Lanchester attrition of interpenetrating forces

To approximate the solutions of detailed simulations of interpenetrating forces (or possibly to assist in curtailing Monte Carlo calculations), this article provides solutions to a simple problem assuming that the speed of advance is constant; the only interactions are local; Lanchester's linear or square law applies; force distributions are continuous if not initially uniform in depth. The resultant partial differential equations are solvable (1) in closed form if attrition is minimal or (2) with pain when attrition is sufficient to annihilate the leading edge of a force. This is exemplified only for the square law, where one must solve an integrodifferential equation for an ancillary function. A general solution is given for either law, and for the latter case a more complete one, assuming that initial force distributions are uniform. Useful properties of an unusual class of Bessel functions needed for this analysis are given in an appendix. Copies of computer programs are available.     

A simple Markov model for the analysis of multiple air combat

It is proposed to describe multiple air-to-air combat having a moderate number of participants with the aid of a stochastic process based on end-game duels. A simple model describing the dominant features of air combat leads to a continuous time discrete-state Markov process. Solution of the forward Kolmogorov equations enables one to investigate the influence of initial force levels and performance parameters on the outcome probabilities of the multiple engagement. As is illustrated, such results may be useful in the decision-making process for aircraft and weapon system development planning. Some comparisons are made with Lanchester models as well as with a semi-Markov model.     

On a sequential test procedure with delayed observations

This paper considers sequential test procedures to decision problems where there exists time delays in obtaining observations.     

A probabilistic evaluation of helicopter lift capability

This paper describes a technique for the calculation of the probability that a helicopter can lift a specified load, or number of loads with a specified frequency distribution, in a given geographical region. This probability is computed by determining the bivariate altitude-temperature probability distribution for the specified region. The payload capability at any given temperature and altitude is calculated from standard performance equations. By integrating this over the altitude-temperature distribution, it is possible to obtain the probability distribution of payload capability, from which the required probabilities of lifting specific loads can be determined.     

On estimation in weibull distributions with random scale parameters

Work by the present authors on life distributions derived from stochastic hazard functions [4] is related to certain articles that have appeared in this journal. This relationship is illustrated. The emphasis of this article is upon problems of parameter estimation.