SRC Forum - Message Replies
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
Posted by: Amir Saeed
Date posted: Wed Jul 13 9:20:00 US/Eastern 2005
Subject: Mission Phases and specified FRs in Relex
I am using vendor specified failure rates in Relex v7.7 for the system. I have many mission phases. The program does not allow me to specify different failure rates for the different phases or it does not do the calculations itself either. Once the different phases are identified in the "mission profile" file, it uses the same failure rate for all mission phases. How can i work around this?
One way I thought about is to have multiple project files for the system and have the different phases in each of those files with updated calculated failure rates. Is there another way to do this? Any Relex experts who know how to do this in a different manner? I have spoken to Relex too about this, they are absolutely of no help.
Subject: MTBF with phased failure rates
Reply Posted by: Larry George
Organization: Problem Solving Tools
Date Posted: Sat Jul 16 13:42:20 US/Eastern 2005
Interesting problem! Sorry, my reply doesn't help with Relex. Presumably you would like to predict MTBF. Consider this work-around.
MTBF = Integral[R(t)dt from 0 to infinity] ~Sum[Rs] over all phases s, where R(t) denotes a continuous reliability function and Rs is a discrete, phase-type reliability function. [This abuses Marcel Neuts' definition of a phase-type distribution. I apologize.]
The discrete reliability function can be expressed in terms of failure rates as
Rs = exp[-Sum[lambda(i)*deltat(i) from 1 to s]],
where lambda(i) is the failure rate in stage i and deltat(i) is the duration of the i-th stage, numbered sequentially. This actuarial approximation is valid as long as age stages correspond to calendar phases. This discrete reliability representation is at the heart of actuarial statistics.
This computation is easily implemented in a workbook
such as those linked to http://www.fieldreliability.com/MH217F1.htm. If you want, send me the phase failure rates, system structure, and phase durations, and I'll set up this MTBF prediction in a workbook, free of charge.
This work-around may be valid only if calendar time corresponds to age. I said "may be valid," because changing failure rates is changing the age-at-failure random variable in different phases. It's like saying the failure rate is constant and, oh by the way, the constant changes. The actuarial MTBF approximation I've described above is valid as long as phases correspond to age.
Let me know if your system structure is not series system of independent components. In that case, system failure rates aren't constant, even within phases. You might also need a Markov process with different transition rates in different phases. Contact me if the actuarial approximation to MTBF is invalid.