Analysis of data from life-test experiments under an exponential model

This paper discusses situations in which the distribution of a lifetime response variable T is taken to depend upon a vector x of regressor variables. We specifically consider the case in which T, given x , has an exponential distribution, and in which x represents levels of fixed factors in an experimental design. Methods of analyzing data under this type of model are discussed, with maximum likelihood and least squares methods being presented and compared.     

Auxiliary procedures for solving long transportation problems

An efficient auxiliary algorithm for solving transportation problems, based on a necessary but not sufficient condition for optimum, is presented.     

On the distribution of the optimal value for a class of stochastic geometric programs

An approach is presented for obtaining the moments and distribution of the optimal value for a class of prototype stochastic geometric programs with log-normally distributed cost coefficients. It is assumed for each set of values taken on by the cost coefficients that the resulting deterministic primal program is superconsistent and soluble. It is also required that the corresponding dual program has a unique optimal point with all positive components. It is indicated how one can apply the results obtained under the above assumptions to stochastic programs whose corresponding deterministic dual programs need not satisfy the above-mentioned uniqueness and positivity requirements.     

Stochastic linear programs with simple recourse: The equivalent deterministic convex program for the normal,exponential, and erlang cases

We consider here stochastic linear programs with simple recourse when all the elements of the technology matrix and the resource vector have certain specific distributions. The distributions considered are the Normal, Exponential and Erlang. For the first two instances we extend the equivalent deterministic program to include the variance of the recourse. Finally, a simple example is given to illustrate the application of the formulas for the Erlang case.     

Spike swapping in basis reinversion

During basis reinversion of either a product form or elimination form linear programming system, it may become necessary to swap spike columns to effect the reinversion and maintain the desired sparsity characteristics. This note shows that the only spikes which need be examined when an interchange is required are those not yet processed in the current external bump.     

A new approach for dealing with the startup problem in discrete event simulation

This article proposes a practical, data-based statistical procedure which can be used to reduce or remove bias owing to artificial startup conditions in simulations aimed at estimating steady-state means. We discuss results of experiments designed to choose good parameter values for this procedure, and present results of extensive testing of the procedure on a variety of stochastic models for which partial analytical results are available. The article closes with two illustrations of the application of the procedure to more complex statistical problems which are more representative of the kinds of purposes for which real-world steady-state simulation studies might be undertaken.