An empirical bayes estimator for the scale parameter of the two-parameter weibull distribution

An empirical Bayes estimator is given for the scale parameter in the two-parameter Weibull distribution. The scale parameter is assumed to vary randomly throughout a sequence of experiments according to a common, but unknown, prior distribution. The shape parameter is assumed to be known, however, it may be different in each experiment. The estimator is obtained by means of a continuous approximation to the unknown prior density function. Results from Monte Carlo simulation are reported which show that the estimator has smaller mean-squared errors than the usual maximum-likelihood estimator.     

Optimal allocation of unreliable components for maximizing expected profit over time

In the present paper, we solve the following problem: Determine the optimum redundancy level to maximize the expected profit of a system bringing constant returns over a time period T; i. e., maximize the expression \documentclass{article}\pagestyle{empty}\begin{document}$ P\int_0^T {Rdt - C} $\end{document}, where P is the return of the system per unit of time, R the reliability of this system, C its cost, and T the period for which the system is supposed to work We present theoretical results so as to permit the application of a branch and bound algorithm to solve the problem. We also define the notion of consistency, thereby determining the distinction of two cases and the simplification of the algorithm for one of them.     

On the relationship between the force ratio and the instantaneous casualty-exchange ratio for some lanchester-type models of warfare

A “local” condition of winning (in the sense that the force ratio is changing to the advantage of one of the combatants) is shown to apply to all deterministic Lanchester-type models with two force-level variables. This condition involves the comparison of only the force ratio and the instantaneous force-change ratio. For no replacements and withdrawals, a combatant is winning “instantaneously” when the force ratio exceeds the differential casualty-exchange ratio. General outcome-prediction relations are developed from this “local” condition and applied to a nonlinear model for Helmbold-type combat between two homogeneous forces with superimposed effects of supporting fires not subject to attrition. Conditions under which the effects of the supporting fires “cancel out” are given.     

On the assignment and sequencing of operations on a crew-served project

This paper is concerned with assigning and sequencing a set of activities for some or all members of a crew of operators so that the completion time of all such operations is minimized. It is assumed that each of the operators in the crew possesses, initially, certain tasks that only he can perform. A branch-and-bound scheme is proposed to treat the problem, and suitable computational experience is provided.     

Toward a multi-stage information conversion model of the research and development process

Research and development activities in a business firm or government laboratory are portrayed as a multi-stage information generation and conversion process. A “basic research” phase generates opportunities, in the form of findings in a set of scientific disciplines, which are available for subsequent exploitation. It is assumed that increments to information in a subject area are stochastic, proportional to the amount of knowledge which already exists in the area, and have values which are randomly distributed. An “exploratory development” phase is viewed as a process of selecting a subset of alternative research opportunities, improving each opportunity in the direction of its applications, estimating the value of the improved opportunity and using these estimates to choose the exploratory development results to be implemented in engineering development. The “engineering development” phase makes the value of exploratory results realizable without changing value or risk. Engineering development costs are assumed to increase as value increases. If exploratory development is not successful, additional costs in engineering development must be incurred to bring the design up to a minimum desirable level. The model is intended as a step toward formulating and analyzing problems in management planning and control of the several interrelated stages of the research and development process.     

Stochastic duels with displacements (suppression)

The stochastic duel is extended to include the possibility of a near-miss on each round fired, which causes the opponent to displace. During displacement, the displacing contestant cannot return the fire but is still a target for his opponent. An alternative interpretation of this model is to consider the displacement time as the time a contestant's fire is suppressed by his opponent's fire and that he does not move, but merely ceases fire temporarily. All times are exponentially distributed.     

On a generalized bin-packing problem

In this paper we address a bin-packing problem which possesses a variety of modifications of the classic theme. Among these are bin-dependent chip weights, bin costs, and bin-dependent penalties for unused capacity. Lagrangian relaxations are employed in the context of a branch-and-bound framework in order to solve the problem after which substantial computational experience is provided.     

Time minimizing flows in directed networks

An important class of network flow problems is that class for which the objective is to minimize the cost of the most expensive unit of flow while obtaining a desired total flow through the network. Two special cases of this problem have been solved, namely, the bottleneck assignment problem and time-minimizing transportation problem. This paper addresses the more general case which we shall refer to as the time-minimizing network flow problem. Associated with each arc is an arc capacity (static) and a transferral time. The objective is to find a maximal flow for which the length (in time) of the longest path carrying flow is minimized. The character of the problem is discussed and a solution algorithm is presented.     

Nonadjacent extreme point methods for solving linear programs

In this article we present some advanced basis or block-pivoting, relaxation, and feasible direction methods for solving linear programming problems. Preliminary computational results appear to indicate that the former two types of simplex-based procedures may hold promise for solving linear programming problems, unlike the third type of scheme which is shown to be computationally unattractive.