Mathematical Methods in Defense Analyses.

Cover -- Title -- Copyright -- Forword -- Table of Contents -- Preface -- Chapter 1. Scientific Methods in Military Operations -- 1.1 Introduction -- 1.2 Mathematical Methods -- Theory of Combat -- Decision Theory -- Linear Programming -- Queuing Theory -- Network Analysis -- Game Theory -- Differential Games -- War-Gaming and Simulation -- Future Directions of Research -- 1.3 Quantitative Competence -- References -- Problems -- Chapter 2. Characteristic Properties of Weapons -- 2.1 Weapon Performance Data -- 2.2 Empirical Averages -- Arithmetic Mean (Average) -- Median -- 2.3 Scatter or Dispersion -- Range -- Interquartile Range -- Mean Deviation -- Standard Deviation -- Coefficient of Variation -- 2.4 Mean Point of Impact: Systematic Error -- Problems -- Chapter 3. Passive Targets -- 3.1 Binomial Distribution -- 3.2 Normal (Gaussian) Distribution -- 3.3 Poisson Distribution -- 3.4 Probability Density Distribution: Linear Error Probable (LEP) -- 3.5 Single-Shot Probability of Hit for a Rectangular Target -- 3.6 Probability of Target Kill or Hit for Multiple Shots -- 3.7 Probability of Destruction of a Point Target: Circular Error Probable (CEP) -- Case 1: Zero Offset and Equal Variances -- Case 2: Offset Distribution and Equal Variances -- Case 3: Zero Offset and Unequal Variances -- Case 4: Offset Distribution and Unequal Variances -- 3.8 Probability of Hit of a Rectangular Target:The Polya-Williams Approximation -- Case 1: Equal Variances: Square Target -- Case 2: Nonequal Variances: Rectangular Target -- 3.9 Probability of Hit of an Elliptic Target with Unequal Variances -- 3.10 Probability of Destruction of a Point Target in Space -- 3.11 Linear, Circular, and Spherical Error Probables -- 3.12 Expected Fractional Damage of a Uniform-Valued Target -- 3.13 Damage Functions for a Point Target in a Plane -- Gaussian Damage Function.