A.4. REFERENCES 223
e Monte Carlo method needs to have a huge amount of trials for an acceptable accuracy
of the estimated reliability. MATLAB software has a function to generate a matrix 1 N of
random numbers of a specified distributed random variable, as shown in Equation (A.39):
RX
i
D random
0
name
0
; A; B; 1; N
; (A.39)
where RX
i
is a matrix 1 N with N of random samplings of a distributed random variable X
i
.
random is the MATLAB command for generating a random number.
0
name
0
is to specify the
type of distribution. A and B are the distribution parameters of the distributed random variables.
“1, N ” in Equation (A.39) means that the matrix for these random number will be stored as one
row with N column.
e flowchart of a MATLAB program for the Monte Carlo method is displayed in Fig-
ure A.3.
A.4 REFERENCES
[1] Hasofer, A. M. and Lind, N., An exact and invariant first-order reliability format, Journal
of Engineering Mechanics, ASCE, vol. 100, no. EM1, pp. 111–121, February 1074. 213
[2] Le, Xiaobin, Reliability-Based Mechanical Design, Volume 1: Component under Static Load,
Morgan & Claypool Publishers, San Rafael, CA, 2020. 213, 216, 220, 222
[3] Andrzej, S. N. and Collins, K. R., Reliability of Structures, 2nd ed., CRC Press, Boca
Raton, FL, 2013. 220
[4] Rackwitz, R. and Fiessler, B., Structural reliability under combined random load se-
quences, Computers and Structures, vol. 9, pp. 489–494, 1978. DOI: 10.1016/0045-
7949(78)90046-9. 216, 222
[5] Singiresu, S. R., Reliability Engineering, Pearson, 2015. 220
224 A. COMPUTATIONAL METHODS FOR THE RELIABILITY OF A COMPONENT
j
Figure A.3: e flowchart of a MATLAB program for the Monte Carlo method.
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