Statistical flowgraphs represent multistate semi-Markov processes using integral transforms of transition time distributions between adjacent states; these are combined algebraically and inverted to derive parametric estimates for first passage time distributions between nonadjacent states. This dissertation extends previous work in the field by developing estimation methods for flowgraphs using empirical transforms based on sample data, with no assumption of specific parametric probability models for transition times. We prove strong convergence of empirical flowgraph results to the exact parametric results; develop alternatives for numerical inversion of empirical transforms and compare them in terms of computational complexity, accuracy, and ability to determine error bounds; discuss (with examples) the difficulties of determining confidence bands for distribution estimates obtained in this way; develop confidence intervals for moment-based quantities such as the mean; and show how methods based on empirical transforms can be modified to accommodate censored data. Several applications of the nonparametric method, based on reliability and survival data, are presented in detail.
Level of Degree
Mathematics & Statistics
First Committee Member (Chair)
Second Committee Member
Third Committee Member
Graham, Edward Jr
Flowgraphs--Data processing, Failure time data analysis, Nonparametric statistics.
Collins, David. "Nonparametric estimation of first passage time distributions in flowgraph models." (2009). https://digitalrepository.unm.edu/math_etds/68