A Lanchester-type model of combat with stochastic rates

The effects of environmental stochasticity in a Lanchester-type model of combat are investigated. The methodology is based on a study of stochastic differential equations with random parameters characterized by dichotomous Markov processes. Exact expressions for the Laplace transforms of the time evolution of the first- and second-order moments of the system are obtained. A special case when the fluctuations in the parameters occur with great rapidity in comparison with the natural time scale of the system is also analyzed. The stochastic stability in the mean-square sense is discussed by using the Routh–Hurwitz criterion and it is found that the stochastic perturbations tend to destabilize the system.     

A characterization of the wald distribution

Suppose X is a random variable having an absolutely continuous distribution function F(x). We assume that F(x) has the Wald distribution. A relation between the probability density function of X⁻¹ with that of X is used to characterize the Wald distribution.     

A cost-benefit analysis of military aircraft replacement policies

This paper describes a method of solving aircraft service life problems. The particular application concerns aircraft in the Naval Advanced Jet Training Command. The method of solution is comparative present value analysis of alternative replacement policies. The likely risks of estimation errors are reflected in the comparisons of present values. Differences are noted in the benefits associated with each policy, but external to Naval Aviation. Since the values of these benefits can be determined only at a higher level of decision-making, the result of the study is not a conclusive selection among policies, but a schedule of present values on the basis of which, together with values of the external benefits, a decision can be reached. This paper discusses replacement policies for aircraft used in the Naval Advanced Jet Pilot Training mission. Taking engineering technology and the training syllabus as given, four feasible plans for introducing replacement aircraft into service are evaluated in terms of the present values of differential costs associated with the plans and in terms of the likely errors in cost estimates used in calculation of the present values. The trade-off between present value of costs and planning flexibility is emphasized in choosing a recommended time pattern of aircraft replacement. The specific aircraft mixes considered are the TF–9J/TAF–9J and the TA–4F/A–4B. The first is the currently employed mix; the second is the proposed replacement. The problem is to select an optimal time-pattern of replacement of F–9's by A–4's, given technological differences favoring the A–4 and increasing costs of maintaining squadrons of F–9's. Replacements by aircraft types other than the A–4 are considered impractical. Four feasible plans for introducing A–4's through a 5-year period are evaluated in terms of current best estimates of the related costs of the plans and in terms of the flexibility of modifying each plan given future better information concerning the relevant costs. The method of analysis is comparative present value of expected costs.     

Allocation of resources to randomly occurring opportunities

An allocation problem is considered in lvhich different kinds of resources must be allocated to various activities, within a given time period. The opportunities for allo'cation appear randomly during this period. Certain assumptions about the values of possible allocations and the distribution of occurrences of opportunities lead to a dynamic programming formulation of the problem. This leads to a system of ordinary differential equations which are (in theory) solvable recursively, and can be solved numerically to any desired degree of precision. An example is given for the allocation of aircraft-carried weapons to targets of opportunity.     

A note on the influence of missing operations on scheduling problems

This paper attempts to resolve the existing confusion concerning missing operations. Scheduling problems are classified in two groups: (i) null-continuous (NC)—comprising the problems where an optimal schedule remains optimal on replacement of arbitrarily small processing times (existing operations) with zeros (missing operations); (ii) null-discontinuous (NDC)—comprising those problems which are not null-continuous.     

Optimal sample size allocation for tests with multiple levels of stress with extreme value regression

In this article, we discuss the optimal allocation problem in a multiple stress levels life‐testing experiment when an extreme value regression model is used for statistical analysis. We derive the maximum likelihood estimators, the Fisher information, and the asymptotic variance–covariance matrix of the maximum likelihood estimators. Three optimality criteria are defined and the optimal allocation of units for two‐ and k‐stress level situations are determined. We demonstrate the efficiency of the optimal allocation of units in a multiple stress levels life‐testing experiment by using real experimental situations discussed earlier by McCool and Nelson and Meeker. Monte Carlo simulations are used to show that the optimality results hold for small sample sizes as well. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Economic Losses From a Fire in a Dense-Packed U.S. Spent Fuel Pool

In 2013, the staff of the U.S. Nuclear Regulatory Commission estimated the reduction of the off-site economic losses from a fire in a drained U.S. spent fuel pool if fuel that had cooled for more than five years were transferred to dry cask storage—an option it called “expedited transfer.” In this article, it is shown that the savings would be much higher than the NRC estimated. Savings increase to about $2 trillion if: losses beyond 50 miles are included; the land-contamination threshold for long-term population relocation is changed to that used for the Chernobyl and Fukushima accidents and recommended by the U.S. Environmental Protection Agency; and, based on the experience of Japan, decontamination of land areas to levels acceptable for population return is assumed to take at least four years. If expedited transfer were implemented, the off-site economic losses would be reduced by about 98%.     

Subcontracting State-Building

Abstract

Contemporary development assistance often takes the form of subcontracted state-building. Foreign donors hire for-profit firms to provide services and to improve or create institutions in developing countries, particularly those experiencing internal conflict. This arrangement creates two counterproductive dynamics: first, it introduces agency problems between donors, recipient states, subcontractors, and citizens; and second, it undermines the long-run development of domestic bureaucratic capacity by creating disincentives for the host government to invest. These dynamics hinder, rather than foster, the legitimacy of state institutions. This paper summarizes trends in external support to state-building since the 1970s and illustrates subcontracted state-building with examples from Colombia.     

I Will Follow: Smart Power and the Management of Wartime Alliances

Abstract

This paper employs the concept of smart power to construct an analytical framework for assessing wartime alliance management. It makes two arguments. First, wartime sources of soft power differ from those obtaining during peacetime. Second, the coerciveness with which an alliance leader wields hard power towards actual or prospective allies should vary inversely with the amount of soft power it possesses. The smart power framework illuminates three types of alliance management failure. The paper’s key contentions are illustrated with examples furnished from the record of US alliance leadership since World War II.     

Exact likelihood inference for the exponential distribution under generalized Type‐I and Type‐II hybrid censoring

Chen and Bhattacharyya [Exact confidence bounds for an exponential parameter under hybrid censoring, Commun Statist Theory Methods 17 (1988), 1857–1870] considered a hybrid censoring scheme and obtained the exact distribution of the maximum likelihood estimator of the mean of an exponential distribution along with an exact lower confidence bound. Childs et al. [Exact likelihood inference based on Type‐I and Type‐II hybrid censored samples from the exponential distribution, Ann Inst Statist Math 55 (2003), 319–330] recently derived an alternative simpler expression for the distribution of the MLE. These authors also proposed a new hybrid censoring scheme and derived similar results for the exponential model. In this paper, we propose two generalized hybrid censoring schemes which have some advantages over the hybrid censoring schemes already discussed in the literature. We then derive the exact distribution of the maximum likelihood estimator as well as exact confidence intervals for the mean of the exponential distribution under these generalized hybrid censoring schemes. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004