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Q) 6.30 (Assume operating time to be 1000hrs) A series system is composed of n i

ID: 3225330 • Letter: Q

Question

Q) 6.30 (Assume operating time to be 1000hrs) A series system is composed of n identical components, each having a failure rate of 10^-3 per hour. Find the reliability of the system at time t. Also, plot the reliability function R(t) for n = 1, 2, 5, and 10. Two type of components, one with a failure rate of 10^-4 per hour (type A) and the other with a failure rate of 10^-5 per hour (type B), are arranged to form parallel system. Five components of A are used to form a parallel system X. Find the minimum number of components of type B needed to form a parallel system Y, which matches with the system X in terms of reliability. Ten identical components are connected in parallel to achieve a system reliability of 0.95. Determine the reliability of each component. Ten identical components are connected in parallel to achieve a system reliability of 0.9. Determine the additional number of components to be added in parallel to increase the reliability to 0.95.

Explanation / Answer

6.30

Reliability of a component with failure rate lambda = exp(-lambta*t)

Reliability of each type A component = e^(-10^-4 * 1000) = 0.905

Reliability of parallel system is when at least one component is working = 1 - ((1-0.905)^5) = 0.99999

Let x parallel systems of type B be present

Reliability of each component of type B = e^(-10^-5 * 1000) = e^(-0.01) = 0.99

System reliability = 1 - (1-0.99)^x = 0.99999

0.01^x = 0.00001

x = 2.5 ~ = 3