Application of dirichlet integrals for curtailment problems in sampling inspection

The standard problem in sampling inspection is to consider plans with and without curtailment. Curtailment causes difficulty and authors rarely give exact results (i.e., exact OC and ASN functions) for curtailed procedures. In this article we regard curtailment as an inverse sampling procedure and use Dirichlet integrals to obtain exact formulas for the OC, the ASN, and also the variance of the number of observations required under three types of plans: no curtailment, semicurtailment (for rejection only) and two-sided curtailment. Different sections of the article deal with the single sample, the two-stage, and the multiple-stage sampling problems. New tables for carrying out the single-sample procedure are included in the article. The authors feel that this article presents new directions and new ways of dealing with problems associated with quality control.     

Assemble to order and assemble in advance in a single-period stochastic environment

Faced with stochastic demand, a firm may decide to assemble its products in advance or assemble them once actual demand is realized. In general, the production cost for items assembled in advance (AIA) is lower than for items assembled to order (ATO), because there is no need to expedite, and the production process can be planned and executed well in advance. On the other hand, items assembled in advance (AIA) for which there is no demand incur excessive and unnecessary assembly costs. The two policies, AIA and ATO, as well as a composite one, are compared and analyzed in light of these trade-offs. The composite model, which is shown as the dominating policy, is also extended to deal with the following two scenarios. The first assumes a loss of a fraction of the demand when demand cannot be satisfied from the shelf but rather through ATO. The second considers the effects of budget constraints on the total inventory cost. © 1995 John Wiley & Sons, Inc.     

Optimal layered search

This article investigates the problem of planning an optimal layered search for a stationary target. A search is layered if it assigns each point in the search space an integer number of glimpses or looks. General necessary and sufficient conditions and an existence theorem are obtained. The special case in which the initial target distribution is bivariate normal is considered in detail.     

Book reviews

Encyclopaedia of Modern Air Force Squadrons. By Chris Ashworth. Patrick Stephens, London (1989), ISBN 1-8526-013-6, £19.95

The Future of Sea Power. By Eric Grove. Routledge, London (1990), ISBN 0-415-00482-9, £35.00

Soviet Strategic Interests in the North. By Kirsten Amundsen. Pinter, London (1990), ISBN 0-86187-018-2, £30.00

Soviet Seapower in Northern Waters. Edited by John Skogan and Arne Brundtland. Pinter, London (1990), ISBN 0-86187-038-7, £35.00

Glasnost, Perestroika, and U.S. Defense Spending. By William W. Kaufmann, Brookings Institution, Washington, DC (1990), ISBN 0-8157-4881-7, $8.95

The Educating of Armies. Edited by Michael D. Stephens. Macmillan, London (1989), ISBN 0-333-43447-1, £35.00     

Rectilinear m-Center problem

In this article we consider the unweighted m-center problem with rectilinear distance. We preent an O(n^m–2 log n) algorithm for the m-center problem where m ≥ 4.