrs.

We know that MTTR  (Mean Time to Repair in Hrs) =  ( D1 + D2 + D3 + D4 + D5 + D6 ) / 6 = 18 .

Similarly MTBR (Mean Time Between Repairs in Hrs) = ( U1 + U2 +U3 + U4 + U5 + U6 + U7 ) / 6 = 150 .

Now,

Equipment Availability (%) is: UpTime / Total Time   = (900 / 1008)  * 100  =  89.2

Another formula for Equipment Availability in practice is   [MTBR / (MTTR + MTBR)] * 100   = (150 / 168 )*100   = 89.2

Case2:

No. of Failures  = 2 (Denominator for MTTR, MTBR Calculations)

Suppose here too we get the same total values like:

Total Uptime  = U1 + U2 +U3  = Say 900 Hrs

Total Downtime = D1 + D2 =  Say 108 Hrs

MTTR (H) =  ( D1 + D2) / 2 = 54 .

MTBR (H) = ( U1 + U2 + U3) / 2 = 450 .

Equipment Availability (%) is: Uptime / Total Time   = (900 / 1008)  * 100  =  89.2

Through other formula for Equipment Availability :  [MTBR / (MTTR + MTBR)] * 100   = (450 / 504 )*100   = 89.2

We have seen the Availability, Now let’s see the Reliability. What is Reliability?

Reliability can be broadly defined as the probability that an Equipment will perform its intended functions continuously for a specified duration.

How do we measure Reliability

1. MTBR (H) value is a direct measure of Reliability. More the MTBR more is the Reliability.
2. The Failure Rate (ʎ): In simple expression this can be calculated as No of Failures / Total Time

Now Let’s tabulate the results

Case Duration (H) Failures Downtime (H) Availability (%) MTBR (H) Failure Rate (ʎ)
1 1008 6 108 89.2 150 0.00595
2 1008 2 108 89.2 450 0.00198

We have clearly seen that for the same amount of Equipment Availability, Equipment Reliability changes drastically. So our Equipment in Case2  is more reliable.

Here I want to share a screen-shot ( used in one of my previous documents ) . This has a realtime data of an Equipment with performance relevant to present discussion. See this picture.

The Equipment03 in Year 1314 has Availability of the order 99.58% but lowest Reliability (MTBR) of 95.57 Hrs. Compare this with the 2nd line: Equipment02 has lowest Availability 99.39% but good Reliability (MTBR) around 400 Hrs.

So, we understand that

A Highly Reliable Machine is Highly Available Machine too, but the converse need not be true.

Lastly, let’s try to understand the practical significance of the term Reliability. In process industries if a chain of machines run without any problem for several hours then a stage comes for the final equipment deliver the finished product. Often paper industry is quoted  as an example. If a machine breaks down like case1, the finished paper will never come-out of the paper machine.

Then, a question might arise, that ‘Why Reliability can not be directly based on the No. of Failures?’  The answer could be ‘Yes, it is ! But it is calculated as a function of No. of Failures per a Specified period , where this period might differ from process to process and hence the acceptability of Reliability Index‘.

Hope members will be benefited by this post .

Thank you & Regards

KJogeswaraRao

Note:

The formulae used here in this post are in their simplest form for understanding purposes. They might not exactly match with those mentioned in different contexts like OEE calculations etc.

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Another good document, thanks for sharing Sir...

K Jogeswara Rao
Blog Post Author

Thank you Kalyan,

awesome document.... thank you so much sir

K Jogeswara Rao
Blog Post Author

Thank you hitendra for your encouraging words

hi

Clearly I am running out of words to appreciate your efforts in clarifying the doubts and the amount of time you are spending for the same

From behalf of all our SDN members many thanks for the same and hope the same will continue.

Regards

Thyagarajan

K Jogeswara Rao
Blog Post Author

Dear Sir,

I am grateful to you, for posting the biggest compliment ever. Active participation started from June last year, with sole idea in mind that 'Let me return some to SCN'. Initially encouraged by you (I do not forget) afterwards by space itself and also the moderators.

Best Regards

Jogeswara Rao K

Dear Jogeswara,

thanks for putting so much effort in this oustanding business case description.

My compliments, you achieved again to outline a rather complex topic in a well structured and understandable ( ! ) way.

I'm sure many followers like me, can take some inspirations from your documents and try to adapt the shown functions in their own company landscape.

Keep going!

Bye,

Patrick

K Jogeswara Rao
Blog Post Author

I constantly feel your presence and resounding inspiring words towards such work, though you do not communicate through alphabets. But when you find time to do so, I am really glad. Thank you very much for your motivating words Patrick!

Bye

Jogeswara Rao K

K Jogeswara Rao
Blog Post Author

DS,

Thansk again.

Dear Rao,

The document is really nice and simple.

Kind regards,

K Jogeswara Rao
Blog Post Author

Thanks Muhammed Ali Asim, for your review.

Hi Jogeswara Rao,

Really good document explained complex thing in simple and easy to understand manner .Please give Tc code where we can see availability percentage

Regards

Anand

K Jogeswara Rao
Blog Post Author

Anand,

That was a deveopment. No standard Tcode is there for Availability % in SAP. As the formula indicates it will be easy to compute through Infoset Query or a simple ABAP program using table S070 (Inostructure).

Thank you for the review.

Jogeswara Rao K

Very Nice Document to understand MTTR and MTBR.

Thank you very much sir such a nice document.

Thanks ,

Sunil Boya

K Jogeswara Rao
Blog Post Author

Thank you Sunil

KJogeswaraRao

Jogeswara,

Very nice document... very helpful and self explanatory.

Your document always encourage me for trying new areas in Plant Maintenance.

You are directly/ indirectly a role model to me.

Thank you so much.

Chin2.

K Jogeswara Rao
Blog Post Author

Chintan,

I feel honored to receive such appreciation.

Thank you

Regards

Jogeswara,

You really deserve that sir.

Chin2.

Nice document, I agree with all other members , you have contributed immensely to SCN. WHEN CREDIT IS DUE IT  MUST BE GIVEN!!

K Jogeswara Rao
Blog Post Author

Hello Taurai Chitsiga,

That is very kind of you.

Thank you for the great compliments and

Best Regards

KJogeswaraRao

Thank you for this document

K Jogeswara Rao
Blog Post Author

My pleasure Christophe Sturzel and thanks for appreciation.

Thank you so much sir for your valuable explanation.... it helped me a lot

K Jogeswara Rao
Blog Post Author

Hello Govardhan,

I am glad this post helped you. Thank you for the compliments.

Regards

KJogeswaraRao

Thank you very much sir for providing such a valuable document.

K Jogeswara Rao
Blog Post Author

Thank you pramod !

Regards

KJogeswaraRao

Dear Mr Jogeswara,

Keep it up for another one document,Really its very important.

Regards.

Swapnil

K Jogeswara Rao
Blog Post Author

Thank you swapnil ,

Very glad to know that the content is useful to you.

Regards

KJogeswaraRao

Sir,

it s very nice document to understand availability and reliability of machine.

Thanks sir for sharing such valuable documents,

Regards,

Ganesh

K Jogeswara Rao
Blog Post Author

My pleasure.ganesh,

And thank you

Thank you Mr Jogesswara Rao. It is an awesome explanation of reliability and Equipment Availability.

Best regards,

N.Nagaraju

K Jogeswara Rao
Blog Post Author

Thank you Nagaraju

Short of words ....

Good post Sir,

Kindly keep posting such knowledge.

thanks.

Kunal

K Jogeswara Rao
Blog Post Author

Thank you Kunal !

You can have my other contributions here: MyContent

Regards

KJogeswaraRao

Thank you for providing the link I shall check all your sharings!!!

Regards,

Kunal

Dear Sir.....your document made the concept really simple and understandable. I always look forward to your documents. Thanks, Piyush.

Mr Rao, the document is well articulated and cogent, thanks for sharing

regards

Kaushik

K Jogeswara Rao
Blog Post Author

Thank you Mr. Kaushik

Regards

KJogeswaraRao

Very Nice and clear explanation sir.

Regards

Pavan

K Jogeswara Rao
Blog Post Author

Thanks Pavan

Hi,

Thanks for the clear explanation. There is, however, something I don't understand still. You state that "A Highly Reliable Machine is Highly Available Machine too, but the converse need not be true.".

However, since

Reliability = MTBR and

Availability =  [MTBR / (MTTR + MTBR)] * 100

I would think that all it takes is a long MTTR to make a highly reliable system have poor availability. It seems to me that, in principle, Reliability and Availability are not necessarily related.

Could you explain if I've misunderstood the definitions?

Regards,

Han.

K Jogeswara Rao
Blog Post Author

You are right in saying that Availability and Reliability not necessarily be related. This is a simple post on the Reliability concept. Actual Reliability through OEE calculations are very complex. Repeating the same thing, a highly Available machine need not be always Reliable, because the Reliability has got dependence on the Production Process.  In descrete manufacturing there might not be big difference, but in  process industries where machines need to perform without fail for sometime to get the product delivered  has got a big dependency.

As I said if context like above is not taken into account, the more MTBR or least number of Breakdowns can be a measure for Reliability.

Regards

KJogeswaraRao

Thank you sir, for such a valuable information

Regards,

Vijaya

Hello,

Thank you for posting valuable information.

What should be ideal ratio/relationship between MTBR and MTTR for process industries, which will take care of ''conservation of spare and man hours required for breakdown maintenance.''

K Jogeswara Rao
Blog Post Author

Thank you.

The simple answer is: 'It depends' . After knowing these concepts, it is you to establish local relationships as per your process demands.