Research for MARKOV Models and Processes

To make a drug-testing program successful and to minimize the cost of the program, the minimum number of tests that must be given in a specified period to identify a fixed percentage of drug users must be determined. This memorandum presents a Markov model that can be used to determine the number of tests that should be given. In addition, three applications of the model, showing how it can be used to analyze the drug-user population, are presented.

This paper derives a probability model which analyzes multiple spell data by taking into account both the probability of changing states and the length of time an individual remains in each state.

This paper calculates the distribution of the number of survivors of a set number of attacks with given parameters, for various missile-allocation situations, and the expected number of missiles fired. The emphasis is on eliminating the complexity arising from a large number of missiles attacking simultaneously. Computer programs for these calculations are presented in Appendix A.

This study describes two stochastic models for evaluating air combat maneuvering (ACM) engagements. The Maneuver Conversion Model is applicable to engagements where a successful outcome is determined primarily by maneuvering effectiveness of the combatants. In this model, the events of air-to-air engagements are assumed to behave as a semi-Markov process with various absorbing states. The Firing Sequence Model is intended for analysis of engagements where a successful outcome depends on aircrew ability to capitalize on weapon performance. This model also assumes a Markov process, but analyzes test-range data as tabulations of weapon-firing incidents for each engagement. Common measures of effectiveness, such as the probability of achieving first weapon-firing opportunity and the expected exchange ratio, may be used in both models to estimate ACM performance. Volume I presents the analytic methodologies for both models, and provides under CNO Project P/V2 (Battle Cry), and illustrates the Maneuver Conversion Model methodology.