The estimation of P(x < Y) for distributions useful in life testing

In this paper the reliability function K = P(X < Y) has been estimated when X and Y follow gamma, exponential or bivariate exponential distributions. The paper is partly expository.     

Optimal state-dependent pricing policies for a class of stochastic multiunit service systems

This paper models a k-unit service system (e.g., a repair, maintenance, or rental facility) with Poisson arrivals, exponential service times, and no queue. If we denote the number of units that are busy as the state of the system, the state-dependent pricing model formalizes the intuitive notion that when most units are idle, the price (i.e., the service charge per unit time) should be low, and when most units are busy, the price should be higher than the average. A computationally efficient algorithm based on a nonlinear programming formulation of the problem is provided for determination of the optimal state-dependent prices. The procedure ultimately reduces to the search on a single variable in an interval to determine the unique intersection point of a concave increasing function and a linear decreasing function. The algorithm takes, on the average, only about 1/2 second per problem on the IBM 360/65 (FORTRAN G Compiler). A discrete optimal-control approach to the problem is shown to result in essentially the same procedure as the nonlinear-programming formulation. Several properties of the optimal state-dependent prices are given. Comparisons of the optimal values of the objective function for the state-dependent and state-independent pricing policies show that the former is on the average, only about 0.7% better than the latter, which may explain partly why state-dependent pricing is not prevalent in many service systems. Potential generalizations of the model are discussed.     

Evaluation of effectiveness of polymer coatings in reducing blast-induced deformation of steel plates

Incorporating elastomers such as polymers in protective structures to withstand high energetic dynamic loads, has gained significant interest. The main objective of this study is to investigate the influence of a Polyurea coating towards the blast-induced response in steel plates. As such, Polyurea coated steel plates were tested under near-field blast loads, produced by the detonation of 1 kg of spherical nitromethane charges, at a standoff distance of 150 mm. Mild steel (XLERPLATE 350) and high-strength steel (BIS80) plates with thicknesses of 10 mm were Polyurea coated with thicknesses of 6 mm and 12 mm on either the front (facing the charge) or the back face. The deformation profiles were measured using 3D scanning. Numerical simulations were performed using the non-linear finite element code LS-DYNA. The strain-dependent behaviour of the steel and Polyurea were represented by Johnson-cook and Money-Rivlin constitutive models, respectively. The numerical models were validated by comparing the plate deflection results obtained from the experiments and were then used in the subsequent parametric study to investigate the optimum thickness of the Polyurea coating. The results indicate that back face coating contributes towards an approximately 20% reduction in the residual deformation as well as the absence of melting of the Polyurea layer, while the front-face coating can be used a means of providing additional standoff distance to the steel plates.     

East versus West in the defeat of Nazi Germany

One of the most commonly expressed opinions about victory in the Second World War is that the Soviet Union was mostly responsible for beating Nazi Germany. Supposedly the great land war fought between these two powers in the East was the decisive front in Europe. The West's contribution to German defeat, on the other hand, is often seen as somewhat marginal. The Anglo‐American strategic bombing campaign in 1943 paid few dividends and it was not until after the Normandy landings in June 1944 that the West really began to divert a large amount of German resources.

The purpose of this article is to challenge some of these basic notions. Through analysing what Germany produced, where it was sent and how it was destroyed, the West's contribution to defeating Germany moves from an ancillary position to a dominant one. Taking German war production as a whole, from 1943 onwards the West was responsible for tying down and destroying a significantly larger share than the Soviet Union.     

Lanchester for cyber: The mixed epidemic‐combat model

Future conflict between armed forces will occur both in the physical domain as well as the information domain. The linkage of these domains is not yet fully understood. We study the dynamics of a force subject to kinetic effects as well as a specific network effect–spreading malware. In the course of our study, we unify two well‐studied models: the Lanchester model of armed conflict and deterministic models of epidemiology. We develop basic results, including a rule for determining when explicit modeling of network propagation is required. We then generalize the model to a force subdivided by both physical and network topology, and demonstrate the specific case where the force is divided between front‐ and rear‐echelons. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013