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

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.