CUSUM charts for monitoring the mean of a multivariate Gaussian process

In this paper control charts for the mean of a multivariate Gaussian process are considered. Using the generalized likelihood ratio approach and the sequential probability ratio test under an additional constraint on the magnitude of the change various types of CUSUM control charts are derived. It is analyzed under which conditions these schemes are directionally invariant. These charts are compared with several other control schemes proposed in literature. The performance of the charts is studied based on the maximum average delay.     

ROBUST METHODS APPLIED TO ENERGY-CONSUMPTION DATA

In many instances a model is based on nonexperimental data and is used for prediction. In this situation, using both the least-squares and the robust methods simultaneously can result in models with improved predictive performance.     

FOUR APPROACHES TO THE CLASSIFICATION PROBLEM IN DISCRIMINANT ANALYSIS: AN EXPERIMENTAL STUDY*

Four discriminant models were compared in a simulation study: Fisher's linear discriminant function [14], Smith's quadratic discriminant function [34], the logistic discriminant model, and a model based on linear programming [17]. The study was conducted to estimate expected rates of misclassification for these four procedures when observations were sampled from a variety of normal and nonnormal distributions. In contrast to previous research, data were taken from four types of Kurtotic population distributions. The results indicate the four discriminant procedures are robust toward data from many types of distributions. The misclassification rates for both the logistic discriminant model and the formulation based on linear programming consistently decreased as the kurtosis in the data increased. The decreases, however, were of small magnitude. None of these procedures yielded statistically significant lower rates of misclassification under nonnormality. The quadratic discriminant function produced significantly lower error rates when the variances across groups were heterogeneous.     

A STEPWISE PROCEDURE FOR CONSTRAINED UTILITY MAXIMIZATION*

Constrained utility maximization underlies much consumer behavior in economics. Opportunities for solving important problems are ever present. However, most potential applications remain potential because existing software packages are not able to estimate the systems of equations necessary to identify the utility function. At least three features often conspire to make these problems intractable: the size of the system of equations that must be estimated, the lack of any theory for imposing zero restrictions on many of the parameters of the nonadditive utility functions, and the necessity to insure negative definiteness consistent with the axioms of consumer behavior. This paper develops an approach and illustrates the stepwise least squares estimator of a group of equations by application to the demand for food items.     

Mathematical Programming Formulations for the Discriminant Problem: An Old Dog Does New Tricks*

In recent years, much research has been done on the application of mathematical programming (MP) techniques to the discriminant problem. While promising results have been obtained, many of these techniques are plagued by a number of problems associated with the model formulation including unbounded, improper, and unacceptable solutions as well as solution instability under linear transformation of the data. In attempting to solve these problems, numerous formulations have been proposec involving additional variables and/or normalization constraints. While effective, these models can also become quite complex. In this paper we demonstrate that a simple, well-known special case of Hand's [13] original formulation provides an implicit normalization which avoids the problems for which various complicated remedies have been devised. While other researchers have made use of this formulation, its properties have not previously been fully recognized.     

A COMPARISON OF INFORMATION STRUCTURES FOR A RIGID DECISION RULE CASE

The information economics model of individual decision assumes that decision makers are capable of instantly modifying their decision rules in response to signal changes from the information structure. Individuals, however, often tend to stick to rigid decision rules, particularly when they are trained to respond with conditioned reactions, such as to a traffic light. This article modifies the individual decision model for such cases. It discusses probabilistic information structures as well as the deterministic information function. It results in an ordering of information structures that differs from the ordering imposed by the Blackwell Theorem. When deterministic information functions are considered, an ordering that is finer than the prevailing one is proposed. Transformations between deterministic and probabilistic information functions and the relationship between the proposed model and the previous theory are also discussed.     

Decision Power and Solutions of LP Discriminant Models: Rejoinder

A major problem of LP discriminant analysis is the validity of the solution. This note shows that to comprehend the effectiveness of the solution, conditions for unacceptable solutions need to be tightly characterized.     

Optimal Selection Strategy for the Group Interview Problem

We propose a more generalized version of the secretary problem, called the group interview problem, in which each group contains several alternatives and each group of alternatives is presented and evaluated sequentially over time. Using the assumptions corresponding to the classical secretary problem, we derive an optimal selection strategy which maximizes the probability of winning or selecting the single best choice in a given sequence of groups. We further address the problem of choosing at the beginning of the evaluation process a sequence of groups to maximize the winning probability. Because of formidable computational requirements to obtain an optimal solution to this sequencing problem, we then develop a heuristic algorithm based on several properties inherent in an optimal selection strategy. The heuristic procedure is evaluated experimentally using Monte Carlo simulation and is shown to be effective in obtaining near-optimal (within 5 percent) solutions.     

Burn-in Time and Estimation of Change-Point with Weibull-Exponential Mixture Distribution*

Many industrial products have three phases in their product lives: infant-mortality, normal, and wear-out phases. In the infant-mortality phase, the failure rate is high, but decreasing; in the normal phase, the failure rate remains constant; and in the wear-out phase, the failure rate is increasing. A burn-in procedure may be used to reduce early failures before shipping a product to consumers. A cost model is formulated to find the optimal burn-in time, which minimizes the expected sum of manufacturing cost, burn-in cost, and warranty cost incurred by failed items found during the warranty period. A mixture of Weibull hyperexponential distribution with shape parameter less than one and exponential distribution is used to describe the infant-mortality and the normal phases of the product life. The product under consideration can be either repairable or non-repairable. When the change-point of the product life distribution is unknown, it is estimated by using the maximum-likelihood estimation method. The effects of sample size on estimation error and the performance of the model are studied, and a sensitivity analysis is performed to study the effects of several parameters of the W-E distribution and costs on the optimal burn-in time.