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# Reliability & MTTF for constant failure rate paralleled systems

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Q1. Which one of the following is the correct definition of equipment monitoring?

a. Managing the day to day work using equipment maintenance procedures and work management systems.

b. Managing the reliability of mechanical, electrical, process, and instrumentation equipment.

c. Understanding the impact that equipment has on other equipment and the overall plant.

d. Using diagnostic tools such as vibration to monitor the health of plant equipment.

Q2. For a system of two parallel CFR components with component MTTF = 900 hours and common-mode CFR of 0.00001, find the system reliability at 1100 hours. Please round your answer to 3 decimals.
Q3. Consider a system with two parallel and identical components with CFR of 0.000353. Assume a common-mode CFR of 0.00001 in addition to the components' independent rates. Find the MTTF. Round your answer to the nearest integer.
Q4. A system has two identical components in parallel with CFR of λ. A system reliability of Rs (1000) =0.95 is desired. What should the component MTTF be? Please round your answer to the nearest integer.

Q5. Consider a system with two parallel and identical components with CFR of 0.000353. Assume a common-mode CFR of 0.00001 in addition to the components' independent rates. Find RS(1000). Please round your answer to 3 decimals.

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Please find attached solutions & guidance. Please note that I have not had a chance to check the math due to short turn around to answer the posting before expiry of deadline. In any case it would be good for you to double check the arithmetic. Thanks

Q1. Equipment monitoring just, observes, checks, reports back on the general health or otherwise of the system. Thus equipment monitoring when set up correctly is a passive process (although equipment may run active monitoring processes in the background these should be transparent to the overall system monitoring). Looking at the choices the only option that is passive, in my opinion is answer (d) Using diagnostic tools such as vibration to monitor the health of plant equipment. The other options purport to active interaction to manage the system through set procedures and maintenance plans or to understand and manage system reliability by certain actions.
Q2. For a system of two parallel CFR components with component MTTF = 900 hours and common-mode CFR of 0.00001, find the system reliability at 1100 hours. Please round your answer to 3 decimals.
Let the parallel components have a CFR of λ_p
For CFR the MTTF is given as the reciprocal of the failure rate or we can write for a parallel component
〖MTTF〗_p=1/λ_p
Thus
λ_p=1/〖MTTF〗_p =1/900=0.00111 〖hr〗^(-1)
The reliability at time t for CFR component is given by
R(t)=e^(-λt)
We draw the RBD noting that common-mode failure is represented ...

#### Solution Summary

Various five questions and solutions involving reliability and MTTF for constant failure rate paralleled systems are determined. The impact that equipment has on other equipment and the overall plant is discussed.

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