John S. Ramberg

An approximate method for generating asymmetric random variables

A method for generating values of continuous symmetric random variables that is relatively fast, requires essentially no computer memory, and is easy to use is developed. The method, which uses a uniform zero-one random number source, is based on the inverse function of the lambda distribution of Tukey. Since it approximates many of the continuous theoretical distributions and empirical distributions frequently used in simulations, the method should be useful to simulation practitioners.

A Probability Distribution and its Uses in Fitting Data

A four-parameter probability distribution, which includes a wide variety of curve shapes, is presented. Because of the flexibility, generality, and simplicity of the distribution, it is useful in the representation of data when the underlying model is unknown. A table based on the first four moments, which simplifies parameter estimation, is given. Further important applications of the distribution include the modeling and subsequent generation of random variates for simulation studies and Monte Carlo sampling studies of the robustness of statistical procedures.

Generalized Linear and Quadratic Discriminant Functions Using Robust Estimates

Abstract Two new methods of constructing robust linear and quadratic discriminant functions are introduced. The first is a generalization of Fishers procedure for finding a linear discriminant function. It places less weight on those observations that are far from the overlapping regions of the two populations. The second new method substitutes M-estimates of the means and the covariance matrices into the usual expressions for the linear and quadratic discriminant functions. Monte Carlo results indicate lower misclassification probabilities for these schemes compared to Fishers linear discriminant function in cases of heavy-tailed or contaminated distributions.

Designing simulation experiments: Taguchi methods and response surface metamodels

G. Taguchi (1987) has made an innovative contribution to quality planning activities through the integrated use of loss functions and orthogonal arrays. The authors focus on the improvement and implementation of some of these techniques in the simulation arena. The orthogonal arrays advocated by Taguchi are related to classical experimental designs, which have played important tactical roles in the exploration of mathematical metamodels for the simulation response surface. However, the loss function and the associated robust design philosophy provide fresh insights into the process of optimizing or improving the simulations performance. The authors use examples to illustrate concepts such as the simultaneous treatment of variability and mean of performance measures, strategies for achieving system robustness, and implementation of noise through factorial designs. Relationships to other issues in designing and analyzing simulation experiments, such as response surface metamodels and variance reduction, are discussed.<<ETX>>

Discriminant Analysis Based on Ranks

Abstract A model-free rank procedure is proposed for the two-population discrimination problem that enables the practitioner to better control the balance between the two probabilities of misclassification. The method is applied to the discriminant functions resulting from normal assumptions and also to an adaptive one which is a weighted average of the linear and quadratic discriminant functions, where the weights are determined from the data. A Monte Carlo study shows that the rank method can greatly improve the balance between the two misclassification probabilities while keeping their average comparatively small.

An Overview of the Shainin System™ for Quality Improvement

ABSTRACT The Shainin System™ (SS) is the name given to a problem solving system, with its associated strategies and tools, developed by Dorian Shainin, and widely used and promoted in the manufacturing sector. Dorian Shainin also called this system Statistical Engineering, reflecting his engineering education and background. The consulting firm, Shainin LLC, offers the system under the trademarked name Red X® Strategy. Much of SS is neither well documented, nor adequately discussed in peer-reviewed journals. The goal of this article is to provide an overview of SS, a critical assessment, and a brief comparison with other industrial problem solving systems. The emphasis is on a discussion of the guiding philosophy and principles. Some specific SS tools are examined and compared with alternative methods. In our assessment, the Shainin System is valuable for many types of problems and many of its elements have been, or should be, incorporated into other process improvement methodologies. However, many of the statistical tools and methods promoted in conjunction with SS are neither novel nor necessarily the best.

Effective Engineering Design through Simulation

Abstract This paper presents a framework for designing, analyzing and improving systems and processes via discrete event simulation. The framework incorporates a robust design philosophy into a response surface metamodeling approach, and the simulation setting provides the analyst with an increased level of control relative to industrial experimentation. System optimization and improvement efforts can be carried out efficiently and effectively, providing insights into system behavior and suggesting optimal system configurations which may yield substantial improvements over those selected using more traditional approaches. One noteworthy benefit of the simulation framework is that robust design methodologies can be applied prospectively — at the inception and conceptualization phases of an engineering design project. We illustrate the method by considering the design of a small job shop.

On Spiring's normal loss function

Loss functions express the loss to society, incurred through the use of a product, in monetary units. Underlying this concept is the notion that any deviation from target of any product characteristic implies a degradation in the product performance and hence a loss. Spiring (1993), in response to criticisms of the quadratic loss function, developed the reflected normal loss function, which is based on the normal density function. We give some modifications of these loss functions to simplify their application and provide a framework for the reflected normal loss function that accomodates a broader class of symmetric loss situations. These modifications also facilitate the unification of both of these loss functions and their comparison through expected loss. Finally, we give a simple method for determing the parameters of the modified reflected normal loss function based on loss information for multiple values of the product characteristic, and an example to illustrate the flexibility of the proposed model and the determination of its parameters.

An Adaptive Procedure for Selecting the Population With Largest Location Parameter

An adaptive procedure for selecting the population with the largest (smallest) location parameter is given. A Monte Carlo sampling study is presented indicating that this procedure performs as well as the means procedure when the underlying distribution is medium tailed like the normal. It is shown to be superior to both the means procedure and the rank sum procedure when the underlying distribution is either very light tailed (e.g., the uniform distribution) or very heavy tailed (e.g., the Cauchy distribution).

Generation of Continuous Multivariate Distributions for Statistical Applications

SYNOPTIC ABSTRACTTwo general and several specific schemes are described for generating variates from continuous multivariate distributions. Algorithms are provided for the multivariate normal, Johnson system, Cauchy, elliptically contoured (including Pearson Types II and VII), Morgenstern, Plackett, Ali, Gumbel, Burr (and related), Beta-Stacy and Khintchine distributions. Issues in designing multivariate Monte Carlo studies are discussed.