Covariance of weibull order statistics

Let X₁ < X₂ <… < X_n denote an ordered sample of size n from a Weibull population with cdf F(x) = 1 - exp (?x^p), x > 0. Formulae for computing Cov (X_i, X_j) are well known, but they are difficult to use in practice. A simple approximation to Cov(X_i, X_j) is presented here, and its accuracy is discussed.     

Computerized scheduling of seagoing tankers

Computerized Scheduling of Seagoing Tankers The tanker scheduling problem considered in this paper is that of the Defense Fuel Supply Center (DFSC) and the Military Sealift Command (MSC) in the worldwide distribution of bulk petroleum products. Routes and cargoes which meet delivery schedule dates for a multiplicity of product requirements at minimum cost are to be determined for a fleet of tankers. A general mathematical programming model is presented, and then a mixed integer model is developed which attempts to reflect the true scheduling task of DFSC and MSC as closely as possible. The problem is kept to within a workable size by the systematic construction of a set of tanker routes which does not contain many possible routes that can be judged unacceptable from practical considerations alone.     

Generalized programming by linear approximation of the dual gradient: Equality constraints

A modified generalized programming procedure is presented for solving concave programming problems with equality constraints. The procedure constructs convenient linear approximations of the gradient of the dual and finds points where the approximating functions vanish. In the quadratic programming case, the procedure is finitely convergent. Global convergence is established for the non-quadratic case. Illustrative numerical examples are included.     

An n-step, 2-variable search algorithm for the component placement problem

The component placement problem is a specialization of the quadratic assignment problem that has been extensively studied for a decade and which is of considerable practical value. Recently, interest in component placement algorithms has risen primarily as a result of increased activity in the field of computer-aided design automation. This paper deals with the methodology of component placement and is based on the results of considerable operational experience. A tutorial presentation of tree search placement algorithms is provided, and an improved placement procedure is described which is demonstrated to be effective in generating near optimal solutions to the component placement problem. These solutions are completely reproducible and are obtained at an acceptable expenditure of computational resources. An additional objective is an assessment of performance of the class of near optimal algorithms. In particular, the question- how close to optimal are the near optimal solutions- is examined.     

The Hungarian method for the assignment problem

This paper has been presented with the Best Paper Award. It will appear in print in Volume 52, No. 1, February 2005.     

What is Doctrine?

‘Doctrine’ has been part of military vernacular for at least a century. Nonetheless, it is a concept which is rather under-explored. The aim of this article is thus to break doctrine down into its component parts in order to grasp what a military doctrine actually is. Thereafter, the article points out different ways to utilise doctrine as a military devise. A doctrine cannot be, or rather should not be, all things to all men. On the contrary, doctrine can be a tool of command, tool of education or a tool of change. The main upshot of the article is that the future of doctrine is far brighter than its critics want us to believe.     

Churchill's naval holiday: Arms control and the Anglo‐German naval race, 1912–1914

Brian Johnson, The Secret War. London: BBC, 1978. Pp. 352; £6.50.

R. V. Jones, Most Secret War: British Scientific Intelligence 1939–45. London: Hamish Hamilton, 1978. Pp. xx + 556; £7.95.

Solly Zuckerman, From Apes to Warlords 1904–46. London: Hamish Hamilton, 1978. Pp. 00 (Information not available from publisher); £8.50.

Adrian Preston, ed., General Staffs and Diplomacy before the Second War. London: Croom Helm, 1978. Pp. 138; £5.95.

W. G. F. Jackson. ’Overlord’: Normandy 1944. London: Davis Poynter, 1978. Pp. 250; £6.75.

Richard K. Betts, Soldiers, Statesmen, and Cold War Crises. Cambridge, Mass. and London: Harvard University Press, 1977. Pp. 292 + index + appendices; Np.

Gerard J. Mangone, Marine policy for America—The United States at Sea. Lexington, Mass.: Lexington Books, 1977. Pp. 370, £17.50.

F. M. Richardson, Fighting Spirit. London: Leo Cooper, 1978. Pp. 189 + xv; £7.50.

Allen R. Millet, Ed., A Short History of the Vietnam War. London &; Bloomington: Indiana University Press, 1978. Pp. 169; £2.75.

Robert P. Berman, Soviet Airpower in Transition. Washington: Brookings, 1978. Pp. 82; $2.95 (Paper).     

Comparison between constant‐stress and step‐stress accelerated life tests under Time Constraint

By running life tests at higher stress levels than normal operating conditions, accelerated life testing (ALT) quickly yields information on the lifetime distribution of a test unit. The lifetime at the design stress is then estimated through extrapolation using a regression model. In constant‐stress testing, a unit is tested at a fixed stress level until failure or the termination time point of test, whereas step‐stress testing allows the experimenter to gradually increase the stress levels at some prefixed time points during the test. In this work, the optimal k‐level constant‐stress and step‐stress ALTs are compared for the exponential failure data under complete sampling and Type‐I censoring. The objective is to quantify the advantage of using the step‐stress testing relative to the constant‐stress one. Assuming a log‐linear life–stress relationship with the cumulative exposure model for the effect of changing stress in step‐stress testing, the optimal design points are determined under C/D/A‐optimality criteria. The efficiency of step‐stress testing to constant‐stress one is then discussed in terms of the ratio of optimal objective functions based on the information matrix. © 2013 Wiley Periodicals, Inc. Naval Research Logistics 00: 000–000, 2013