Non-Normality and the Design of Control Charts for Averages*

Non-normality has a significant effect on the performance of control charts for averages. The design considerations for a control chart for averages must include recognition of the degree of non-normality of the underlying data. The performance of a control chart may be judged on its ability to correctly identify the probabilities of assignable causes of variation and chance causes of variation in a process. This paper examines the effects of non-normality, as measured by skewness and kurtosis, on the performance, and hence the design, of control charts for averages and provides an alternative method of designing charts for averages of data with non-normal distributions.     

The Detection of Nuclear Materials Losses*

The identification and location of materials losses in nuclear facilities is an important issue. Many complexities arise in monitoring such losses. These complexities include the dependency among materials balance observations and the influence of errors (outliers) on parameter estimates of various monitoring methods. The proposed Joint Estimation procedure is superior to standard methods (control chart and CUSUM) and to methods that build in correlation (ARMA control chart, ARMA CUSUM, and the Generalized M procedure) in the detection of nuclear materials losses. The Joint Estimation procedure is robust to the influence of outliers, is flexible in accommodating a range of dependencies among observations, and provides information on the type of loss. Further, the procedure is reliable in that it yields a probability of false alarms and a probability of detecting losses closer to specifications.     

METHODS FOR ANALYZING EXPERIMENTS WITH MULTIPLE CRITERIA*

An approach to analyzing experimental data with multiple criteria is explained and demonstrated on data from a test of the effectiveness of two posters. As a supplement to traditional multivariate analysis of variance and covariance, the application of a step-down F test is advocated when an ordering of the criterion is meaningful, and an analysis of contrasts is recommended when such an ordering is not managerially relevant. The step-down procedure has the advantage of simultaneously testing an overall hypothesis and hypotheses on each criterion variable.     

A Bayesian Approach for Analyzing Results of Vehicle Collision Tests

Certain motor vehicle safety standards stipulate a collision test speed and a set of performance criteria that vehicles must satisfy during or after the collision test. For example, Federal Motor Vehicle Safety Standard 301 requires a 30 mile per hour (mph) barrier collision and specifies a certain maximum allowable limit on the total spillage of fuel. Vehicle designs are required to meet this standard; however, when collision tests are conducted at speeds higher than the standard, vehicles do not always satisfy the performance criteria. This paper develops a mathematical model for estimating the probability of meeting the standard by using a Bayesian framework to incorporate engineering judgment with collision test results. The model is based on the idea that there are random features to a vehicle's ability to meet performance standards in a collision, especially at such elevated speeds. Example calculations are included to illustrate the estimation of the probability of meeting the standard and to compare it with a maximum likelihood approach.     

The Interpretation of Coefficients in Models with Qualitative Dependent Variables*

A substantial body of empirical accounting, finance, management, and marketing research utilizes single equation models with discrete dependent variables. Generally, the interpretation of the coefficients of the exogenous variables is limited to the sign and relative magnitude. This paper presents three methods of interpreting the coefficients in these models. The first method interprets the coefficients as marginal probabilities and the second method interprets the coefficients as elasticities of probability. The third method utilizes sensitivity analysis and examines the effect of hypothetical changes in exogenous variables on the probability of choice. This paper applies these methods to a published research study.     

A Maximum-Entropy Based Heuristic for Density Estimation from Data in Histogram Form*

We look at a specific but pervasive problem in the use of secondary or published data in which the data are summarized in a histogram format, perhaps with additional mean or median information provided; two published sources yield histogram-type summaries involving the same variable, but the two sources do not group the values of the variable the same way; the researcher wishes to answer a question using information from both data streams; and the original, detailed data underlying the published summary, which could give a better answer to the question, are unavailable. We review relevant aspects of maximum-entropy (ME) estimation, and develop a heuristic for generating ME density estimates from data in histogram form when additional means and medians may be known. Application examples from several business and scientific areas illustrate the heuristic's use. Areas of application include business and social or market research, risk analysis, and individual risk profile analysis. Some instructional or classroom applications are possible as well.     

Estimation of Nonlinear Models in the Presence of Measurement Error*

Techniques used in decision sciences and business research to estimate interactions between latent variables are limited in controlling for measurement error. This article uses a latent structure modeling approach that substantially controls for measurement error in nonlinear relationships. The results of this technique are compared to the results obtained applying hierarchical regression analysis and the impact of measurement error is assessed. The paper provides a unique assessment of the validity of the multi-attribute attitude model. The validity of the multiplicative rule in the model is supported.     

Inference in a Binary Response Model with Applications to Data Analysis*

Standard errors of the coefficients of a logistic regression (a binary response model) based on the asymptotic formula are compared to those obtained from the bootstrap through Monte Carlo simulations. The computer intensive bootstrap method, a nonparametric alternative to the asymptotic estimate, overestimates the true value of the standard errors while the asymptotic formula underestimates it. However, for small samples the bootstrap estimates are substantially closer to the true value than their counterpart derived from the asymptotic formula. The methodology is discussed using two illustrative data sets. The first example deals with a logistic model explaining the log-odds of passing the ERA amendment by the 1982 deadline as a function of percent of women legislators and the percent vote for Reagan. In the second example, the probability that an ingot is ready to roll is modelled using heating time and soaking time as explanatory variables. The results agree with those obtained from the simulations. The value of the study to better decision making through accurate statistical inference is discussed.     

ON THE IMPLICATIONS OF SPECIFICATION UNCERTAINTY IN FORECASTING*

Forecasters typically select a statistical forecasting model from among a set of alternative models. Subsequently, forecasts are generated with the chosen model and reported to management (forecast consumers) as if specification uncertainty did not exist (i.e., as if the chosen model were the “true” model of the forecast variable). In this note, a well-known Bayesian model-comparison procedure is used to illustrate some of the ambiguities and distortions of forecasts that do not reflect specification uncertainty. It is shown that a single selected forecasting model (however chosen) will generally misstate measures of forecast risk and lead to point and interval forecasts that are misplaced from a decision-theoretic point of view.     

Improved Linear Programming Models for Discriminant Analysis*

Discriminant analysis is an important tool for practical problem solving. Classical statistical applications have been joined recently by applications in the fields of management science and artificial intelligence. In a departure from the methodology of statistics, a series of proposals have appeared for capturing the goals of discriminant analysis in a collection of linear programming formulations. The evolution of these formulations has brought advances that have removed a number of initial shortcomings and deepened our understanding of how these models differ in essential ways from other familiar classes of LP formulations. We will demonstrate, however, that the full power of the LP discriminant analysis models has not been achieved, due to a previously undetected distortion that inhibits the quality of solutions generated. The purpose of this paper is to show how to eliminate this distortion and thereby increase the scope and flexibility of these models. We additionally show how these outcomes open the door to special model manipulations and simplifications, including the use of a successive goal method for establishing a series of conditional objectives to achieve improved discrimination.     

A Comparison of Linear Programming and Parametric Approaches to the Two-Group Discriminant Problem*

Recent simulation-based studies of linear programming models for discriminant analysis have used the Fisher linear discriminant function as the benchmark for parametric methods. This article reports experimental evidence which suggests that, while some linear programming models may match or even exceed the Fisher approach in classification accuracy, none of the fifteen models tested is as accurate on normally distributed data as the Smith quadratic discriminant function. At the minimum, further testing is warranted with an emphasis on data sets that arise from significantly non-Gaussian populations.     

TIME-VARYING PARAMETER ESTIMATION AS EXPLORATION*

A sequential time-variation method is utilized in an attempt to detect changes over time in the effectiveness of market communication for an ethical drug. Sudden changes are indicated at three different points in time, and two of these are confirmed by subsequent analysis and information. Gradual changes are also indicated, but these are not confirmed by market information or statistical analysis.     

Introducing Discriminant Analysis to the Business Statistics Curriculum*

Recently a good deal of interest and effort has been directed toward making statistics courses more effective in business schools. It is believed that a key to success in this area involves giving a more prominent role to statistical tools which are useful in actual business practice. If the research literature is any indication, discriminant analysis (DA) has many potential applications in virtually all areas of business. Yet, DA is rarely taught in undergraduate business and/or M.B.A. statistics courses. This is partially due to the fact that most presentations of DA are relegated to multivariate statistics texts that assume an advanced knowledge of linear algebra. This paper attempts to rectify this situation by proposing a simplified pedagogical approach for introducing linear DA in undergraduate and/or M.B.A. business statistics courses.     

Necessary and Sufficient Conditions of Unacceptable Solutions in LP Discriminant Analysis*

Characterization of unacceptable solutions for linear programming (LP) discriminant models have been discussed in the literature and the results presented so far are not satisfactory. This paper establishes necessary and sufficient conditions of unacceptable solutions for a number of LP models, addresses the practical implications of these conditions, and discusses the relationship between unacceptable solutions and multiple solutions.     

Characterization of Unacceptable Solutions in LP Discriminant Analysis*

Many linear programming models have been proposed for performing discriminant analysis. Partial characterizations for unacceptable solutions have been presented and new models proposed to circumvent these problems. In this paper those conditions leading to unacceptable solutions for all two-group models are characterized.     

A Computational Study of Replicated Clustering with an Application to Market Segmentation*

In most commercial applications of k-means clustering, researchers choose one set of kseed points to start the partitioning process; often, the initial set of seeds is chosen randomly. Using Monte Carlo simulation, we show that significant benefits are associated with replicated starting configurations that incorporate seed selection procedures based on a hierarchical clustering of sample points drawn from the original data matrix. A real-world application of the approach is then presented.     

A Robust Multivariate Procedure for the Identification of Problem Savings and Loan Institutions*

The 1980s have seen a great increase in the number of failed savings and loan institutions. In order to prevent such failures, it would be helpful if regulators have an early warning model. Such a model should be able to flag potential failed firms to prevent failure. In this paper, a robust multivariate procedure is used to successfully identify potentially failed firms well ahead of an actual failure date.     

Solving the Classification Problem in Discriminant Analysis Via Linear and Nonlinear Programming Methods*

This paper demonstrates the feasibility of applying nonlinear programming methods to solve the classification problem in discriminant analysis. The application represents a useful extension of previously proposed linear programming-based solutions for discriminant analysis. The analysis of data obtained by conducting a Monte Carlo simulation experiment shows that these new procedures are promising. Future research that should promote application of the proposed methods for solving classification problems in a business decision-making environment is discussed.     

Estimating the Geographic Extent of Part-Time Labor Markets: U.S. Army Reserves*

Local labor market supportability is becoming an increasingly important issue for the United States Army Reserves. As military bases close and Reserve units are consolidated at fewer Reserve centers, the appropriate reassignments of units to Reserve centers require accurate measures of the ability of local labor markets to support such consolidations. A two-stage random effect model is applied to evaluate the geographical extent of the labor market for Army Reserve centers. In the first stage model, a lognormal distribution is used to describe the commuting distance behavior of the Reserve center members. In the second stage model, we estimate the mean of log transformed commute distance as a function of regional characteristics of the Reserve center. An iterative weighted stepwise selection method is used to find a set of characteristics that adequately predict variation of the mean commute distance over Reserve centers. The resulting model is used as inputs to location and market assessment models to assist the marketing decisions of the Army Recruiting Command.