Redundancy Equations for Calculating Reliability

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Redundancy Equations for Calculating Reliability Configuration

Reliability, R(t)=

Active Redundancy: Redundancy: "n" fully energized energized identical parallel parallel units. 1 of 2 Must Be Working

2e - λt  - e -2λt

1 of 3 Must Be Working

3e - λt  - 3e -2λt  + e -3λt

1 of 4 Must Be Working

4e - λt  - 6e -2λt  + 4e -3λt  - e - 4λt

1 of n Must Be Working

n

!

(-1)k + 1

k =1

n! e -kλt k!(n − k)!

2 of 3 Must Be Working

3e -2λt  - 2e -3λt

3 of 4 Must Be Working

4e -3λt  - 3e - 4λt

n-1 of n Must Be Working

ne -(n-1)λt - (n-1) e nλt

2 of 4 Must Be Working

3e - 4λt  - 8e -3λt  + 6e -2λt

3 of 5 Must Be Working n-2 of n Must Be Working

m of n Must Be Working

6e -5λt  - 15e - 4λt  + 10e -3λt n! (n - 1)! -nλt '   $ e -(n-2)λt  + % 2n - n2 " e -(n-1)λt  + e 2(n - 2)! 2(n - 3)! &   # n

! k =m

k (n − k) n! '  - !t $ '   $ %e " %1 - e- λt " k!(n - k)! &   # &   #

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System Reliability Center 201 Mill Street Rome, NY 13440-6916 888.722.8737 or 315.337.0900 Fax: 315.337.9932

Redundancy Equations for Calculating Reliability (Cont'd) Standby Redundancy: 1. All units are identical; 2. Standby units are not energized and assumed to have a failure rate of zero; 3. The failure rate of the switching device is assumed to be zero. 1 of 2 Must Be Working

e - λt  + λ te - λt

1 of 3 Must Be Working

e - λt  + λ te - λt  + .5( λ t) 2 e - λt

1 of n Must Be Working

n −1

!

e - λt

r =0 m of n Must Be Working

e -mλt

(λt)r r!

n− m

!

k =0

(mλt)k k!

Note: These equations assume a constant failure rate. Copyright

© 2001

IIT Research Institute. All rights reserved.

Source: •

•

RAC Publication, CPE, Reliability Toolkit: Commercial Practices Edition. RADC-TR-77-287, A Redundancy Notebook, In-House Report, December 1977. Available through National Technical Information Services, Order No. AD-A050-837.

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