Nonparametric estimation of first passage time distributions in flowgraph models

Statistical flowgraphs represent multistate semi-Markov processes using integral transforms of transition time distributions between adjacent states; these are combinedalgebraically and inverted to derive parametric estimates for first passage time distributions between nonadjacent states. This dissertation extends previous work inthe field by developing estimation methods for flowgraphs using empirical transformsbased on sample data, with no assumption of specific parametric probability models for transition times. We prove strong convergence of empirical flowgraph results tothe 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.