Controlling rates in a double queue

A double-ended queue with a Poisson arrival pattern is examined in a situation where the rates depend (in a restricted sense) on both the time and the state of the system. Under some circumstances, the rates can be controlled. This article studies the distribution of the difference in queue sizes for each member of a large class of control strategies and introduces the problem of determining the optimal times at which the control should be in effect in order to maximize certain objective functions.     

Minimum-cost mixtures of area and point defenses assuming simultaneous attack

It is desired to select numbers of area and point interceptors that minimize the cost of such defensive missiles under the condition that the maximum total expected damage produced by an unknown number of attacking missiles A be bounded above by a given function of A. Area coverages may overlap. The attacker is assumed to know the numbers of area and point interceptors and to launch a simultaneous attack (of arbitrary size A) against all targets, which is optimal against the given defenses. The defender is assumed to observe the attack and then allocate his area and point interceptors against attacking missiles so as to minimize the total expected damage. Upper and lower bounds on the minimal cost are obtained by solving integer programming problems.     

Algorithms and heuristics for variable-yield lot sizing

We consider the multiperiod lot-sizing problem in which the production yield (the proportion of usable goods) is variable according to a known probability distribution. We review two economic order quantity (EOQ) models for the stationary demand continuous-time problem and derive an EOQ model when the production yield follows a binomial distribution and backlogging of demand is permitted. A dynamic programming algorithm for an arbitrary sequence of demand requirements is presented. Heuristics based on both the EOQ model and appropriate modification of the underlying perfect-yield lot-sizing policies are discussed, and extensive computational evaluation of these heuristics is presented. Two of these heuristics are then modified to include the notion of supply safety stock. The modified heuristics consistently produce near-optimal lot-sizing policies for problems with stationary and time-varying demands.     

Likelihood estimation for generalized mixed exponential distributions

The class of functions expressed as linear (not necessarily convex) combinations of negative exponential functions is dense in the set of all square integrable functions on the nonnegative reals. Because of this and resultant mathematical properties, linear combinations of exponential densities have excellent potential for wide application in stochastic modeling. This work documents the development and testing of a practical procedure for maximum-likelihood estimation for these generalized exponential mixtures. The algorithm offered for the problem is of the Jacobi type and guarantees that the result will provide a legitimate probability function of the prescribed type. Extensive testing has been performed and results are very favorable: convergence is rapid and the use of computer resources rather limited.     

四轴超精密车床的改进坐标驱动装置

带微进给方式步进电机的PC控制轴系驱动装置可生产光学质量的表面。超精密车床可生产诸如球体和非球体之类的集合体,其表面粗糙度≤5nmRa,可用于光学装置的反光镜或空气轴承转轴的超精密零件。     

Application of level crossing analysis to discrete state processes in queueing systems

In this paper we introduce a discrete state level crossing analysis and present some basic results and a key theorem of level crossings. We illustrate the fertility of the discrete state level crossing analysis by applying it to queueing systems with (i) bulk arrival, (ii) instantaneous feedback, (iii) limited waiting space, and (iv) to machine interference problems.     

A time series analysis of some interrelated logistics performance variables

This paper is a case study. We show how the powerful methods of time series analysis can be used to investigate the interrelationships between Alert Availability, a logistics performance variable, and Flying Hours, an operational requirement, in the presence of a major change in operating procedures and using contaminated data. The system considered is the fleet of C-141 aircraft of the U.S. Air Force. The major change in operating procedures was brought about by what is known as Reliability Centered Maintenance, and the contaminated data were due to anomalies in reporting procedures. The technique used is a combination of transfer function modeling and intervention analysis.     

Characterizations of the exponential distribution by higher-order gap

Suppose X₁,X₂, ?,X_n is a random sample of size n from a continuous distribution function F(x) and let X_1,n, ≦ X_2,n ≦ ? ≦ X_n,n be the corresponding order statistics. We define the jth-order gap g_i,j as g_i,j = X_i+j,n ? X_i,n, 1 ≦ i < n, 1 ≦ j ≦ n ? i. In this article characterizations of the exponential distribution are given by considering the distributional properties of g_k,n-k, 1 ≦ k ≦ n.     

Optimal maintenance models for systems subject to failure–A Review

This paper is a state-of-the-art review of the literature related to optimal maintenance models of systems subject to failure. The emphasis is on work appearing since the 1976 survey, “A Survey of Maintenance Models: The Control and Surveillance of Deteriorating Systems,” by W.P. Pierskalla and J.A. Voelker, published in this journal.