Q 30
Consider the system shown in the accompanying figure. The reliability of each component is provided in the figure. Assuming that the components operate independently, calculate the system reliability.
Homework Answers
The given problem is as per the above image. There are 3 different sections in this system. The system is reliable if either the top parts function correctly or the bottom part functions correctly
The reliability of bottom part is 0.999
We first need to calculate the reliability of the top section. To calculate this we need to find the reliability of each of the enclosed section. The first section is reliable or works of atleast one of the component works. This means that either top or bottom component works or both of them work. Thus reliability of first section is 1-probability that both components fails
Reliability of first section =1- ((1-0.995)*(1-0.995)) = 1-(0.005*0.005) = 1-0.000025 = 0.999975
Similarly reliability of second box is 1-((1-0.980)*(1-0.950)) = 1-(0.02*0.05) = 1 - 0.001 = 0.999
The entire reliability of the top section is then when both these sections works = 0.999975*0.999 = 0.998975
The reliability of bottom section is 0.999
Using similar logic as above reliability of entire system = 1-(probability that both top and bottom section fail)
= 1 - ((1-0.998975)*(1-0.999)) = 1-(0.001025*0.001) = 1-0.000001025 = 0.999998975
Thus the system reliability is 0.999998975
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