Question

Given the reliability function for a power unit in a satellite is
R(t)=10/(10+t), t>=0
a) How many units must be placed in parallel in order to achieve a reliability of 0.98 for 5 year operation?
b) If there is an additional common mode with constant failure rate of 0.002 as a result of environmental factor. How many units should be placed in parallel?

Answer 1

Given :   reliability function for a power unit in a satellite is R(t)=10/(10+t), t>=0

To find : a) How many units must be placed in parallel in order to achieve a reliability of 0.98 for 5 year operation?

Solution:

R(t)  = 10/(10 + t)

for t = 5 years

R(t)  = 10/15 = 2/3

Let say n units are in parallel

Reliability of 0.98  =   1   -  ( 1 - R(t))ⁿ

0.98 = 1 - ( 1 - 2/3)ⁿ

=> (1/3)ⁿ  = 0.02

n log (1/3)  = log (0.02)

n = 3.56

=> 4 units must be placed in parallel in order to achieve a reliability of 0.98 for 5 year operation

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