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.
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?