Date of Award


Degree Type


Degree Name

Master of Science (MS)


Mathematics and Statistics

First Advisor

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).