Reliability
207
E. Reliability of Parallel Components
The reliability of parallel components is
Rp= 1 - Ii=l~l (1 - exp[-2it])
(4,27)
for two components in parallel with different failure rates
Rp --- 1 - (1 - exp[-21t])(1 - exp[-22t])
= exp[-21t] + exp[-22t] - exp[-2~ + 22)t]
(30
= ] Rpdt
MTTF
(4.28)
0
[
exp[-~t]
exp[-~t]
exp[-(21 + 22)t]]~
Two parallel components
1
1
1
MTTF = ~ + ~2 2~ + 2~
(4.29)
Two and more parallel components can be developed in the same derivation.
For three parallel components of different failure rates [4.8],
1 1 1
1
1
MTTForMTBF=~+~+~-(2~+22)
(22+2~)
(4.~0)
1
1
~+
(2~ + 2~) (2~ + ~ +
When the rates are equal 2~ = 2~ for two components [4.29]
2 1 3
MTBF
....
(4.31)
2 22 22
The failure rates equal for 3 parallel components
M~F_3
3 1 1[
3 1]
11
(4.32)
x ~ ~=~ 3-g+ 5 =~
The constant failure rates [4.8,4.20] for two to five parallel components
yields the following reliabilities.
Two parallel components
R~ = 2 exp[-2t] - exp[-22t]
(4.33)
Three parallel components
Rp = 3 exp[-2t] - 3 exp[-22t] + exp[-32t]
(4.34)