Properties of an approximate hazard transform

The calculation of the exact reliability of complex systems is a difficult and tedious task. Consequently simple approximating techniques have great practical value. The hazard transform of a system is an invertible transformation of its reliability function which is convenient and useful in both applied and theoretical reliability work. A simple calculus for finding an approximate hazard transform for systems formed by series and parallel combinations of components is extended so that it can be used for any coherent system. The extended calculus is shown to lead to conservative approximations. A first order version of the extended calculus is also discussed. This method of approximation is even more simple to use, but is not always conservative. Examples of its application indicate that it is capable of giving quite accurate results.     

Damage modeling of ballistic penetration and impact behavior of concrete panel under low and high velocities

This work presents a numerical simulation of ballistic penetration and high velocity impact behavior of plain and reinforced concrete panels. This paper is divided into two parts. The first part consists of numerical modeling of reinforced concrete panel penetrated with a spherical projectile using concrete damage plasticity (CDP) model, while the second part focuses on the comparison of CDP model and Johnson-Holmquist-2 (JH-2) damage model and their ability to describe the behavior of concrete panel under impact loads. The first and second concrete panels have dimensions of 1500 mm × 1500 mm × 150 mm and 675 mm × 675 mm × 200 mm, respectively, and are meshed using 8-node hexahedron solid elements. The impact object used in the first part is a spherical projectile of 150 mm diameter, while in the second part steel projectile of a length of 152 mm is modeled as rigid element. Failure and scabbing characteristics are studied in the first part. In the second part, the com-parison results are presented as damage contours, kinetic energy of projectile and internal energy of the concrete. The results revealed a severe fracture of the panel and high kinetic energy of the projectile using CDP model comparing to the JH-2 model. In addition, the internal energy of concrete using CDP model was found to be less comparing to the JH-2 model.     

The relationship between decision variables and penalty cost parameter in (Q,R) inventory models

This paper is concerned with the optimum decision variables found using order quantity, reorder point (Q, R) inventory models. It examines whether the optimum variables (Q* and R*) are necessarily monotonic functions of the backorder cost parameter (or equivalently of the performance objective). For a general class of models it is proved that R* must increase as the performance objective is raised, and an inequality condition is derived which governs how Q* will change. Probability distributions of lead time demand are cited or found for which Q* increases, Q* decreases, and Q* is independent of increases in performance objectives or backorder cost parameter.     

On estimating survival for reliability models based on age-related stochastic comparisons

A new class of nonparametric reliability models is introduced and studied. A distribution is said to be better at age s than at age t (sBt) if the residual lifetime at age s is stochastically greater than or equal to the residual lifetime at age t. Applications to various forms of replacement policies, including the cannibalization of failed systems, are noted. For fixed s < t, the problem of estimating a survival curve assumed to belong to the sBt class is addressed using recursive methods. An sBt estimator is derived in closed form, and its uniform strong consistency at an optimal rate of convergence is demonstrated. A simulation study strongly supports the claim that the sBt estimator tends to outperform the empirical survivor function in small- and moderate-size samples. © 1993 John Wiley & Sons, Inc.     

MILITARY EXPENDITURE AND GRANGER CAUSALITY: A CRITICAL REVIEW

A large literature has used tests for Granger (1969) non‐causality, GNC, to examine the interaction of military spending with the economy. Such tests answer a specific although quite limited question: can one reject the null hypothesis that one variable does not help predict another? If one can reject, there is said to be Granger causality, GC. Although the limitations of GNC tests are well known, they are often not emphasised in the applied literature and so may be forgotten. This paper considers the econometric and methodological issues involved and illustrates them with data for the US and other countries. There are three main issues. First, the tests may not be informative about the substantive issue, the interaction of military expenditure and the economy, since Granger causality does not correspond to the usual notion of economic causality. To determine the relationship of the two notions of causality requires an identified structural model. Second, the tests are very sensitive to specification. GNC testing is usually done in the context of a vector autoregression, VAR, and the test results are sensitive to the variables and deterministic terms included in the VAR, lag length, sample or observation window used, treatment of integration and cointegration and level of significance. Statistical criteria may not be very informative about these choices. Third, since the parameters are not structural, the test results may not be stable over different time periods or different countries.     

Unrestricted warfare: Review essay I

During the Nigerian Civil War (1967–1970), France chose to support Biafra, but only on a limited scale, providing mercenaries and obsolete weaponry to Ojukwu's regime. General Charles de Gaulle's assistance to Ojukwu was conditioned by the French military drawdown after 1961, the increased power of French secret services on the continent, and the interventions in Katanga (1960–1963), Gabon (1964) and Chad (1968–1972). France supported Biafra primarily to protect its former colonies from Nigeria, stop Soviet subversion and acquire an economic foothold in the oil-rich Niger Delta. De Gaulle chose a limited strategy for two reasons. If Biafra won the war, France would be Biafra's greatest ally. If Nigeria won the war, France could extricate itself from the situation relatively easily and re-establish relations with the Nigerian government, which is what ultimately occurred.