Semi-Markov Processes Toward Applications in National Security

• Activity Number: 334
• Type: Topic Contributed
• Date/Time: Tuesday, August 2, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Richard Warr*+
• Companies: Air Force Institute of Technology
• Keywords: Semi-Markov ; Statistical Flowgraph ; Bayesian Statistics ; Laplace Transform ; National Security

Abstract

Multistate models possess an intuitive approach to modeling complex systems. A common simplifying assumption used in multistate models is the semi-Markov property, this assumes that transitions are conditionally independent and readily allows the expression of a likelihood function. The limiting or asymptotic properties of semi-Markov models are well known and widely used, however, their interim properties, or properties before the limiting behavior is accurate, are seldom considered; in-fact it is a common misconception that solutions to these interim properties are not feasible. We demonstrate that solutions are possible and methods to calculate them, specifically, how to compute the state probabilities, first passage distributions, expected number of visits to a state, and others quantities of interest. Additionally, we advocate the use of semi-Markov models in national security problems such as reliability of weapon systems, cost estimation, and projecting personnel requirements. A notional example of projecting the expected costs of the U. S. Government's national threat level is presented.