Book reviews

John Horsfield, The Art of Leadership in War. The Royal Navy From the Age of Nelson to the End of World War II. Westport, Conn. and London: Greenwood Press, 1980. Pp. 240; £14.75.

John Joseph Timothy Sweet, Iron Arm: The Mechanization of Mussolini's Army, 1920–1940. Westport, Connecticut &; London: Greenwood Press. 1980. Pp. 207; £15.50.

Peter H. Merkl, The Making of a Stormtrooper. Princeton, N.J: Princeton U.P., 1980. Pp. 328; £8.60.

Greg Herken, The Winning Weapon: The Atomic Bomb in the Cold War 1945–1950. New York: Alfred A. Knopf, 1980. Pp. 425; $15.00.

Geoffrey Smith and Nelson W. Polsby, British Government and its Discontents. New York: Basic Books, and London: Harper and Row, 1981. Pp. 202; £7.95.

Seweryn Bialer (ed.), The Domestic Context of Soviet Foreign Policy. Boulder, Colorado: Westview Press and London: Croom Helm, 1981. Pp. 441; £14.95.

Jerry F. Hough, Soviet Leadership in Transition. Washington, D.C.: Brookings Institution and Oxford, Basil Blackwell, 1981. Pp. 175; £12.00 (hb.) and £3.95 (pb.)

Edward F. Mickolus, Transnational Terrorism: A Chronology of Events 1968–1979. London: Aldwych Press, 1980. Pp. 967; £39.95.

Barry Rubin, The Great Powers in the Middle East, 1941–47; The Road to the Cold War, London: Frank Cass, 1980. Pp. 254; £14.50;

Daniel Heradstveit, The Arab‐Israeli Conflict; Psychological Obstacles to Peace. Oslo: Universittsforlaget, 1979. Pp. 234; £11.60;

Janice Gross Stein, and Raymond Tanter, Rational Decision‐making; Israel's Security Choices 1967. Columbus. Ohio; Ohio State University Press, 1980. Pp. 399; $35.     

On estimating population characteristics from record-breaking observations II. Nonparametric results

Consider an experiment in which only record-breaking values (e.g., values smaller than all previous ones) are observed. The data available may be represented as X₁,K₁,X₂,K₂, …, where X₁,X₂, … are successive minima and K₁,K₂, … are the numbers of trials needed to obtain new records. Such data arise in life testing and stress testing and in industrial quality-control experiments. When only a single sequence of random records are available, efficient estimation of the underlying distribution F is possible only in a parametric framework (see Samaniego and Whitaker [9]). In the present article we study the problem of estimating certain population quantiles nonparametrically from such data. Furthermore, under the assumption that the process of observing random records can be replicated, we derive and study the nonparametric maximum-likelihood estimator F̂ of F. We establish the strong uniform consistency of this estimator as the number of replications grows large, and identify its asymptotic distribution theory. The performance of F̂ is compared to that of two possible competing estimators.     

New purification algorithms for linear programming

Two new algorithms are presented for solving linear programs which employ the opposite-sign property defined for a set of vectors in m space. The first algorithm begins with a strictly positive feasible solution and purifies it to a basic feasible solution having objective function value no less under maximization. If this solution is not optimal, then it is drawn back into the interior with the same objective function value, and a restart begins. The second algorithm can begin with any arbitrary feasible point. If necessary this point is purified to a basic feasible solution by dual-feasibility–seeking directions. Should dual feasibility be attained, then a duality value interval is available for estimating the unknown objective function value. If at this juncture the working basis is not primal feasible, then further purification steps are taken tending to increase the current objective function value, while simultaneously seeking another dual feasible solution. Both algorithms terminate with an optimal basic solution in a finite number of steps.     

Log‐concave and concave distributions in reliability

Nonparametric classes of life distributions are usually based on the pattern of aging in some sense. The common parametric families of life distributions also feature monotone aging. In this paper we consider the class of log‐concave distributions and the subclass of concave distributions. The work is motivated by the fact that most of the common parametric models of life distributions (including Weibull, Gamma, log‐normal, Pareto, and Gompertz distributions) are log‐concave, while the remaining life of maintained and old units tend to have a concave distribution. The classes of concave and log‐concave distributions do not feature monotone aging. Nevertheless, these two classes are shown to have several interesting and useful properties. We examine the closure of these classes under a number of reliability operations, and provide sharp reliability bounds for nonmaintained and maintained units having life distribution belonging to these classes. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 419–433, 1999     

A model for critical crack size estimation in fatigue failure of gun barrels

With repeated firing, fatigue cracks are produced in a gun barrel, and the barrel is no longer useful when a crack reaches a critical size. The initial crack size and the critical crack size, as well as the number of firings producing the critical crack size, may be considered as random variables. Assuming a proportional damage model for crack growth, a method for estimating the critical crack size distribution is presented. From these results, an estimate of the barrel life, or the residual barrel life once a crack of a given size is measured, can be obtained.     

Transient analysis of multiple-unit reliability systems

A general Markovian model representing several multiple-unit redundant repairable systems is proposed and its transient behavior is studied. Specifically, for multiple-unit reliability system the reliability and availability functions are derived in an explicit form for the transient case. The stationary availability and mean time to system failure are deduced from the main results as special cases.     

Incorporating redundancy considerations into stockage models

This article is concerned with evaluating the impact on weapon system availability of component and assembly redundancy. The evaluation must be efficient, and it must be possible to integrate the evaluation into multiechelon stockage models whose objective is to find the least cost mix of stockage consistent with the availability goals for weapon (or other type) systems. The mathematics to be discussed here provides a rigorous solution to the evaluation problem when there is only a single supply echelon; there can be upper-echelon repair, but not supply, unless the supply is from a “perfect” supplier, always in stock. For the more general multiechelon case, approximate approaches are presented.     

Facility location on a grid with a diagonal line

This article extends the traditional median problem on a grid to include a diagonal line (e.g., a street). In contrast to the traditional median problem, this generalized problem is nonconvex and nonseparable, invalidating some of the properties on which well-known median-seeking algorithms are based. This work presents an algorithm for finding the median on this generalized grid and discusses the relationship between it and the traditional median.