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Forum: Reliability & Maintainability Questions and Answers

Topic: Reliability & Maintainability Questions and Answers

Topic Posted by: Reliability & Maintainability Forum ( )
Organization: System Reliability Center
Date Posted: Mon Aug 31 12:47:36 US/Eastern 1998

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Posted by: Andrew Comons
Date posted: Mon Mar 4 20:47:32 US/Eastern 2002
Subject: MTBF and Redundent Systems
I am trying to write a system specification for equipment which will be fielded in pairs, the second system will act as backup system. Each system will be required to have a spare parts package on-board, where the fulltime attending operator will be required to employ built in diagnostics and correct faults within a period of 5 minutes. If faults can't be corrected in 5 minutes the decision is to switch to the backup system. Mission duration is 120 hours. Reliability goal is 95%. I need to determine MTBF of the system, including the redundent but I do not know how to account for a failure if it is correctable by the 5 minute fault detection/correction requirement. Sample calcs, references or advice available? Thanks in advance.

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Subject: MTBF and Redundant Systems
Reply Posted by: Gary Sunada ( )
Organization: Reliability Analysis Center
Date Posted: Tue Mar 12 10:00:03 US/Eastern 2002
Hello -- perhaps this may be of help:
First, you'll need the failure rate of one field unit.
One of our books, Reliability Toolkit: Commercial Practices Edition, contains a redundancy-with-repair equation (n active units, one offline on standby, with immediate repair):
lambda(standby) = n [n*lambda+(1-P)*mu] lambda ---------------------------------- mu + n (P + 1) lambda
n = number of active on-line units (in this case, = 1) lambda = failure rate of one unit mu = repair rate = 1 / mean corrective maintenance time in hours = 1 / 5 min (assuming that the repair will take 5 minutes, no more, no less -- you can adjust this, depending on the nature of the failure modes and their respective repairs) = 1 / 0.0833 = 12.0 P = probability of successful switching over to backup (in this case, with a live human operator, assume 100%) = 1
Plug in the values, and you get lambda(standby). Assuming an exponential distribution for the system's failure rate, 1 over lambda(standby) gives you MTBF.

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