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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 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
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
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.