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

ME 4723 Reliability and Quality Control Fall 2021
Mechanical Engineering – U. Texas at San Antonio 1
Homework #3
Due: 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 your
numbers during calculations. Rounding too much may lead to rejection in auto-grading.
Part I: Fault Tree Simplification
The 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 is that “+” is
“OR” and “
•
” is “AND” as logic gates, where
the results can only be ON or OFF (i.e. X=0 or 1, not X=2). So in
Idempotent Law,
X+X=X and X
•X=X . I n Law of Absorption, X•(X+Y)=X and X+ X•Y=X , because status of Y
does 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.