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