where N is the sample size of the MCS. The accuracy of MCS can also be expressed in
terms of percentage error corresponding 95% confidence interval as
(1 Pof ")
E% = x 196% (5-3)
Nx Pof "
where Pof is the true probability of failure. Table 5-9 shows the accuracy and error
bounds for MCS. Together with Table 5-8 the error calculation indicates that the
probability of failure of the rounded design is still below the target probability of failure
of 0.0001. The errors can be reduced by more accurate approximations and advanced
Monte Carlo simulations. Another reliability-based design cycle in a reduced size design
region can be performed to obtain more accurate result.
Table 5-9. Accuracy of MCS
Coefficient of Variation Percentage errors (Absolute
(COV) errors) for 95% CI
MCS of lx107 samples 4.2% 8.2% (f4.66x10-6)
MCS of lx106 Samples 12.05% 23.6%(fl.63x10- )
Effects of Quality Control on Laminate Design
Comparing deterministic designs to the reliability-based design, there is an increase
of 20% in the thickness. In addition, the design failure probability of 10-4 is quite high. In
order to improve the design the possibility of limiting the variability in material
properties through quality control (QC) is considered. Here, quality control means that
materials will be tested by the manufacturer and/or fabricator, and that extremely poor
batches will not be accepted. Normal distributions assume the possibility (though very
small) of unbounded variation. In practice, quality control truncates the low end of the
distribution. That is, specimens with extremely poor properties are rejected. It is also