Exam 1
Please put your answers in the following table.
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1. The standard deviation is always non-negative. (true of false)
2. Six components failed out of 1000 manufactured components, determine the reliability of the components.
A. 0.006
B. 0
C. 1
D. 0.994
3. The factor of safety is defined by 
, where 
and 
are the means of yield strength 
and stress 
, respectively. Denote 
and 
as the standard deviations of and , respectively. The reliability is defined by 
. Which of the following statements is not true to
improve reliability?
A. Keep 
constant,
and increase and
.
B. Keep and
constant,
and increase .
C. Keep constant,
and decrease and
.
D. Keep constant,
and decrease .
4.
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Two cases are shown for the normally distributed stress of a component. Which case has probability of failure?
A. Case 1
B. Case 2
C. Equal probability
D. Cannot determine
5. A hollow tube has an inside diameter of 
and an outside diameter of 
. What is the distribution of the thickness 
of the tube?
A. 
B. 
C. 
D. 
6.
The length of a shaft is 
. What
is the 
?
A. 0.9545 B. 0.9973
C. 0.6827 D. 0.9999
7.
A circular rod with a diameter of 
is subjected to a tensile force 
. The
yield strength of the rod is .
If the reliability of the rod is defined by the probability 
,
which of the following actions cannot improve the reliability?
A. Do not change 
and decrease 
B. Do not
change 
and increase 
C. Do not
change and increase 
D. Do not
change and decrease
8.
For the above problem, if the limit-state function is defined by 
, and
denote 
and
as
the mean and standard deviation of 
, respectively. Which of the following
statements is true?
A. The larger is ,
the larger is
B. The larger is ,
the larger is
C. The smaller is ,
the larger is
D. The larger is ,
the larger is
9.
A cylindrical part is loaded by an axial force , causing a stress
of 
. The modulus of elasticity is 
.
What is the mean and standard deviation of the normal strain 
?
A. 
, 
B. , 
C. , 
D. , 
10. For
problem 9, if the allowable strain is 
, what
is the probability of failure?
