A Continuous Time Markov Process Model of Naval Operational Readiness
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 31, 1968
- Accession Number
- AD0681695
Entities
People
- Irwin S. Tolins
Organizations
- George Washington University