• Journal of the Korean Statistical Society
• /
• v.7 no.1
• /
• pp.61-80
• /
• 1978

This paper presents general solutions for stochastic square duels with continuous interfiring times and various firing strategies such as standby (S), concentrated (C), seperated (I) and random (R) firings. Analysis of these square duels with negative exponential interfiring times and equivalent values of rates of fire and single shot kill probabilities reveal three important facts: i) Strategy (C) is advantageous against the opponent's strategy (S) and the advantage becomes more pronounced for lower values of single shot kill probabilities. ii) Strategy (I) is always better than strategy (C) no matter which of (C) and (I) the opponent uses and its relative advantege increases to a quarter as single shot kill probabilities increase to one but decreases to zero as they go to zero. iii) However, strategy (I) has no advantage over strategy (C) for small values of single shot kill probabilities. In this paper, square duels with strategies (C) and (I) are based on the assumptions that duelists are homogeneous and both duelists of one side fire simultaneously. The problem of relaxing these assumptions and extension of square ($2 \times 2$) duels to more general ($m \times n) duels are now being investigated.

• Journal of the military operations research society of Korea
• /
• v.6 no.2
• /
• pp.69-88
• /
• 1980

A stochastic fundamental duel with continous interfiring times is considered for including the kill effect of multiple hits and fixed duel time. Two alternatives, 'vital hit' and 'damage coefficient' approaches, are developed. Since a large quantity of ammunition is consumed when a sure kill is obtained through repetitive multiple hits, limitation of initial ammunition supply is included in the stochastic duel models with multiple hits and fixed duel time. General solutions are obtained and examples with negative exponential interfiring times and geometric ammunition supply are given.

• Journal of the military operations research society of Korea
• /
• v.28 no.2
• /
• pp.56-69
• /
• 2002

A technique of finding both probability density and distribution function for interkilling times is considered and demonstrated. An important result is that any arbitrary interfiring time random variables fit to this study, The interfiring renewal density function given a certain interfiring probability density function can be applied to obtain the corresponding interkilling renewal density function which helps us to estimate the expected number of killing events in a time period. The numerical inversion of Laplace transformation makes these possible and the results appear to be excellent. In case of ammunition supply is limited, an alternative way of getting the probability density function of time to the killing is investigated. The convolution technique may give us a means of settling for this new problem.

• Journal of the Korean Statistical Society
• /
• v.7 no.2
• /
• pp.121-130
• /
• 1978

This paper presents a method of incorporating detection capability of weapon systems into the "fundamental" stochastic duels of Williams and Ancker when both detection and interfiring times are continuous random variables. An example with negative exponential detection and firing times is also given.lso given.

• Journal of Korean Institute of Industrial Engineers
• /
• v.5 no.2
• /
• pp.2-7
• /
• 1979

The fundamental stochastic duel of Williams and Ancker is combined with the probabilistic linear, square and mixed laws of Brown and Smith when the battle time is limited and interfiring times are continuous. The Probability of a given side's winnig or a draw is derived in a recursive equation with Laplace transforms. Examples with negative exponential firing times are given. In linear law an exact closed form solution is obtained, whereas for square and mixed laws only square ($2{\times}2$) duels are considered.

• Journal of the Korea Society for Simulation
• /
• v.18 no.1
• /
• pp.53-62
• /
• 2009

The real data obtained from field exercises has a crucial role in modeling and simulation of a combat or a wargame. This becomes an important input especially in analyzing weapon systems realization. Many existing models have been using the mean value of the time between each fire. The firing data can be incorporated into a known probability distribution or used directly as an empirical distribution. Data of field exercises are very useful instead of the real combat outcomes. This study finds a new modeling approach and techniques to compare the data with the previously generated outcomes. This fundamental research work will continue to consider more of the various weapon systems, the sizes, and other tactical aspects.