Post on 23-Jan-2017
Reliability if m of n Must be WorkingCalculation done using Mathcad 13
f 200 106
Failure Rate, (failures per hour)
t 10 Operating Time (Hours)
n 4 m 4
When 4 out of 4are NeededR t( )
m
n
k
n
k n k( )e
f t k 1 ef t
n k
R t( ) 0.992031914837061
Probability of Failure = 1 R t( ) 0.0079680852
M0
106
tR t( )
d MTBF (Hours) M 1250
n 4 m 3
R t( )
m
n
k
n
k n k( )e
f t k 1 ef t
n k
When 3 out of 4are Needed
R t( ) 0.999976111704559
Probability of Failure = 1 R t( ) 0.0000238883
M0
106
tR t( )
d MTBF M 2916.6666666667
n 4 m 2
When 2 out of 4are NeededR t( )
m
n
k
n
k n k( )e
f t k 1 ef t
n k
R t( ) 0.999999968143649
Probability of Failure = 1 R t( ) 0.0000000319
M0
106
tR t( )
d MTBF M 5416.6666666667
n 4 m 1
When 1 out of 4is Needed
R t( )
m
n
k
n
k n k( )e
f t k 1 ef t
n k
R t( ) 0.999999999984064
Probability of Failure = 1 R t( ) 1.5936141295 1011
M0
106
tR t( )
d MTBF M 10416.6666666667