The Elsmar Cove Forum The Anomaly of Calculating MTBF from Reliability
 Forum User Name Keep Me Logged In Password
 Register Photo Albums Blogs FAQ Social Groups Calendar Search Today's Posts Mark Forums Read

 Elsmar Cove Forum Visitor Notice(s) It is the Memorial Day holiday weekend in the US so activity in the forum will be slow through the weekend. Since Memorial Day is observed on Monday 27 May this year, I expect activity here to be somewhat slow. Normal activity in the forum will start to pick up again next week. Please see the forum Calendar for more information on the holiday.Logged In Registered Members can click the red X to close this notice box.

 Elsmar Cove Forum Sidebar @import url(http://www.google.com/cse/api/branding.css); Custom Search Monitor the Elsmar Forum Monitor New Forum Posts Follow Marc & Elsmar Elsmar Cove Groups Sponsor Links Donate and \$ Contributor Forum Access Sponsored Links Courtesy Quick Links Links that Elsmar Cove visitors will find useful in your quest for knowledge: Howard'sInternational Quality Services Atul'sSymphony Technologies Marcelo Antunes'SQR Consulting Bob Doering'sCorrect SPC - Precision Machining NIST's Engineering Statistics Handbook IRCA - International Register of Certified Auditors SAE - Society of Automotive Engineers Quality Digest Portal IEST - Institute of Environmental Sciences and Technology ASQ - American Society for Quality

#1
26th May 2007, 05:25 AM
 itKiwi Inactive Registered Visitor   Registration Date: May 2007 Location: near Milan, Italy Posts: 1 Thanks Given to Others: 0 Thanked 0 Times in 0 Posts Karma Power: 25 Karma: 10
The Anomaly of Calculating MTBF from Reliability

I would like some help in practical, non-numeric, terms to explain the following “anomaly”.

We all know that Reliability, A = MTBF /(MTBF + MTTR)

So, the higher(longer) the MTBF and the lower(shorter) the MTTR, the better (more 9's) our Reliability.

At the end of our spreadsheet, we have calculated the reliability of our complex system including all the series and parallel elements, redundant elements, etc. A = 0.9999999, etc. Great.

Now, the client wants to know the MTBF of his system. OK. We rearrange the above formula, and we get,

MTBF = A x MTTR/(1-A)

What's this ? MTBF is directly proportional to MTTR, which means the longer my MTTR, the better my MTBF !!! This is contrary to the original basic concept, that a short MTTR is best.

How do we explain this to a non-numeric client ?

It also raises the question; “Which MTTR do I use in this system calculation ? In practical terms, one would think it ethical to use the longest MTTR, (gives us the lowest Reliability). However, this gives us our best system MTBF.

Any answers or discussions on these two points would be appreciated.

Thanks.

#2
26th May 2007, 11:15 AM
 Tim Folkerts Forum Moderator   Registration Date: Sep 2003 Location: Kansas, USA Age: 50 Posts: 975 Thanks Given to Others: 29 Thanked 351 Times in 211 Posts Karma Power: 148 Karma: 5804
Re: The Anomaly of Calculating MTBF from Reliability

itKiwi,

The variable A is typically called the Availability. Reliability is the probability of working at a particular time under specific circumstances. Availability typically considered a constant (a long-term average of how much of the time the system is available); reliability decreases with time.

The two are obviously related, but not the same. A common function to express reliability is
R = exp(-t/MTTF)
but the actual function to use depends on the situation.

Quote:
 MTBF = A x MTTR/(1-A) What's this ? MTBF is directly proportional to MTTR, which means the longer my MTTR, the better my MTBF !!! This is contrary to the original basic concept, that a short MTTR is best.
Ah, but MTBF is not directly proportional to MTTR. MTBF also depends on A, which in turn depends on MTTR. So when you change, MTTR, you also change A.

With a little algebra, it is easy to show that the equation above reduces to
MTBF = MTFB

In other words, MTBF in independent of MTTR, as would be expected.

If you did want to use this equation to calculate to MTBF, you would need the MTTR of the system. This would be some sort of average of the MTTR for each element combined with the probability of each component actually failing.

To calculate the MTBF, the best answer is probably just to go back to the original numbers. If you know the MTBF for each element and the appropriate series & parallel combinations, you should be able to find the overall MTBF directly.

Tim F
__________________
To wonder is to begin to understand.
 Thank You to Tim Folkerts for your informative Post and/or Attachment!

 The Elsmar Cove Forum The Anomaly of Calculating MTBF from Reliability

 Bookmarks

 Visitors Currently Viewing this Thread: 1 (0 Registered Visitors (Members) and 1 Unregistered Guest Visitors)

 Forum Posting Settings You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is Off Forum Rules

 Similar Discussion Threads Discussion Thread Title Thread Starter Forum Replies Last Post or Poll Vote jag53 Reliability Analysis - Predictions, Testing and Standards 8 24th July 2008 04:41 AM bucky88 Reliability Analysis - Predictions, Testing and Standards 1 3rd November 2007 05:44 AM jaz732 Reliability Analysis - Predictions, Testing and Standards 1 23rd April 2007 02:18 PM jag53 Reliability Analysis - Predictions, Testing and Standards 1 31st May 2006 06:52 AM jag53 Reliability Analysis - Predictions, Testing and Standards 4 17th April 2006 08:20 AM

The time now is 01:38 AM. All times are GMT -4.