Applications and Extensions of Signature Theory to Modeling and Inference Problems in Engineering Reliability.

摘要

Research accomplished during the period 3/2/08-9/2/11 in ten specific areas of study is reported. This work includes the treatment of the problems of (1) comparing coherent or mixed systems of different sizes, and obtaining representation results for system reliability under relaxed assumptions on component lifetimes (e.g., exchangeability), (2) deriving new representations of system reliability for used systems known to be working at an inspection time t, (3) developing extensions of the notion of system signatures to dynamic reliability settings, with applications to nonparametric models in reliability and to the engineering practice of burn-in, (4) inference about a common component distribution F from system failure time data, (5) the derivation and application of the joint signature of pairs of systems with shared components, (6) a comparison of the Bayesian and frequentist approaches to estimation (a research monograph), (7) skewness and dispersion among convolutions of independent gamma variables, (8) signature-based representations for the reliability of systems with heterogeneous components, (9) network reliability (10) a proof of the 'no internal zeros' property of system signatures.