
Accession Number : AD0681695
Title : A CONTINUOUS TIME MARKOV PROCESS MODEL OF NAVAL OPERATIONAL READINESS,
Corporate Author : GEORGE WASHINGTON UNIV WASHINGTON D C LOGISTICS RESEARCH PROJECT
Personal Author(s) : Tolins,Irwin S.
Report Date : 31 JUL 1968
Pagination or Media Count : 26
Abstract : A model of readiness of naval units is presented which treats a time series of readiness grades as a continuous time Markov chain, having stationary transition probabilities. The state space is a finite set of readiness grades, such as naval authority might assign a naval unit such as a ship, airplane, squadron, etc. First, a set of ordinary differential equations is derived for the transition probabilities pertaining to an individual unit of a given type. Then, solutions of such equations for a population of several units of this type having assumed identical stochastic properties are combined, and their mean number in each readiness grade is calculated as a function of time. The corresponding variance is also calculated. Mathematical expressions for such means and variances for the naval unit population are collected in a table which treats both finite future time and indefinitely large future time for units having identical, or different, stochastic properties. The twograde case is presented in detail to illustrate the above general presentation. Finally, the problem of estimating transition probabilities from time series data is discussed. (Author)
Descriptors : (*NAVAL OPERATIONS, OPERATIONAL READINESS), (*COMBAT READINESS, MATHEMATICAL MODELS), TIME SERIES ANALYSIS, PROBABILITY, STATISTICAL PROCESSES, DEPLOYMENT, LOGISTICS, MANAGEMENT PLANNING AND CONTROL, DIFFERENTIAL EQUATIONS, POPULATION(MATHEMATICS), ANALYSIS OF VARIANCE
Subject Categories : Logistics, Military Facilities and Supplies
Naval Surface Warfare
Distribution Statement : APPROVED FOR PUBLIC RELEASE