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 two-grade 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