The logistic–exponential survival distribution

For various parameter combinations, the logistic–exponential survival distribution belongs to four common classes of survival distributions: increasing failure rate, decreasing failure rate, bathtub‐shaped failure rate, and upside‐down bathtub‐shaped failure rate. Graphical comparison of this new distribution with other common survival distributions is seen in a plot of the skewness versus the coefficient of variation. The distribution can be used as a survival model or as a device to determine the distribution class from which a particular data set is drawn. As the three‐parameter version is less mathematically tractable, our major results concern the two‐parameter version. Boundaries for the maximum likelihood estimators of the parameters are derived in this article. Also, a fixed‐point method to find the maximum likelihood estimators for complete and censored data sets has been developed. The two‐parameter and the three‐parameter versions of the logistic–exponential distribution are applied to two real‐life data sets. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Book reviews

Use of Force: The Practise of States by A. Mark Weisburd, Penn: Penn State Press, University Park, 1997, ISBN 0-271-01679-5 (hbk), $65.00/£58.00, ISBN 0-271-01680-9 (pbk), $25.00/£22.50

Late Breaking Foreign Policy: the News Media's Influence on Peace Operations by Warren P. Strobel, Washington DC: United States Insititute of Peace Press, 1997, ISBN 1-878379-68-2 (hbk), £23.25, ISBN 1-878379-67-4 (pbk)

The Reluctant Sheriff: The United States After the Cold War by Richard N. Haass, New York: Council on Foreign Relations, 1997, 148pp, index, ISBN 0-87609-201-6 (hbk), $24.95

The UN, Peace and Force edited by Michael Pugh, London: Frank Cass, 1997, ISBN 0-7146-4795-4 (hbk), £29.50, ISBN 0-7146-4320-3 (pbk), £15.00

Confidence-Building in South East Asia by Malcolm Chalmers, Oxford: Westview Press, 1996, ISBN 1-85143-116-0 (pbk), £19.95

Britain's Strategic Nuclear Deterrent: From Before the V-Bomber to Beyond Trident by Robert H. Paterson, London: Frank Cass, 1997, ISBN 0-7146470-3 (hbk), £35.00, ISBN 0-7146-4297-5 (pbk) £18.00

OSS in China: Prelude to Cold War by Maochun Yu, London: Yale University Press, 1997, ISBN 0 300 06698-8 (hbk), £25.00

Preventing Violent Conflicts: A Strategy for Preventive Diplomacy by Michael S. Lund, Washington DC: US Institute of Peace Press, 1996, ISBN 1-878379-52-6 (pbk), £11.75     

Volume discount decisions: Wealth maximization or EOQ approach?

A recent paper finds that when volume discounts are available, in some cases, reliance on the Economic Order Quantity (EOQ) model can induce purchasers to make wealth reducing decisions, and the Present Value (PV) approach should be preferred. While this finding is theoretically correct, the magnitudes of wealth reductions suggested by the paper's numerical examples seem to be questionable. Furthermore, the paper also finds that, in some other cases, a purchaser using the EOQ approach realizes a net increase in current wealth compared to a purchaser using the PV approach. Logic suggests that such a finding cannot be correct, since by its very definition, it is the PV approach that seeks to maximize the current wealth. We offer an alternative frame of comparison and a modified model to show that, under the paper's assumptions, the EOQ approach can never realize a net increase in current wealth compared to the current wealth generated by the PV approach. On the other hand, we also show that when typical values of the relevant parameters prevail, the additional costs imposed by the EOQ approach are not significant. Finally, we suggest that insofar as the PV approach requires greater administrative costs to implement, it may even be counterproductive to the goal of wealth maximization. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 377–389, 1998     

Joint determination of optimum variable and attribute target means

This article considers the problem of joint control of attribute and variable quality characteristics of a given product. Items are acceptable if they meet the specifications for both types of quality characteristics at the same time. Otherwise, the items are sold as scrap at reduced prices. The objective is to determine simultaneously the target values for each characteristic so as to maximize the expected profit per item. Several item-by-item quality-inspection plans are formulated on the basis of various inspection strategies. These strategies are defined in terms of whether the inspection is to be carried out simultaneously for both characteristics, or sequentially, or whether inspection for one of the characteristics is to be ignored. All these plans are shown to differ in terms of their profitability. However, they all yield equivalent quality standards. A numerical example is provided to illustrate the application of these models.     

Vector processing approach to constrained network problems

Modification of algorithms designed for scalar computing, to take advantage of vector processing, raises several challenges. This article presents the vectorization of the primal simplex based network algorithm and results in a 50% improvement in computational time. One of the major contributors to this improvement is the matching of the size of the pricing candidate list to the vector register size. The side constraints are relaxed into a single surrogate constraint. The single constraint network algorithm is vectorized and used as the basis for solving large-scale constrained network problems. Computational experiments are presented which illustrate the vectorization of the network code as well as the ability of the surrogate constraint approach to deal with large constrained network problems.     

Estimating a survival curve when new is better than used with respect to a distinguished set

Hollander, Park, and Proschan define a survival function S of a positive random variable X to be new better than used at age t₀ (NBU-{t₀}) if S satisfies $ \begin{array}{*{20}c} {\frac{{S(x + t_0)}}{{S\left({t_0} \right)}} \le S\left(x \right),} & {{\rm for}\,{\rm all}\,x\, \ge \,0,} \\ \end{array}$ where S(x) = P(X > x). The NBU-{t₀} class is a special case of the NBU-A family of survival distributions, where A is a subset of [0, ∞). These families introduce a variety of modeling possibilities for use in reliability studies. We treat problems of nonparametric estimation of survival functions from these classes by estimators which are themselves members of the classes of interest. For a number of such classes, a recursive estimation technique is shown to produce closed-form estimators which are strongly consistent and converge to the true survival distribution at optimal rates. For other classes, additional assumptions are required to guarantee the consistency of recursive estimators. As an example of the latter case, we demonstrate the consistency of a recursive estimator for S ∈ NBU-[t₀, ∞) based on lifetime data from items surviving a preliminary “burn-in” test. The relative precision of the empirical survival curve and several recursive estimators of S are investigated via simulation; the results provide support for the claim that recursive estimators are superior to the empirical survival curve in restricted nonparametric estimation problems of the type studied here.     

An infiltration game on k arcs

An infiltrator, starting at a safe base, tries to pass, undetected by a guard and within a time limit, along one of k nonintersecting arcs to a safe destination. Optimal strategies and the value are obtained for this discrete zero-sum search-evasion game.     

Stochastic comparisons for single-server queues

We consider single-server queueing systems with the queue discipline “first come, first served,” interarrival times {u_k, k ≥ l}, and service times {u_k, k ≥ l}, where the {u_k} and {u_k} are independent sequences of non-negative random variables that are independently but not necessarily identically distributed. Let X_k = u_k − u_k (k ≥ 1), S₀ 0, S_n = X₁ + X₂ … + X_n(n≥1). It is known that the (possibly nonhomogeneous) random walk {S_n} determines the behavior of the system. In this paper we make stochastic comparisons of two such systems σ₁,σ₂ whose basic random variables X and X are stochastically ordered. The corresponding random walks are also similarly ordered, and this leads to stochastic comparisons of idle times, duration of busy period and busy cycles, number of customers served during a busy period, and output from the system. In the classical case of identical distributions of {u_k} and {u_k} we obtain further comparisons. Our results are for the transient behavior of the systems, not merely for steady state.