Table 5-7. Refined reliability-based design [+6]s (Monte Carlo simulation with a sample
size of 10,000,000)
B (degree) h (inch) Probability of failure
21.000 0.120 0.0001832
22.000 0.120 0.0001083
23.000 0.120 0.0000718
24.000 0.120 0.0000605
25.000 0.120 0.0000565
26.000 0.120 0.0000607
27.000 0.120 0.0000792
Quantifying Errors in Reliability Analysis
The reliability analysis has errors due to MCS with limited sample size and due to
the approximation of CLT analysis by analysis response surfaces. To evaluate the amount
of errors in reliability analysis, the probability of failure of the rounded design was
evaluated by using MCS with the exact analysis (classical laminate theory, CLT), but
only one million analyses were performed due to the cost of computation. Table 5-8
compares the results of MCS based on ARS and that based on CLT. The difference is
about 1.25x105
Table 5-8. Comparison of probability of failure from MCS based ARS and CLT
Failure
Optimal Design Laminate Failure probability
probability from
[81, 62, tl, t2] thickness from MCS of ARS
7MC Sof CLT
(degree and inch) (inch) 1x 107 samples 106 ape
[25, 25, 0.015, 0.015] 0.120 (0.120) 0.0000565 0.000069
By assuming each simulation as a Bernoulli trial and the N trails as Binomial
distribution, the coefficient of variation (COV) of the probability (PoJ) obtained by MCS
can be estimated by
(1- Pof )Pof
CO V(Pof ) (5-2)
Pof