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