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 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.     

The discrete max-min problem

The historic max-min problem is examined as a discrete process rather than in its more usual continuous mode. Since the practical application of the max-min model usually involves discrete objects such as ballistic missiles, the discrete formulation of the problem seems quite appropriate. This paper uses an illegal modification to the dynamic programming process to obtain an upper bound to the max-min value. Then a second but legal application of dynamic programming to the minimization part of the problem for a fixed maximizing vector will give a lower bound to the max-min value. Concepts of optimal stopping rules may be applied to indicate when sufficiently near optimal solutions have been obtained.     

A new derivation of the logistic distribution

Logistic distribution is widely used in describing biological, engineering, industrial, and various other types of data. In this paper it is shown that this distribution is a special case of a compound generalized extreme value distribution which is derived by compounding a generalized extreme value distribution with a gamma distribution. The paper contains several useful results relevant to these distribution functions.     

Prediction with zero-one loss structure

This paper poses a prediction problem in which a linear model is assumed. With a “zero-one” loss structure as the loss from incorrect prediction, it is suggested that least squares may not be appropriate for estimating the parameters of the model. An alternate criterion is proposed and integer programming is used in order to find the estimates, given the proposed criterion.     

Simulation of multi-echelon macro-inventory policies

Alternative repair part inventory policies are examined for a multi-echelon logistics system. The policies assessed pertain to the design of multi-echelon systems rather than the evaluation of stock level decisions for individual repair parts. Although the context is one of a military inventory system, the policies examined are of importance in nonmilitary systems where item failure rates are low, and only periodic access to resupply is possible.     

A backward recursive technique for optimal sequential sampling plans

This paper presents a procedure akin to dynamic programming for designing optimal acceptance sampling plans for item-by-item inspection. Using a Bayesian procedure, a prior distribution is specified, and a suitable cost model is employed depicting the cost of sampling, accepting or rejecting the lot. An algorithm is supplied which is digital computer oriented.     

Control variable methods in the simulation of a model of a multiprogrammed computer system

One approach to the evaluation of the performance of multiprogranmed computer systems includes the development of Monte Carlo simulations of transitions of programs within such systems, and their strengthening by control variable and concomitant variable methods. An application of such a combination of analytical, numerical, and Monte Carlo approaches to a model of system overhead in a paging machine is presented.