DRAW the fans in SERIES and determine the overall SYSTEM RELIABILITY

A new titanium “Z” Mill, a reversing cold rolling mill, is being built to create flat-rolled titanium sheets for both commercial and military aircraft. The motors that turn the rolling mill, however, run at very high RPM’s and tend to become very hot due to both the ambient air temperature of the region during the summer, the speed at which the motors drive the rolls, and the pressure at which the rolls bear down on the titanium. The motors are cooled by two fans pulling hot air away from the motors and replacing it with cooler air. If one motor of the two overheats, however, the entire cooling system shuts down. This, in turn, shuts down the mill, tearing the titanium strip and causing a delay of several hours until the motor cools off and the wrecked titanium can be removed – and each hour the line is down the company loses $1000.

Your assignment, as the Reliability Engineer, is to help the company determine if it is worth installing a redundant system. The current system of two fans in SERIES looks like this with individual fan reliabilities as shown:
Fan #1: R1 = .98
Fan #2: R2 = .90
Again, both fans are in a SERIES – arranged one after another – and both pull air from one giant duct that draws air off of the Z Mill. If ONE FAN in the series goes down, the entire system shuts down!
Make it good, show all your work, draw it neatly in blocks, and let me see how you calculated it.

QUESTIONS TO ANSWER:

1. DRAW the fans in SERIES and determine the overall SYSTEM RELIABILITY (RS).
2. You decide to install a PARALLEL REDUNDANT SYSTEM with the EXACT same reliabilities as the original three fans. DRAW the PARALLEL REDUNDANT SYSTEM and determine the reliability for RS1 and RS2.
3. You decide, as the engineer, to built a BACKUP REDUNDANT SYSTEM with one fan backing up each of the two. The back-up reliability is the same as the original two – so the back-up to Fan #1 has a R1a of .98 and the back-up to Fan #2 has a R2a of .90. DRAW the system with BACKUP REDUNDANCY.
4. Write up a one-page analysis and attach it to describing your work and which of the three systems you would recommend and why!

If you are curious, this is what a “Z” Mill looks like – one fan cooling each side!

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