HW3-Develop-and-Capability--problem.pdf - ME 4723...

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ME 4723 Reliability and Quality ControlFall 2021Mechanical EngineeringU. Texas at San Antonio1Homework #3Due: 10/17 (Sunday) by 11:59pm. Three attempts allowed. Highest score among the three will be recorded.Important Note: For calculated answers, keep at least 4 decimal places in your answer. Try not to round yournumbers during calculations. Rounding too much may lead to rejection in auto-grading.Part I: Fault Tree SimplificationThe Boolean operations are similar to arithmetic operations, so you can do things like (A+B+C)•(E+F) =A•E+A•F+B•E+B•F+C•E+C•F.The major difference between Boolean and arithmetic algebra isthat “+” is“OR” and “” is “AND”as logic gates, wherethe results can only be ON or OFF (i.e. X=0 or 1, not X=2). So inIdempotent Law,X+X=X and X•X=X. In Law of Absorption, X•(X+Y)=Xand X+X•Y=X, because status of Ydoes not affect the results. You can try plug in (X,Y)=(0,0) or (1,0) or (0,1) or (1,1) to see if the results match.

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