Computational results for a stopping rule problem on averages

Suppose x₁, x₂, … are independently distributed random variables with Pr (x_i = 1) = Pr(x_i = ?1) = 1/2, and let s_n =

     

On a sequential rule for estimating the location parameter of an exponential distribution

Let us assume that observations are obtained at random and sequentially from a population with density function In this paper we consider a sequential rule for estimating μ when σ is unknown corresponding to the following class of cost functions In this paper we consider a sequential rule for estimating μ when σ is unknown corresponding to the following class of cost functions Where δ(X_I,…,X_N) is a suitable estimator of μ based on the random sample (X₁,…, X_N), N is a stopping variable, and A and p are given constants. To study the performance of the rule it is compared with corresponding “optimum fixed sample procedures” with known σ by comparing expected sample sizes and expected costs. It is shown that the rule is “asymptotically efficient” when absolute loss (p=-1) is used whereas the one based on squared error (p = 2) is not. A table is provided to show that in small samples similar conclusions are also true.     

Test for the extreme value and weibull distributions based on normalized spacings

Discussed in this article are tests for the extreme-value distribution, or, equivalently, for the two-parameter Weibull distribution when parameters are unknown and the sample may be censored. The three tests investigated are based on the median, the mean, and the Anderson-Darling A² statistic calculated from a set zⁱ of values derived from the spacings of the sample. The median and the mean have previously been discussed by Mann, Scheuer, and Fertig [10] and by Tiku and Singh [14]. Asymptotic distributions and points are given for the test statistics, based on recently developed theory, and power studies are conducted to compare them with each other and with two other statistics suitable for the test. Of the normalized spacings tests, A² is recommended overall; the mean also gives good power in many situations, but can be nonconsistent.     

Problems in life cycle support cost estimation

Although industry is expected to design hardware to fit into a general support system and to be capable of arguing life-cycle system costs, adequate information has not been available on the support system in terms of policies and operating decision rules. Policies and operating decisions by users dominate engineering design decisions in determining life-cycle support costs. The relative effect of each of these decision areas on support costs has yet to be resolved empirically. Without an understanding of the sensitivity of support costs to alternative designs, capability is limited in design improvement and support of end items. Life-cycle costing of analysis under cost-effectiveness and the maintainability of integrated logistics support is open to question.     

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.     

Server scheduling on parallel dedicated machines with fixed job sequences

We consider server scheduling on parallel dedicated machines to minimize the makespan. Each job has a loading operation and a processing operation. The loading operation requires a server that serves all the jobs. Each machine has a given set of jobs to process, and the processing sequence is known and fixed. We design a polynomial‐time algorithm to solve the two‐machine case of the problem. When the number of machines is arbitrary, the problem becomes strongly NP‐hard even if all the jobs have the same processing length or all the loading operations require a unit time. We design two heuristic algorithms to treat the case where all the loading times are unit and analyze their performance.     

Texas Ranger Auxiliaries: Double-Edged Sword of the Campaign for Northern Mexico, 1846–1848

This essay explores how federalized Texas Rangers, in the form of scout companies and larger mounted rifle regiments, provided controversial, and ultimately cost-effective, versatility to the US Army during its campaign in Northern Mexico between 1846 and 1848. It argues that their contributions centered on three tactical tasks that enhanced the invading army's maneuvers: reconnaissance, direct assault, and counterguerrilla patrolling. Each of these actions reflected a distinctive skill-set at which the auxiliaries excelled, marking them as exceptionally multifunctional assets. The Texans' augmentation coincided with, and was necessitated by, the evolving stages of the war in Northern Mexico, beginning with the American army's initial invasion, then transitioning to the assault on Monterrey, and finally ending with a troubled occupation where the rangers' brutality both enabled and undermined American pacification efforts.