On the moments of gamma order statistics

A recurrence relation between the moments of order statistics from the gamma distribution having an integer parameter r is obtained. It is shown that if the negative moments of orders -(r?1), …, ?1 of the smallest order statistic in random samples of size n are known, then one can obtain all the moments. Tables of negative moments for r = 2 (1) 5 are also given.     

Simulation of nonhomogeneous poisson processes by thinning

A simple and relatively efficient method for simulating one-dimensional and two-dimensional nonhomogeneous Poisson processes is presented The method is applicable for any rate function and is based on controlled deletion of points in a Poisson process whose rate function dominates the given rate function In its simplest implementation, the method obviates the need for numerical integration of the rate function, for ordering of points, and for generation of Poisson variates.     

Damage calculations for unreliable warheads

For large numbers of perfectly reliable, optimally targeted warheads the square-root law approximates the expected fraction damage achieved on an area target. In this paper a more exact expression is derived for this damage fraction which Holds for all numbers of warheads. This expression is shown to converge to the square-root law when a large number of warheads are fired. The more exact expression is used in a procedure to calculate expected damage when warheads are unreliable, and this procedure is shown to be superior to a modified square-root approximation which has been used previously.     

An algorithm (GIPC2) for solving integer programming problems with separable nonlinear objective functions

This paper presents an algorithm for solving the integer programming problem possessing a separable nonlinear objective function subject to linear constraints. The method is based on a generalization of the Balas implicit enumeration scheme. Computational experience is given for a set of seventeen linear and seventeen nonlinear test problems. The results indicate that the algorithm can solve the nonlinear integer programming problem in roughly the equivalent time required to solve the linear integer programming problem of similar size with existing algorithms. Although the algorithm is specifically designed to solve the nonlinear problem, the results indicate that the algorithm compares favorably with the Branch and Bound algorithm in the solution of linear integer programming problems.     

Duality for quasi-concave programs with application to economics

A duality theory is developed for mathematical programs with strictly quasi-concave objective functions to be maximized over a convex set. This work broadens the duality theory of Rockafellar and Peterson from concave (convex) functions to quasi-concave (quasi-convex) functions. The theory is closely related to the utility theory in economics. An example from economic planning is examined and the solution to the dual program is shown to have the properties normally associated with market prices.     

Computational results with a branch-and-bound algorithm for the general knapsack problem

In this paper, a branch-and-bound procedure is presented for treating the general knapsack problem. The fundamental notion of the procedure involves a variation of traditional branching strategies as well as the incorporation of penalties in order to improve bounds. Substantial computational experience has been obtained, the results of which would indicate the feasibility of the procedure for problems of large size.     

The optimum design of multivariate acceptance sampling plans

A model is developed which may be used to determine the expected total cost of quality control per inspection lot under acceptance sampling by variables where several characteristics are to be simultaneously controlled. Optimization of the model is accomplished through the application of a conventional search procedure. The sensitivity of the model and the optimum solution to the shape of the underlying probability distributions is discussed and associated analyses are presented through an example.     

An early-accept modification to the test plans of military standard 781C

This paper is concerned with the statistical test plans contained in Military Standard 781C, “Reliability Design Qualification and Production Acceptance Tests: Exponential Distribution” and the selection and use of these plans. Modifications to the fixed-length test plans of MIL-STD-781C are presented which allow early-accept decisions to be made without sacrificing statistical validity. The proposed plans differ from the probability ratio sequential tests in the Standard in that rejection is permitted only after a fixed number of failures have been observed.     

Sequential tests for hypotheses concerning the product of poisson parameters with applications to problems in reliability and biometry

Sequential tests for the product of Poisson parameters based on the generalized incomplete modified Bessel (g.i.m.B.) distributions are given. Applications to reliability and biometry are indicated.     

Book reviews

Winning the Next War: Innovation and the Modern Military. By Stephen Peter Rosen. Cornell Studies in Security Affairs, Cornell University Press, New York (1991), ISBN 0-8014-2566-5. Price £40.00

Post-Military Society. By Martin Shaw. Polity Press, Cambridge (1991), ISBN 0-7456-01987 (hardback) £35.00,0-7456-01995 (paperback) £11.95

Big Boys' Rules—The Secret War Against the IRA. By Mark Urban. Faber and Faber, London (1992), ISBN 0-571-16112-X, £14.99