Date of Award
Master of Science (MS)
Mathematics and Statistics
Ronald V. Canfield
It is very difficult to construct a reliability model for a complex system. However, the reliability model for a series configuration is relatively simple. In the simplest case in which the components are mutually independent, the system reliability can be represented as follows:
Rs(x) = ∑ni=1Ri(x),
where Ri is the reliability for the ith component. It is also known that for moderate levels of system reliability for large systems, the component reliability must be high.
Extreme Value Theory indicates that under very general conditions, the initial form of the distribution function is the dominating contribution to the system reliability. In addition, under proper conditions (i.e., the component reliability distribution is such that its related extreme value type is of the limits type, [Gumbel, 1958]), the initial forms of these distributions are Weibull, i.e.,
1 - F(x) = exp(-(x/θ)Y).
Yueh, Jia-Jinn, "A Monte Carlo Comparison of Nonparametric Reliability Estimators" (1973). All Graduate Plan B and other Reports. 1154.
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