A generalization of the entropy model for brand purchase behavior

Hemiter's entropy model for brand purchase behavior has been generalized for Renyi's measure of entropy which is a more general concept than Shannon's measure of entropy used by Herniter and which includes Shannon's measure as a limiting case. The generalized model considered here is more flexible than Herniter's model since it can give different marketing statistics for different products and it can give these statistics even when only some of the brands are considered.     

Optimal arrangement of systems

To location L_i we are to allocate a “generator” and n_i “machines” for i = 1, …,k, where n₁ … n₁ ≧ … ≧ n_k. Although the generators and machines function independently of one another, a machine is operable only if it and the generator at its location are functioning. The problem we consider is that of finding the arrangement or allocation optimizing the number of operable machines. We show that if the objective is to maximize the expected number of operable machines at some future time, then it is best to allocate the best generator and the n₁ best machines to location L₁, the second-best generator and the n₂-next-best machines to location L₂, etc. However, this arrangement is not always stochastically optimal. For the case of two generators we give a necessary and sufficient condition that this arrangement is stochastically best, and illustrate the result with several examples.     

Two-characteristic markov-type manpower flow models

A two-dimensional state space Markov Model of a Manpower System with special structure is analyzed. Examples are given from the military services. The probabilistic properties are discussed in detail with emphasis on computation. The basic equations of manpower stocks and flows are analyzed.     

Estimation of ordered parameters from k stochastically increasing distributions

There are given k (? 2) univariate cumulative distribution functions (c.d.f.'s) G(x; θ_i) indexed by a real-valued parameter θ_i, i=1,…, k. Assume that G(x; θ_i) is stochastically increasing in θ_i. In this paper interval estimation on the i^th smallest of the θ's and related topics are studied. Applications are considered for location parameter, normal variance, binomial parameter, and Poisson parameter.     

A partitioning technique for obtaining solutions to the modularization problem

A significant problem in electronic system design is that of partitioning the functional elements of an equipment schematic into subsets which may be regarded as modules. The collection of all such subsets generated by a particular partitioning forms a potential modular design. The specific problem is to determine that partitioning of the schematic that minimizes a cost function defined on the subsets subject to specified hardware, design, packaging, and inventory constraints. This problem is termed the modularization problem. This paper presents a method for obtaining restricted solutions to the modularization problem by employing some recent developments in linear graph theory obtained by one of the coauthors. Numerical results from the solution of several typical problems are presented.     

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.