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Old October 16th, 2008, 10:47 AM
avanti avanti is offline
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Default Reliability/Confidence of One Shot Components in a System

I have three one-shot components that are assembled together to form a system. Each component was tested with no-failures.
Test quantities and reliability (from beta equation R=(1-c)^(1/n) where c = confidence level (CL)) are:
Component 1: 50 tests R1 = .955 at 90% CL
Component 2: 60 tests R2 = .962 at 90% CL
Component 3: 27 tests R2= .918 at 90% CL
How do I calculate the system reliability for a 90% confidence level taking into account the different test quantities (I understand that the product of R1, R2, R3 will be underestimate the system reliability)?
Thanks
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Old November 13th, 2008, 09:42 PM
avanti avanti is offline
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Default Re: Reliability/Confidence of One Shot Components in a System

Quote:
Originally Posted by avanti View Post
I have three one-shot components that are assembled together to form a system. Each component was tested with no-failures.
Test quantities and reliability (from beta equation R=(1-c)^(1/n) where c = confidence level (CL)) are:
Component 1: 50 tests R1 = .955 at 90% CL
Component 2: 60 tests R2 = .962 at 90% CL
Component 3: 27 tests R2= .918 at 90% CL
How do I calculate the system reliability for a 90% confidence level taking into account the different test quantities (I understand that the product of R1, R2, R3 will be underestimate the system reliability)?
Thanks
Here is some additional info re my question:
The components cited above are dependent.
Comp1 must function before compt 2 can function, and comp 2 must function before comp 3 can function.
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  #3  
Old November 8th, 2010, 02:09 PM
Oleg_I Oleg_I is offline
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Default Re: Reliability/Confidence of One Shot Components in a System

Hi avanti,

By my calculation the system reliability is RS=R3=0.918 for 90 % CL (method in LCSimulator.ppt and youtu.be/0_RtgmAzATg).
By method in http://www.reliasoft.com/pubs/2010_R...ot_systems.pdf the system reliability RS = 0.874 for 90 % CL (see attachment).
The thread http://reliability-discussion.com/showthread.php?t=50 contains discussion of different methods.

Best regards,
Oleg
Attached Files
File Type: xls ApproxBeta.xls (14.5 KB, 7 views)

Last edited by Oleg_I; February 16th, 2014 at 10:26 AM.
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  #4  
Old November 10th, 2010, 08:41 PM
avanti avanti is offline
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Default Re: Reliability/Confidence of One Shot Components in a System

Oleg,

Thanks for your reply - although I've yet to research the references you cited.

But here is an interesting response from two well known reliability experts:
If you test three components separately then use the typical R^3 you derive a low reliability. If you assemble and test the three components as a system you will get a higher reliability number for a given confidence level.
The problem being that many reliability formulae taught in colleges assume devices are not dependent on one another. But when they are interdependent you could just accept the lowest reliability component in a series and use that reliability for the system.

This sounds heretical does kinda make sense (practically if not mathematically) and does correspond to your calculation (RS = 0.918) below.

Last edited by avanti; November 10th, 2010 at 08:48 PM.
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  #5  
Old November 11th, 2010, 03:23 AM
Oleg_I Oleg_I is offline
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Default Re: Reliability/Confidence of One Shot Components in a System

Yes, I see a paradox "whole - parts" here.
If we estimate a reliability of each component separately and use the typical R^3 we derive a low reliability of a system.
But if we do not estimate a reliability of each component separately as we do it in tests of system we will get a higher estimation of reliability of a system. I saw it in simulation.
Mathematically it can be defined as:

1. Testing the n systems with two components
1-CL = (r1*r2)^n => rs = (r1*r2) = (1-CL)^(1/n)

2. Testing all components separately (the n tests of each component):
1-CL = r1^n * r2^n => rs = (r1*r2) = (1-CL)^(1/n) - the same

3. Testing all components separately (the n1 tests of 1st component and n2 tests of 2nd component, n1>n2):
1-CL = r1^n1 * r2^n2 => rs = (r1*r2) = ((1-CL)/r1^(n1-n2))^(1/n2) - rs depend on r1 here.
Find rs->min (the worst case) therefore
r1=1
rs = r2 = (1-CL)^(1/n2)=(1-0.9)^(1/27)=0.918

(I reduced your example up to two components for clearness.)
This doesn't seem heretical.
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File Type: pdf ThisPost.pdf (14.8 KB, 11 views)

Last edited by Oleg_I; November 11th, 2010 at 11:05 AM.
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  #6  
Old April 3rd, 2017, 09:18 PM
Oleg_I Oleg_I is offline
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Default Re: Reliability/Confidence of One Shot Components in a System

There is a continuation of this topic http://nomtbf.com/2016/04/lifetime-e...t-2/#more-1888
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