In this talk we introduce a notion of actionability of the data mining results. Typically, a data miming process is applied to a large, "unclean" data source with many attributes, potentially highly correlated, and one or more performance measurements (yield, transaction amount, life-time value, etc). One of the goals is to discover important relationships between attributes and the performance values, in a multivariate context, and to characterize the nature of these relationships. With many potential candidates, a further requirement is posed: that an important attribute be "actionable", i.e., that it clearly identify a way to improve the performance metric. We introduce a simple actionability score in the context of process optimization in silicon chip manufacturing, using Friedman's MART model as an underlying data mining tool. We will overview the MART model, its variable importance ranking, as well as its partial dependence plots, stressing the underlying fast and memory-efficient algorithm. Hence we will define the actionability metric that ranks the attributes by their realistic potential to improve the yield of the process. Finally we will show some results from a real, high-volume silicon chip manufacturing data.

Increasing automation and computerization in manufacturing industries has lead to the collection of large volumes of data. Sometimes each item produced may have hundreds or even thousands of values measured on it. This talk considers a production process in which a sleeve is force-fitted by a ram into a cylindrical tube. The force exerted is automatically measured at about 1000 time points during each insertion. Distance traveled by the ram is similarly measured as a function of time. The resultant curves can be thought of as very high dimensional data, but with a special functional structure. The goal is to use these curves to detect anomalous insertions and also understand how the process is varying over time. Methods for reducing the dimensionality of the data and extracting relevant information from these curves will be discussed, including smoothing, clustering and functional data analysis.

Although highly complex research and development projects provide statisticians with exciting analytical problems, the large amounts of data, information and knowledge involved in such projects can make model building quite challenging. To address complex problems, the Statistical Sciences group at the Los Alamos National Laboratory has developed a multidisciplinary approach known as Information Integration Technology, or IIT. This framework combines research methods from the social sciences with statistics to develop complex analytical models that draw together and analyze diverse data sources in a way that is comprehensible to clients. This panel uses a ballistic missile research and development reliability model as a case study to explain the IIT approach, focusing particularly on the processes for translating qualitative problem representations into quantitative models.

Eliciting and representing expert design knowledge can be a tricky business, particularly in the context of dynamic and evolving projects where knowledge is distributed among many individuals. Doing so for the purpose of building any kind of predictive model complicates the situation, as statisticians and their clients often approach problems from different perspectives. Using a case study from a ballistic missile defense project, we present a set of hybrid methods from cultural anthropology and knowledge representation for eliciting and representing expert knowledge, for the purpose of creating mathematically tractable ontologies that translate fluidly between engineers and statisticians.

Many of the statistical problems addressed at Los Alamos involve assessing large, complex systems. Data directly assessing the system is often sparse or non-existent, but many other data and information sources, such as subsystem tests, test on similar systems, computer models, and expert opinion are available. In the context of the ballistic missile research and development reliability case study, this talk will address the development of graphical models to represent the system and its metrics of interest, the population of these models with data, and the resulting analysis and computational issues.

Design of experiments is a systematic approach to develop a cost effective test plan. Standard approaches are not appropriate when experimental factors consist of continuous factors that can be absent or present. There are many engineering systems that possess this feature. This presentation describes the design, analysis and assessment of an experiment of placing chines (air deflectors) on aircraft nacelles conducted in a wind tunnel. The issues of optimization with these factors, and model selection are discussed using this experiment. The emphasis is placed on the design.

This presentation will describe experiments done to improve the robustness of a chemical process used to synthesize a pharmaceutical intermediate. Given a process that occasionally produced out-of-specification material, design of experiment work was used to find the critical process parameters for the addition of a tert-butyloxycarbonyl protecting group to an amine. Relying heavily on laboratory automation, a five-factor, fractional-factorial study screened factors for their effect on the isolated product. A response –surface model was then generated from a three-factor central composite design. Verification runs confirmed the robust conditions found for this reaction. Details of this work will be presented with an emphasis on the statistical techniques used.

Although strip block designs have been known and applied in the agricultural field since the late thirties, their use in industrial settings has been very limited. Strip block designs provide not only an economical, but also an operational advantage in executing experiments. These designs are appropriate in three basic scenarios: robust product experimentation, presence of factors difficult to change and multistage processes, that is, processes with a sequence of at least two steps. When there is a need to investigate the effects of factor associated with different stages, the use of a strip plot configuration may be an alternative to reduce costs of experimentation by decreasing the number of runs required, and consequently less time and resources are consumed. Its use is especially beneficial in situations where several production units can be processed simultaneously as a group. In this study, we explore the use of this configuration in industrial settings. We also present an example of a strip block experiment aiming at defective rate reductions, which illustrates this design’s appeal to engineers and industrial practitioners. Finally, we show how much we can gain by choosing a suitable design to accommodate all the environmental and process characteristics, as well as the limitations inherent in a working place.

Planning of scientific experiments involves a variety of challenges, both statistical and logistical in nature. Interesting questions arise in the planning of multi-level experiments that involve assessing the tradeoffs between run number, selection of levels, ability to estimate effects, and the degree to which orthogonality can be achieved. The relative merits of fractional factorials, orthogonal arrays, and near-orthogonal arrays for achieving desirable statistical properties are explored, while facing the realities of practical constraints. These issues are examined as they arise in the process of designing an experiment for a materials study.

In the automotive industry, an important marketing problem is the determination of which vehicle options consumers prefer. We apply methods of survival analysis to the numbers of days vehicles remain in inventory and determine how vehicle options, incentives, etc. affect the days vehicles stay in inventory.

Automotive engineers use statistical accommodation models to predict the proportion of the user population that will be accommodated by a particular vehicle design. However, modeling accommodation can be challenging because of the difficulties inherent in modeling the tails of a distribution. In this paper, the authors present a set of statistical strategies for approaching the problem of modeling accommodation. This approach is illustrated throughout the paper using the example of passenger-vehicle design to accommodate driver's preferred seat position. The general approach begins with operationally defining accommodation and identifying key subject and design factors that affect accommodation. Next, a model of the relationship between design factors and accommodation of an individual is developed. Finally, the model of individual accommodation is combined with the population distribution of the key subject variables. Each step in this process raises different statistical issues. Future directions for refinement are discussed.

Preparatory and syndicate survey are often used in assessing appeal and initial quality of new vehicles by J.D. Power for many auto manufactures. When the two types of survey are conducted using different or partially different new vehicle owner registrations, it is not clear whether the results are still comparable. This study discusses the difference between the two types of studies, and proposes a computer simulation based method for checking the appropriateness of using the syndicate study to predict future score of J.D Power general study. Simulated examples for Mercedes-Benz M-Class are also included.

Although the U.S. consumer preferences for automobiles shifted from passenger cars to minivans and SUVs during the last two decades, Japanese automobile manufacturers maintained their share of passenger cars somewhere between 13.6% to 20.0%, while their cars have been priced higher than the domestic counterparts. Motivated by the finding, we investigate automobile pricing policies of domestic versus Japanese manufacturers by total cost of ownership (TCO), which includes the initial purchasing price, the fuel cost, the maintenance and repair expenditure, and the trade-in value. The maintenance and repair expenditure is far more difficult to estimate, although the automobiles reliability scores based on the experiences of actual owners are available in Consumer Reports. In this paper we propose and illustrate a method to convert that knowledge on the automobile reliability to monetary maintenance and repair expenditure. We find the maintenance and repair expenditure differential plays an important part of the TCO calculation.

In early phases of life cycle design of a new vehicle, designer needs tools to evaluate the goodness of his ideas and, consequently, whether his design choices could satisfy the end user. A current challenge is to realize these evaluations on virtual prototypes instead of physical ones. To get the best results, using specific and expensive simulation software in virtual environment, designer need adoption of well-tested methodologies.

In this paper, the authors present some results of research projects aimed to optimize:

a. Comfort of a new vehicle in the concept design phase;

b. Tolerance allocation for complex mechanical systems in the tolerance design phase.

The first research project, since comfort evaluation depends primarily on man-machine interaction, deals with human model experimentation to simulate man behavior in virtual environment. Integrating statistical and industrial design competencies, a classical parameter design approach has been adopted and performed. Furthermore a multiresponse loss function has been formulated in order to discriminate among various configuration settings and to eventually find the optimal design in terms of comfort for driver. The results obtained by virtual experimentation concern the improvement of design in terms of comfort and the increase of designer knowledge about the effects of design parameters on the ergonomics of the vehicle. The fully developed case study shows that some design factors can be fixed at the optimum value and other ones need direct user control to attain optimal comfort requirements. These results improve the concept design of the vehicle, suggesting if and where, for example, to introduce adjustment devices.

The second research project deals with tolerance design of complex assemblies of parts, frequently occurring in the aeronautical and automotive fields. Using Computer Aided Tolerancing (CAT) systems, the designer can verify the effect on the response (or responses) of design factor tolerance by developing a feature based model in virtual environment. Two main needs must be reached using CAT systems in tolerance analysis: the first consists of the capacity to orient the steps of the simulation processes towards the optimal solution; the second deals with the possibility to reach the optimal solution in a short time. In this paper, the authors show a new procedure using CAT systems to find the set of dimensional and geometrical tolerances that assure the fulfillment of product functional requirements, in a lower cost condition, using a limited number of simulation steps. This procedure involves the application of parameter design methodologies.

These case studies have been fully developed in a virtual lab available at PRODE (PROduct DEsign), a recently established consortium between University of Napoli Federico II and Elasis-Sistema Ricerche FIAT nel Mezzogiorno.

The application of multidisciplinary design optimization (MDO) to automotive vehicle design for safety has been of significant interest over the last several years. Sobieski et al. and Kodiyalam et al. reported a very significant reduction in computing time for such large-scale MDO problems - from months to days - through the efficient use of shared memory multiprocessor systems. The present work is an extension of work reported in Sobieski et al. and Kodiyalam et al. with a substantial increase in computational complexity. The focus of this presentation is on a large-scale reliability based design optimization of a car body structure for crash safety. The Finite element based full vehicle structural crash simulation is a design tool commonly used throughout the automotive industry to evaluate vehicle crash performance. This presentation describes how this simulation technique has been extended to perform reliability based design optimization for key response variables using nonlinear response surface methods. Monte Carlo and performance measure methods are used to perform reliability based design optimization. This technology uses computer based design of experiments and lends itself readily to parallel implementation.

Massive data sets distributed over a network are becoming more common as more widely distributed data collection devices are installed and because of increasing collaborations over the Internet. Even if it is possible to centralize a massive distributed data set on local storage devices, we have few means of analyzing such data. A recent Scientific American article reports that our data storage capacity doubles every 9 months, while processor speed and memory still follow Moore's law of doubling roughly every 18 months. Although the size of data sets we analyze with centralized methods is increasing with available memory, we are losing ground relative to the size of available data sets. The effect this has on the nature of massive data sets is that they are increasingly stored as massive collections of manageably small data sets. As a result, most massive data sets are distributed regardless of whether they reside on a single device or multiple devices. In this talk we describe some characteristics of the massive distributed data analysis problem, some components necessary to address the problem of using distributed data, and our approach to developing algorithms for distributed data sets. We conclude with our algorithm for principal components analysis of a set of distributed data sets.

In many applications of supervised learning, automatic feature clustering is often desirable for a better understanding of the interaction among the various features as well as the interplay between the features and the class labels. In addition, for high dimensional data sets, feature clustering has the potential for improvement in classification accuracy and reduction in computational complexity. In this paper, a method is developed for simultaneous classification and feature clustering by extending discriminant vector quantization (DVQ), a prototype classification method derived from the principle of minimum description length using source coding techniques. The method incorporates feature clustering with classification performed by fusing features in the same clusters. To illustrate its effectiveness, the method has been applied to microarray gene expression data for human lymphoma classification. It is demonstrated that incorporating feature clustering improves classification accuracy, and the clusters generated match well with biological meaningful gene expression signature groups.

A graph based tree pruning algorithm is proposed. The new method is computationally comparable with existing ones, but it provides a full spectrum of information regarding a tree pruning:

(1) given the value of the penalization parameter, this method gives the minimum size of a decision tree;

(2) given the size of a decision tree, it provides the range of the penalization parameter, in which the cost penalizing approach will render a tree that has this size;

Tolerance limits are limits that include a specified proportion of the population at a given confidence level. They are used to make sure that the production will not be outside specifications. Tolerance limits are either designed based on the normality assumption, or nonparametric tolerance limits are established. In either case, no provision for autocorrelated processes is made in the available design tables of tolerance limits. It is shown how to utilize EWMA tolerance limits to cover a specified proportion of the population when autocorrelation is present in the process.

Ranked set sampling (RSS) is a sampling procedure that can be considerably more efficient than simple random sampling (SRS). It involves preliminary ranking of the variable of interest. Although ranking processes for continuous variables that are implemented through either subjective judgment or via the use of a concomitant variable have been studied extensively in the literature, the use of RSS in the case of a binary variable of interest has not been investigated thoroughly. The objective of this study is to use a National Health and Nutrition Examination Survey data set to investigate the application of RSS to estimate a population proportion. We use logistic regression to aid in the ranking of the variable of interest. Our results indicate that the use of logistic regression improves the accuracy of the preliminary ranking in RSS and this leads to substantial gains in estimation of population proportion.

Judgment post-stratification is a new estimation method that keeps the benefits of stratification while requiring no knowledge of the population structure. It is based on the collection of a simple random sample of units from the finite population. The units are grouped into sets, and either subjective judgment or objective concomitant measurement is used to rank the units in a set, thereby creating the post-strata. Analytic results and simulations demonstrate that judgment post-stratification yields an unbiased estimator of the population mean with smaller mean squared error than does simple random sampling. We also provide rules for collapsing the strata while retaining satisfactory results. Our study shows some of the many benefits that accrue from judgment post-stratification.

A simulation experiment is frequently performed to estimate a metamodel, which is a functional relationship between the mean response of the simulation model and a set of simulation inputs. Several strategies have been proposed to increase the accuracy of estimation by inducing a desired correlation structure among the responses. This talk proposes a new correlation inducing strategy for a quadratic metamodel. The proposed strategy is shown to be superior to a number of existing and competing strategies in terms of various variance measures.

Optimal Variable EWMA Controller  - Arthur Yeh*, Bowling Green State University (with Sheng-Tsaing Tseng, Fugee Tsung, Yun-Yu Chan) 

The exponentially weighted moving average (EWMA) feedback controller with a fixed discount factor is a popular run-by-run (RbR) control scheme, which primarily uses data from past process runs to adjust settings for the next run. Although the EWMA controller with a small discount factor can guarantee, under fairly regular conditions, a long-term process stability, it usually requires a moderately large number of runs to bring the process output to its target. This could lead to a severe consequence in short production runs. The reason is that the output deviations are usually very large at the first few production runs and, as a result, the process output may be out of specifications. 

In order to reduce a possibly high rework rate, we propose a variable discount factor to tackle the problem. We derive the stability condition and the optimal variable discount factor for the proposed EWMA controller. Examples are given to demonstrate the strength of the EWMA controller with a variable discount factor. Moreover, a heuristic method is proposed to simplify the computation of the optimal variable discount factor. It is seen that the proposed heuristic method is easy to implement and provides a good approximation to the optimal variable discount factor.

Conventional process identification techniques of an open-loop process use the cross-correlation function between historical values of the process input and of the process output. If the process is operated under a linear feedback controller, however, the cross-correlation function has no information on the process transfer function because of the linear dependency of the process input on the output. In this paper, several circumstances where a closed-loop system can be identified by the autocorrelation function of the output are discussed. It is assumed that a Proportional-Integral (PI) controller with known parameters is acting on the process while the output data were collected. The disturbance is assumed to be a member of a simple yet useful family of stochastic models, which is able to represent drift. It is shown that, with these general assumptions, it is possible to identify some dynamic process models commonly encountered in manufacturing. After identification, our approach suggests to tune the controller to a near-optimal setting according to a well-known performance criterion.

Multivariate control chars can be used to monitor the means of two or more correlated variables of a process. We consider processes where the target values of the means, variances, and covariances are estimated from the data. During monitoring, small random samples are collected at equal time intervals. Since estimates based on small samples are unreliable, the estimates of variances and covariances are updated with each new sample. In order to increase the sensitivity of the charts to detect small shifts from the target, past sample information is retained for each variable using an exponentially weighted moving average statistics (EWMA). Three multivariate, EWMA control charts are compared in this paper, each based on the componentwise sample average, sign, and signed rank statistics, respectively. The properties of the chars are evaluated using simulation. We study the advantages and disadvantages of each chart for various cases. Finally, we give recommendations on how to apply these charts in practice.

The use of multivariate SPC has several known advantages in comparison with the use of multiple univariate charts. The T2 control chart has become a popular option for implementing multivariate SPC due to its relative simplicity and the fact that it is the equivalent multivariate scheme of the Shewhart X-chart. However, the main disadvantage of these multivariate charts is the interpretation of an out-of-control signal. The decomposition proposed by Mason, Tracy and Young (1995, 1997) for the T2 chart (hereafter MTY) has the advantage of being an analytic procedure. In this work we study the effectiveness (percent of correct classifications) of MTY versus shift magnitude and type, number of variables, probability, etc. We then introduce a backpropagation neural network designed to solve the same problem (interpreting control chart signals for the T2 chart). A comparison between both methods is made.

A generalized Cook's statistic for detecting multiple outliers in multivariate linear regression models is proposed. An approximate distribution of the proposed statistic is also obtained to get a suitable cutoff point for a test of hypothesis of no outliers. A simulation study has been conducted to examine the performance of the approximate distribution. In addition, an application to process monitoring is also considered.

The prediction of events and related costs in a population of individuals or units at risk for recurrent events will be considered. Structured Poisson models and Bayesian methodology will be used to address problems involving the prediction of warranty claims and the discovery of faults in software.

Recurrent events are prevalent is reliability and engineering studies. In this talk I will describe a general class of models for recurrent events which could simultaneously incorporate effects of intervention or repairs, effects of accumulating event occurrences, and effects of environmental factors or concomitant variables. This new class of models subsumes as special cases many existing models that have been proposed to model recurrent phenomena in reliability and engineering settings. Statistical methods for analyzing data arising from this class of models will be described and illustrated.

Lotfi Zadeh’s seminal 1965 paper introduced the notion of a fuzzy set and established the foundations of a theory for combining and operating with such sets. If U is taken as the universal set of interest in a given problem, then the fuzzy set A Í U is defined and determined by a "membership function" m: U ® [0, 1] which tracks the "extent" to which each x Î U is a member of A. If, for example, A is the set of "rich" people, and x is a particular person’s net worth, then m(x) represents the extent to which x belongs to A. In the arithmetic of fuzzy sets, AÈ B is defined as the set with membership function max{m_A(x), m_B(x)} and AÇ B as the set with membership function min{m_A(x), m_B(x)}. While fuzzy set theory and "fuzzy logic" have been applied in selected statistical contexts, notably in pattern recognition, classification problems and decision analysis, little progress has been made to date on the application of the fuzzy set framework to classical problems of statistical estimation.

High Throughput Screening (HTS) is used in drug discovery to screen large numbers of compounds against a biological target. Data on activity against the target are collected for a representative sample (experimental design) of compounds selected from a collection. The explanatory variables re chemical descriptors of compound structure.

This talk will concentrate on the analysis of such data. Some previous work comparing statistical analysis methods on two HTS data sets shows that local methods perform well. These local methods, namely K-nearest neighbours (KNN) and classification and regression trees (CART) have good predictive performance in comparison with regression, neural network and MARS models, which assume more smoothness. After reviewing these comparisons, we will present some adaptations of KNN and CART, including averaging over subsets of explanatory variables, bagging and boosting. These further improve the models' performance.

Combinatorial chemistry offers new opportunities to generate and analyze QSAR data. Tradition QSAR attempts to correlate activity with structure. With combinatorial chemistry, it is possible to correlate activity directly with the reagents used in a combinatorial library. If one can determine which reagents lead to the compounds of highest activities, it is then possible to predict active compounds in virtual libraries of 10⁶ to 10¹⁰ compounds. This would greatly facilitate library design and provide confidence that the best compounds are being considered for synthesis. An important question is whether the activities of a product molecule can be considered as a sum of its components. This is referred to as additivity between reagents. If there is non-additivity, it is necessary to identify and include the non-additive terms in the model in order to improve QSAR models. 

Presented here is a method for detecting the second and third order effects of side-chain non-additivity. If the reagents in a library are shown to be additive in their contribution to activity, simple QSAR based on additive models can be applied confidently to reagents. Furthermore, methods are presented for identifying non-additive terms in QSAR models. Testing non-additivity can also guide the synthesis of the library. If the contributions are shown to be additive then the strategy for library synthesis may be shifted to include many reagents of a given type but not to make all combinations. The result is a more efficient use of resources.

The Pharmaceutical Industry uses High Throughput Screening (HTS) to rapidly test large numbers of compounds against biological targets. In a primary screen the activity of a compound is judged by its performance at a single concentration. A typical primary screen may be used to test 500,000 or more compounds in a few weeks. Compounds identified as active by the primary screen are typically subjected to concentration-response testing. A typical laboratory group may be responsible for generating thousands of concentration-response curves in a week. The increasing demand for HTS services, and the scarcity of resources, has made it critical that every screen be properly validated before being put into production. This talk outlines experimental procedures and statistical analyses for the validation of screens.

David Stock¹, Lynda Cook², Robert Stoffel², & Ramesh Padmanabha² Xianggui Qu³, C.F. Jeff Wu³

(1) Corresponding author: Dept 716 - Nonclinical Biostatistics, Bristol-Myers Squibb, 5 Research Parkway, Wallingford CT 06438, StockD@BMS.COM (2) Lead Discovery, Bristol-Myers Squibb (3) University of Michigan

Often the vehicle crash testing is conducted using a very small sample size. Results of two or three test samples may be lower than the compliance limit, but the question always arises, " How good is good enough?". For example, if the government compliance limit is 80 g and the test result in an average of 60 g, is this value good enough to establish that the government requirement will be met in a subsequent test? The compliance prediction methods will be discussed to determine the risk in not meeting the government mandated requirement based upon successful test results or the company’s performance objective requirement.

(1) Single test compliance (Normal distribution)
Given X₁, X₂, …, X_n are n independent variables from a normal distribution with mean m and standard deviation s , the Confidence (C) of the next test X_n+1 will be less than the compliance limit will be presented with two cases (s is unknown and s is known). If some historical test data on similar designs exist, then certain variation estimate can be made (i.e., s is known).

(2) Population compliance (Normal distribution)
Given X₁, X₂, …, X_n are n independent variables from a normal distribution with mean m and standard deviation s , the Confidence (C) that at least a given specified proportion of the population complies government requirement will be discussed when s is unknown and s is known.

(3) Population compliance (Weibull distribution)

When the population is not normally distributed, the Weibull distribution is considered. The Confidence (C) that at least a given specified proportion of the population complies government requirement will be discussed when the Weibull slope b (shape parameter) is known.

The conventional method to analyze crash data is the binary logistic model. This talk will discuss other statistical methods that can be used. One method is empirical: maximal likelihood estimates of the probability distribution. Since the data set is censored, parametric survival models can be used. Other methods we discuss include confidence method and median rank method. We will show the resulting distributions and consider the similarities and differences among the various distributions.

The staircase testing method is a common testing procedure used for sensitivity testing. In particular, it is frequently used in defining the fatigue strength of materials used in engineering structures. Literature published in 1948 described the procedure for obtaining and analyzing the data from this test method. While a common test procedure has generally been followed for obtaining the data, a common analysis method has not been followed. This presentation will focus on analysis of staircase fatigue testing of a cast aluminum alloy. The differences in the mean and standard deviation calculated using three analysis methods will be discussed.

Advanced statistical design of experiments, such as the Box-Behnken design illustrated in this paper, provide an efficient and comprehensive evaluation of manufacturing technology research projects. In manufacturing, there are often situations where understanding of variables with 3 levels and their interactions are of primary interest. The data driven results lead the engineers to technical decisions needed in development of new technologies. This article provides details around the optimization of process variables for a bracket welding application for automotive body structures. A 46 run Box-Behnken response surface design was utilized to study a proposed range of process settings for 5 key variables, for a new manufacturing welding process, which attaches a bracket to sheet metal. The drawn-arc welding method butt welds the bracket directly to the base material, eliminating the flange and providing savings in piece price and weight. The method simplifies the tooling, makes installation a one step process, and allows one-sided access, which are all critical to manufacturing operations.

The complete testing strategy included evaluation of 644 samples. This report includes the statistical analysis of the tensile strength and cross sectional area of the weld, with analysis of average effects for the response variables as well as assessments of the variability across sample groups. Results indicated a robust process, within the ranges of the factors studied, hence validating the required quality level for the process settings that were recommended.

In two-level fractional factorial designs, the assumption of constant variance is commonly made. When the variance of the response differs between the two levels of a column in the effect matrix, that column produces a dispersion effect. In this paper we show that two active dispersion effects may create a spurious dispersion effect in their interaction column. Most existing methods for dispersion effect testing in unreplicated fractional factorial designs are subject to these spurious effects. We propose a method of dispersion effect testing based on geometric means of sample variances. This test may be applied to both replicated and unreplicated designs.

Suppose that interest is in the prediction of the response over a specified region of interest. We explore experimental design conditions and the nature of the "true" model such that a simpler model provides a better estimator in the sense of the mean squared error. Following the rationale provided by Toro-Vizcarrondo and Wallace [J. Amer. Statist. Assoc. (1968):558-572], as well as previous related work, we introduce new concepts which we call the model validity region and the optimal model validity region. Based on these concepts, we introduce a new optimal design criterion that measures the extent of robustness of a design to simplified models. Simple examples in polynomial regression and multifactor experiments are given to illustrate the ideas proposed. We also provide a strategy that will enable the researcher to apply the concepts discussed, by using the hypothesis test proposed by Toro-Vizcarrondo and Wallace.

L18 array is one of the most popular designs among experimenters. The problem of factor assignment arises under two situations: 1. The number of factors in an experiment is less than the number of columns of the array; 2. Some factors in an experiment are quantitative and some are qualitative. Bad factor assignment plans could result in less efficiency in modeling. This paper presents the optimal factor assignment plans for L18 based on a generalized minimum aberration criterion.

Improved computational models and simulations offer the potential to reduce design, development and manufacturing time and cost by providing better predictions, and a more complete exploration of system and process design space. However, these models and simulations will not achieve this potential unless credible uncertainty statements about their predictions accompany them. Key to attaining this goal is a model validation process that permits comparison of computational predictions to experimental outcomes over a meaningful set of validation experiments—a process that will provide confidence in the predictive capability of the computational model. The ultimate goal is to design, conduct and analyze validation experiments so as to be able to credibly make statements such as:

"Based on our analysis of the validation experiments, we are 80% confident that if we measured an actual system, it would fall within these bands about the output of the model we just ran".

In this talk, a general validation strategy will be proposed. Both field and computer experiments play a prominent role. An academic example problem will be presented to illustrate the procedure. The results from a spot-weld model validation procedure will also be presented.

During the beginning phase of product development time, engineers, today, rely on computer simulation models to guide their decision making process. These computer simulation models represent complex engineering phenomena, which may be constructed using one-dimensional models from "First Principle" in physics or complex three-dimensional models such as Computational Fluid Dynamics (CFD) and Finite Element. In this talk, several examples of these simulation models (e.g., CFD, structural durability, multi-body dynamics, and Noise Vibration & Harshness) are presented to illustrate the challenges of applying statistical methods. These simulation models share common characteristics such as they are highly non-linear involving large number of input and output variables, and they are computationally intensive. These characteristics pose significant challenge in applying statistical methods to provide timely and accurate (i.e., practical) information to design engineers during the design process. Several statistical challenges in the following area are discussed: model correlations, design of computer experiments, sensitivity analysis, analysis of functional response, multi-response optimization, and robust design optimization.

The pace, scale and scope of the world economy are staggering. Producers recognize the need to maintain and grow their share of the marketplace. Customers demand products that meet and exceed their expectations. Companies who wish to extend their business know their customers must insist on their brands. Global forces drive the need to offer quality products at competitive prices. Combined, these attributes constitute business strategies that align innovative product design within lean cost structures. Corporate leaders understand the factors that directly support customer satisfaction and loyalty. These include reliable products that meet their intended performance and conform to requirements. Visionary corporate leaders understand that quality is imperative for long-term growth. They know the benefits reach beyond satisfied customers by improved productivity, reduced cycle time, enthused employees and lower costs, true characteristics of a successful business. However, visionaries also recognize that variation can stand in their way. Applied systematically, Robust Design, the ability to desensitize a product or process to the effects of variability, will improve quality levels and provide a stimulus for growth and a backbone for success.

We investigate the effects of non-normality on the statistical performance of the multivariate exponentially weighted moving average (MEWMA) control chart, and its special case, the Hotelling's chi-squared chart, when applied to individual observations to monitor the mean vector of a multivariate process variable. We show that the chi-squared chart is highly sensitive to non-normality. We argue that the performance is most sensitive to departures from multivariate normality with individual observations (subgroups of size one). We show that with individual observations, and therefore, by extension, with subgroups of any size, the MEWMA chart can be designed to be robust to non-normality and very effective at detecting process shifts of any size or direction, even for highly skewed and extremely heavy-tailed multivariate distributions.

According to W. Shewhart, the process variation can be classified into assignable cause and common cause variations. The assignable cause variation can be eliminated by statistical process control (SPC) methods through identification and elimination of the root cause of the process shift. The common cause variation is inherent in the process and is generally difficult to reduce by SPC methods. However, if the common cause variation can be modeled by an autocorrelated process and physical variables exist to adjust the output, the common cause variation can be reduced by automatic process control (APC) methods through feedback/feedforward controllers. As suggested by Box and Kramer (1992), integration of SPC and APC methods can result in major improvement in industrial efficiency, which is described as algorithmic statistical process control (ASPC) by Vander Weil et al. (1992).

Integration of SPC and APC involves the problem of detecting parameter changes from autocorrelated processes. Traditional SPC control charts have been shown to have poor performance in monitoring and controlling such processes (Harris and Ross 1991; Alwan 1992). Alwan and Roberts (1988) propose the special cause chart (SCC) to rectify this problem. Their idea is to "whiten" the autocorrelated process by subtracting the one-step-ahead minimum mean squared error (MMSE) prediction, and then monitor the residuals (or the prediction errors) with traditional control charts. Jiang et al. (2001) propose to replace the MMSE predictor by the commonly used proportional-intergrated-derivative (PID) controller with subsequent monitoring of the prediction errors, which denoted as PID charts. On the other hand, Zhang (1998) points out that it is quite efficient to apply the exponentially weighted moving average (EWMA) chart to monitor autocorrelated processes. Jiang et al. (2000) extend the EWMA chart to a general class of control charts based on the autoregressive moving average transformation, called RMA charts.

There are close relationships among modeling and monitoring methods of MMSE controllers, PID controllers, EWMA charts, SCC charts, PID charts, and ARMA charts etc. The objective of this paper is to develop a unified approach to model the relationships among these well-known methods in SPC, APC, and intergated SPC/APC.

The Changepoint Model for Statistical Process Control - Douglas M. Hawkins*, Peihua Qiu, and Chang Wook Kang, University of Minnesota

The Random Fatigue-Limit (RFL) model discussed by Pascual and Meeker (1999) was motivated by the need to describe fatigue life of certain materials. The RFL model describes the relationship between lifetime (measured in cycles) and a single factor, often the applied stress on the material. It has been found to be particularly useful for modeling high-cycle fatigue (HCF), that is, lifetimes that exceed 10 million cycles. Outputs from this model can be used as input for system models for lifetimes of jet engines for design purposes. In such applications, cycles are defined in terms of engine revolutions. Understanding how well the parts hold up as a function of stress and other environmental variables would be valuable to engineers designing new and better engines. Thus, the RFL model needs to be adapted to situations when there are several factors that affect product life. In this article, we investigate how the RFL model can be extended from dependency on stress to dependency on stress and other explanatory variables. We fit the proposed model extensions to available data and describe methods to assess the adequacy of the fits.

Traditional "Life Data Analysis" involves analysis times-to-failure data obtained under "normal" operating conditions in order to quantify the life characteristics of the product, system or component. In many situations, and for many reasons, such life data is very difficult to obtain. The reasons for this difficulty can include the long life times of today’s products the small time period between design and release, and the challenge of testing products that are used continuously under normal conditions. Given this difficulty, and the need to observe failures of products to better understand their failure modes and their life characteristics, people have attempted to devise methods to force these products to fail more quickly than they would under normal use conditions. In other words, they have attempted to accelerate their failures. Many products can be life tested at high stress conditions to yield failures quickly. Analysis of data from such an accelerated life testing yields valuable information on product life at design conditions (low stress).

In fiber optical industry, products normally have long life. In order to better understand products’ failure modes and their life characteristics, accelerated life testing becomes very important.

This paper presents the development of the statistical and experimental basis of accelerated life testing. Weibull and Lognormal distributions have been used to establish these statistical models. Product’s life prediction and qualification tests have also been established based on the accelerated life testing models.

Failure data from a repairable system is commonly modeled by a nonhomogeneous Poisson process (NHPP). A modulated gamma process evolves as a generalization to an NHPP, where the observed failure epochs correspond to every successive k^th event of the underlying Poisson process. We focus on a special class of modulated gamma process, called a modulated power law process (MPLP) that assumes a Weibull form of intensity function. The traditional power law process is a stochastic formulation of certain empirical relationships, often observed in industrial experiments. MPLP retains this underlying physical basis and provides a more flexible modeling environment. Curiously, the MLE's of the MPLP are asymptotically normal with a singular variance-covariance matrix, making its derivation quite non-standard. A set of simple closed-form estimators are proposed that are asymptotically equivalent to the MLE's. Performances of the estimators in small samples are compared and contrasted by means of extensive numerical simulation.

Nondestructive inspections (NDI) have become an important tool in maintaining the structural integrity of both military and civilian aircraft. A key measure of the effectiveness of NDI in the damage tolerance programs is the probability of detection (POD) as a function of crack length. This talk will briefly review the history of methods used to estimate the POD function, the current standard methods used by the US Air Force, and the new concepts under study that may allow more economical estimation of the POD function. A special emphasis will be placed on the sampling issues in trying to conduct more economical POD studies while maintaining accuracy.

The spray pattern produced by a paint gun is an important determinant of the quality of the resulting painted surface. Data from a test device which measures air flow patterns are used to illustrate and compare mixed-effect model and FDA approaches to the analysis of such data.

We consider the problem of remote detection and identification of chemicals in a scene. We introduce a unique approach that uses some image's pixels to establish the background characteristics while other pixels represent the target for which we seek to identify all chemical species present. This leads to a generalized least squares problem in which we focus on subset selection to identify the chemicals thought to be present. Recent results in Bayesian model selection allow us to approximate the posterior probability that each chemical in the library is present by averaging the posterior probabilities of each possible subset. We present results using realistic simulated data for the case with 1 to 5 chemicals present in each target and compare performance to a hybrid of forward and backward stepwise selection procedure using the F statistic.

Recently singular value decomposition has been successfully applied in high-dimensional data analysis, such as information retrieval, feature extraction, and clustering/classification. In this paper, we propose a local version of SVD technique, which may be more effective at finding nonlinear structures in high-dimensional data space. We have developed an SVD-based local polynomial prediction algorithm with the goal of applying it to multi-step prediction of noisy chaotic time series. The algorithm is shown to have the desirable denoising property as well as the ability to find the intrinsic nonlinear structure in arbitrary phase space reconstruction. Very encouraging results have been obtained on several well-known data sets and laboratory data.

The Web is a big place. The search engine google.com, for example, claims to have indexed over a billion separate Web pages. Given the large number of resources on the Web, sites are constantly competing to attract and retain new visitors. To improve a user's experience, it is now common for sites to customize content (generating pages based on a user's previous activities) and to consider creative caching and prefetching schemes to deliver content as quickly as possible. In both cases, a model for describing how visitors navigate a Web site can be invaluable.

Data to support this kind of modeling can come from either access logs for a particular Web site, or proxy access logs which record all the pages requested by users of a given gateway or ISP. We begin this talk by briefly describing a "data browser" that allows an informal assessment of Web site usability. We then develop a predictive model for the pages a user will visit, given some portion of their previous browsing history, and illustrate its application to a cache-based method for prefetching.

Next, given the scale of the Web, we routinely rely on search engines like google.com to find relevant resources. In the second half of this talk, we consider using proxy data to improve Web searching. We begin by describing a template for the searching task that allows us to extract "search sessions" in real time from a proxy. These sessions are then used to train a mixture model that organizes queries into clusters. An online version of the EM algorithm is developed that can be easily implemented in a proxy. The model is then applied to both impose a topic-like structure on search results as well as to improve the ranking of resources within topics.

In analyzing failure data pertaining to a repairable system, perhaps the most widely used parametric model is a nonhomogeneous Poisson process with Weibull intensity, more commonly referred to as the Power Law Process (PLP) model. PLP is a stochastic formulation of certain empirical relationships between the time to failure and the cumulative number of failures, often observed in industrial experiments. The investigations relating to statistical inference of PLP under a frequentist framework abound in the literature. The focus of this talk is to supplement those findings from a Bayesian perspective, which has thus far been explored to a limited extent in this context. Both estimation and future prediction are considered under traditional as well as more complex censoring schemes. Modern computational tools such as Markov Chain Monte Carlo are exploited efficiently to facilitate the numerical evaluation process. Results from the Bayesian inference are contrasted with the corresponding findings from a frequentist analysis, both from a qualitative and a quantitative viewpoint. The developed methodology is implemented in analyzing interval-censored failure data of equipments in a fleet of marine vessels.

In parametric reliability analysis, it is customary to work with the integral of hazard rate function, h(t), known as cumulative hazard function H(t). Conventional probability distributions (exponential, Weibull, Gumbel, lognormal, and normal) do not always provide enough flexibility to model H(t). Some do not fit the data well. Others extrapolate at physically unreasonable rates. This paper considers a quadratic spline with a single free knot as a model for cumulative hazard function. The parameters of the spline and the location of the free knot are optimized so as to best fit the nonparametric estimate of the subject function.

In this paper Generalized Practical Bayes Estimators (GPBE) of the parameters of the Weibull reliability model are presented. The main peculiarity of these estimators is that they enable to directly incorporate into the estimation process the prior information that is truly available in the most advanced technological fields. They are called “Generalized” since their priors include all the previous priors used by the past Practical Bayes Estimators (PBE) and the Modified Practical Bayes Estimators (MPBE). This new feature enables to better fit and control the prior uncertainty. 

A NIST team of physicists, engineers and statisticians are developing methods and associated software for characterization of high-speed optoelectronic devices. A photodiode converts an optical signal into an electrical signal. This electrical signal is detected with a high-speed equivalent time sampling oscilloscope. Both the photodiode and oscilloscope have impulse response functions which distort the signal of interest. We wish to estimate the power and phase of the impulse response function of the photodiode up to 50 GHz. Due to time base distortion errors, the measured signal is not equally spaced in time. Moreover, repeat measurements of noisy signals drift in time and are jittered. I discuss methods for compensating for the effects of time base distortion, methods for aligning noisy signals and estimation of the variance of timing jitter noise.

Selective assembly is a cost-effective approach for high-precision assembly from low-precision components. The quality of an assembly in a manufactured product is often largely determined by the clearance between two mating components. Selective assembly can be used to reduce the deviation of this clearance from a target value without requiring reduction in the tolerances of individual components. In order to accomplish this, the individual components are binned into several classes prior to assembly, and the final assembly is manufactured by selecting components appropriately from the classes. The result is a high quality product manufactured from relatively inexpensive components.

In this talk, we study optimal strategies for selective assembly under various loss functions. Closed form expressions for optimal rules under L₁ and L₂ loss functions are obtained and conditions for existence and uniqueness of the rules are studied. A family of asymmetric loss functions is also examined. We present results for various component distributions and provide comparisons to traditional selective assembly procedures such as equal width and equal area partitioning. We also examine the benefits of allowing non-equal partition probabilities for the components and explore optimal selection for the distribution of one component given a distribution for the second component.

High warranty cost for front suspension alignment is a big concern in current vehicle program. The objective of this project is to apply virtual experimental design (VED) process along with computer simulation code, ADAMS, to study the root causes for the front suspension alignment variation. More than 40 design parameters and associated tolerance specs were investigated in this study. In the VED, 6 alignment characteristics were treated as output responses. An integration computer software, iSIGHT, was applied to design the DOE matrix and then execute automatically ADAMS simulations to generate output response data. All simulation data were stored in the database of iSIGHT and then analyzed to identify critical design parameters for the front suspension alignment variation. The analyses show that vital few factors contribute to the majority of the total variation. Finally, the results and conclusions were presented to release and manufacture engineers for quality improvement purpose.

In today’s industry environment the need to accelerate product development schedules requires that engineers actively engage simulation models to eliminate iterations from the design and test process. Much time is spent on the design and evaluation of component reliability and durability. If accurate descriptions of the fatigue behavior of materials are available, then simulation software such as nCode can be used to simulate component durability and thus provide insight to design flaws more quickly than can the design and test cycle.

A method is presented that facilitates the development of accurate statistical strain-life curves given experimental data from strain controlled uni-axial fatigue tests. The method establishes a series of selection criteria that ensure that the data used in the statistical analysis is significant and representative of the materials true behavior. The method goes on to establish a procedure for the statistical analysis that ensures that each domain of the materials behavior is accurately represented. The result is an R50 strain-life curve that is then scaled to an R90C90 strain-life curve by incorporating a technique presented by Shen and Wirsching. This R90C90 curve represents a strain-life curve which encapsulates the behavior of 90 per cent of samples of a material and in which 90 per cent confidence exits. This R90C90 curve is then suitable for use in industrial simulation software.

The application of probabilistic design to practical engineering design is often hindered by lack of precise statistical information of design variables. Nevertheless, such an application is still considered advantageous for sensitivity analysis to quantitatively identify order of importance of the stochastic variables. In this presentation, we explore and compare possible alternatives to calculating probabilistic sensitivity analysis by decomposing the effects of probabilistic variables to the variability of response variable. We suggest and evaluate the following three methods: Sobol Sensitivity Index (SSI), Extended Fourier Amplitude Sensitivity Test (EFAST), and Reliability Index Sensitivity (RIS). A toy example is used for benchmark comparison among the methods and a real automotive application demonstrates their usefulness in engineering design practice.

Cable-drive glass guidance system has been widely used as the glass lift mechanism of modern vehicles for the benefit of low-cost and light-weight. The entire glass guidance system consists of four major subsystems, which are metal panel (door in white), seal, glass, and regulator. Glass movement is driven by a steel cable powered by either manual effort or an electric motor, which provides required torque to overcome friction within regulator mechanism, friction between glass and seal, and glass weight.

A sophisticated system-level Computer-Aided Engineering (CAE) model was established to analyze the glass guidance system. Through the virtual CAE model, analysts and designers can evaluate the design in an early stage of development process, which significantly reduces time and cost for late design changes and hardware tests. The established CAE model for glass guidance system has been shown to provide a high fidelity prediction for both system and subsystem performance.

The relationship between the system performance and design parameters are established using Response Surface Methodology (RSM). The mean value of performance is approximated with a regression analysis using a quadratic model with central composite design. Variation of performance is then estimated using Taylor Expansion. Design optimization and robustness are conducted afterward. In this paper, a brief introduction to the CAE model and details regarding the statistical quality analysis for cable-drive glass guidance system are presented.

This talk introduces the maximum estimability (Maxest) criterion to address the problem of optimal factor assignment for any fractional factorial designs. The Maxest criterion is a natural extension of the minimum aberration and the MaxC2 criterion for regular designs. It is a refinement of Webb’s concept of resolution. The Maxest criterion is coding dependent, which is distinct from other coding independent criteria, such as the generalized minimum aberration and the minimum moment aberration criteria. The Maxest criterion is used to classify the projections of some useful nonregular designs. Comparing with other projective properties, such as the geometric and the hidden projection properties, the new classification is simpler and takes statistical modeling into consideration.

We use simulation to evaluate the abilities of fractional factorial designs to achieve model identification-related objectives. We compare various automatic approaches for model identification including alternatives to Daniel plots and Bayesian selection methods. The results motivate new classes of fractional factorials that directly maximize the power to identify effects under the assumption of the prior distribution on main effects and interactions from a standard textbook. Both new and established methods are illuminated by novel approaches to support experimental planning decision-making. The proposed methods are also illustrated by a real world case study.

We describe our alternative approach to Taguchi's signal-to-noise ratios based on a direct application of utility theory. We also compare this approach to other alternatives in the literature. Then, we describe our alternative experimental plans to compound arrays derived from a so-called "recourse", utility-based formulation, i.e., a formulation that incorporates the two-stage decision process including choice of the experimental plan in the outside optimization and the choice of the best engineering system in the inside optimization. We compare the proposed method with summary measure-based alternative approaches from the literature and use an example to illustrate how each approach could be implemented.

Quality loss functions play a fundamental role in every quality engineering method. A new set of loss functions is proposed based on Taguchi's societal loss concept. Its applications to robust parameter design are discussed in detail. The loss functions are shown to posses some interesting properties and lead to theoretical results that cannot be handled with other loss functions.

In factor screening, often only a few factors among a large pool of potential factors are active. Under such assumption of effect sparsity, in choosing a design for factor screening, it is important to consider projections of the design onto small subsets of factors. I will present some recent results on hidden projection properties of certain orthogonal arrays. Applications of these results to the construction of supersaturated designs will also be discussed.

When it is impractical to perform the experimental runs of a fractional factorial design in a completely random order, restrictions on the randomization can be imposed. The resulting design is said to have a split-plot error structure. Similar to completely randomized fractional factorials, fractional factorial split-plot designs can be ranked using the aberration criterion. Techniques that generate the required designs systematically presuppose unreplicated settings of the whole-plot factors. In this talk, I use a cheese-making experiment to demonstrate the practical relevance of designs with replicated settings of the whole-plot factors. I present a systematic method to generate the required designs. A key element in the method is the splitting of whole-plots according to one or more sub-plot effects.

The economic globalization brings intense competition among manufacturing enterprises. The key to succeed in this competitive climate is to rapidly respond to market changes and produce high-quality product with low cost. This demands new and efficient process control and management methodologies. On the other hand, with the development of computer and sensing technology, massive information of the manufacturing process (e.g. product design, process planning, in-process sensing information of process status, and product quality information) is now available. This presents us a great opportunity to develop such a new process management methodology that meets the requirements.

This presentation will introduce a model-based methodology for monitoring, diagnosis, and control of multistage manufacturing processes (MMP). A multistage manufacturing process involves more than one workstation or operation to produce products. The complexity of the process variations at each station and the propagation of variation along multiple stations make the fault diagnosis and product variation reduction of MMP a very challenging problem. In this research, a state space modeling approach is developed to describe the variation propagation and links the product dimensional quality and the process faults. This model integrates the product design (CAD) information and the process planning (CAPP) information such as the fixture layout and workpiece setup at each stage. Based on this model, the diagnosability and root cause identification of the system is pursued by integrating advanced statistics with engineering knowledge. Besides the process-level modeling and diagnosis, station-level dynamic control strategies for vibration reduction will also be presented.

The presented math-based methodology not only provides the process monitoring capability as the traditional statistical process control does, but also goes beyond detection of process faults to fault isolation, root cause determination, and in-process compensation/action.

In modern manufacturing processes, large quantities of multivariate measurement data are routinely available through automated in-process sensing. The data typically contain valuable information regarding the nature of each of the (possibly many) individual variation sources that contribute to the overall level of process variability. This work assumes that each source causes a distinct spatial variation pattern in the measurement data. It is argued that a suitable model for representing the variation patterns is of identical structure to one that is widely used in sensor array signal processing. Consequently, methods developed for these signal processing applications, termed blind source separation, can be used to identify spatial variation patterns in manufacturing data. Basic blind separation concepts and their applicability to diagnosing manufacturing variation are discussed.

Recent empirical studies of the Internet and WAN traffic data have observed multifractal behavior at time scales below a few hundred milliseconds. There have been some attempts to model this phenomenon, but there is no model to connect the small time scale behavior with behavior observed at large time scales of bigger than a few hundred milliseconds. There have been separate analyses of models for high speed data transmissions, which show that appropriate approximations to large time scale behavior of cumulative traffic are either fractional Brownian motion or stable Lévy motion, depending on the input rates assumed. This paper tries to bridge this gap and develops and analyzes a model offering an explanation of both the small and large time scale behavior of a network traffic model based on the infinite source Poisson model. Previous studies of this model have usually assumed that transmission rates are constant and deterministic. We consider a non-constant, multifractal, random transmission rate at the user level which results in cumulative traffic exhibiting multifractal behavior on small time scales and self-similar behavior on large time scales. Also, we model the file size and the transmission rate, which are more natural objects than the usually modeled transmission time and rate.

In this talk we examine the network tomography problem whose objective is to recover the loss probabilities of all the internal links in a network by using measurements only on the edge nodes. This problem is of increasing importance due to the fact that it is impossible to measure every single link in a large decentralized network. We introduce a new monitoring scheme, involving bicast measurements, and analyze its theoretical properties on the networks with a tree topology. The link loss probabilities can be calculated from network traces using the EM algorithm. A Bayesian version of our approach will also be discussed.

In probabilistic approach to information retrieval (IR) it is commonly assumed that query terms in a relevant document are stochastically independent. Together with the Probability Ranking Principle, these assumptions have led to the development of binary independence model (BIM) for IR. Recently, due to its simplicity and self-updating property through conjugate prior, Bayesian information retrieval (BIR) using BIM has emerged and demonstrated to be an empirically appealing process. In real world context, however, the assumption of conditional independence of query terms almost never holds. Many models and ideas have been proposed and attempted to circumvent this problem. Lu (2001, Boeing M\&CT-TECH-01-005) developed a Bayesian retrieval model based on the Dirichlet-Multinomial (D-M) distribution without the notion of conditional independence. In this paper, we illustrate that the D-M model for BIR developed by Lu can easily implement the self-updating process of the BIM for BIR. We use simulation to compare the D-M model for BIR to binary independence models under different specification for the initial prior parameters. And finally, we apply this model to actual data and compare the efficiency gained by adopting this model to existing BIMs.

We consider situations where multiple sets of ordinal data are observed from the same experimental unit. We develop Bayesian inference using a multivariate probit regression model. An underlying latent variable framework is used to capture the dependence among the multivariate data. This model includes the special case in which one or more sets of the data are binary. By a judicious choice of priors, we are able to overcome some of the computational difficulties of other Bayesian approaches in the literature. An application to multivariate probe test data from integrated circuit fabrication will be described.

This work is a contribution to the recent research program fusing together Bayes graphical models and times series, that is, graphical models in which every node is a time series. The main task is to derive conditions for conditional independence. This paper concentrates on the stationary Gaussian case. Two cases are distinguished: global conditional independence when two whole (past, present, future) times series, X, Y are conditionally independent given a whole third series, Z, and local conditional independence in which the present of X and Y (at time t) are conditionally independent give the past of Z (time < t). A comparison is made between local and global conditions and computations carried out for autoregressive processes. This work is then applied to data from complicated industrial processes (e.g. waste water treatment plants).

Two adjustments to the F test for variances are introduced which ameliorate the poor robustness properties of the test. A comparison of these adjustments to the classical F test and Levene/Brown-Forsythe's test shows a significant improvement for various sample sizes and distributions. One of the adjustments is extended to testing homogeneous variances in multiple samples and comparisons are made to Levene's and Bartlett's tests for equal variability.

The classical tests of homogeneity, such as the two-sample Kolmogorov-Smirnov test, do not have a natural extension to comparing two multivariate populations. G. J. Szekely and N. K. Bakirov have proposed a new test based on Euclidean distance between sample elements. This test can be applied to testing homogeneity of any two d-dimensional multivariate populations with finite mean vectors, and the test is affine invariant and consistent. The talk will discuss the background of the new test, present the test implementation methods, and discuss applications. We show that a practical implementation of this test is possible via bootstrap for testing the composite hypothesis of equal distributions when both distributions are unspecified. Empirical results in the univariate case suggest that this test compares favorably with existing tests. The talk will also present empirical results for multivariate distributions.

In this paper, the center similar distribution (CSD) of a multivariate distribution is proposed based on the vertical density representation theory. We construct the distribution family of CSD related Gamma distribution and display its relation with the Dirichlet distribution. We can generate a random vector from the Dirichlet distribution by generating a random vector from the center similar distribution. We also give the algorithm for generating the center similar distribution. A random vector X_d has the center similar distribution if X_d=RU_d, where R and U_d are independent of each other, R is a random variable with non-negative values and U_d is a random vector with a uniform distribution on the set D₀ R^d whose Lebesgue measure L(D₀) > 0. A CSD is a generalization of the spherical symmetric distribution. A random vector X_d has a spherical symmetric distribution if X_d=RV_d, but V_d is uniformly distributed on the surface of unit sphere. For a CSD, when D₀ is unit sphere, U_d has a uniform distribution on the body (not the surface) of the sphere. We also point out that they are equivalent.

Early-stage prototypes of single-shot multi-stage systems (missiles or rockets) and certain stage-wise repetitive-usage service (software, communications) systems are often found to be functionally deficient when subjected to acceptance test (Operational Test, or OT). Unanticipated design faults or failure modes are likely to appear. Re-design or "fault removal" is then conducted (a "fix") and re-test is conducted. Question: how to determine when to stop the Test-Fix-Test (TFT) process?

This talk addresses the above problem by probability modeling, and evaluates simple success-run stopping criteria: stop TFT after first achieving a run of r (e.g. 3, or 5) consecutive total system test successes (the SR criterion). The models evaluate the costs and benefits of the TFT system. The models represent more and different sources of inherent variability in the process than is usual: first, the effect of early-stage failure upon testing of later stages where failures are assumed to occur independently and identically for each system realization/copy; secondly, failure processes are individualized by copy, and also across presumed environmental variations. The results provide operational and budgetary information for system program executives, and OT planners.

It has been stated that 80% of corporate information is in the form of unstructured text. Traditional research in statistics and data mining has focused on structured data, typically stored in databases. With the dramatic increase in textual data, particularly from the web, there has been increased interest in text analysis. Text analysis is a broad field encompassing information extraction, information retrieval, and text data mining. Information extraction and retrieval are generally used to present information for human-centered pattern recognition. Conversely, text data mining uses machine learning algorithms to find patterns. This discussion will present examples of text analysis tools and technologies, including our research on the application of text data mining to warranty claims.

A simple real world example is used to illustrate the current paradigm of experimental planning and the limitations of the decision support available to the growing number of novice users. Then, one vision is proposed of how simulation and optimization can be used to provide information and method options that experimental planers might desire. Trade-offs in conceptual clarity, method performance, and apparent complexity are discussed in addition to the implications for teaching experimental planning at various levels. While it is probably true that optimal plans will not obsolete designs derived from combinatorial structures in the short run, it is likely that many approaches derived from realistic optimization formulations besides, e.g., Box-Behnken designs, will start to enjoy wide spread usage.

Canonical analysis is a common method for exploring and exploiting fitted quadratic response surfaces. Much attention in canonical analysis is given to identifying ridge behavior in these surfaces in order to achieve optimal response at minimum cost. However, little attention has been given to classifying the identified ridge as a stationary ridge or a rising ridge. Knowing whether a ridge is stationary or rising is critical for making decisions about how to continue the response surface exploration or for setting process parameters. This talk presents two methods that allow for identification, classification and confirmation of ridge behavior. The first method is based on linear regression and though easily implemented, can be imprecise. The second method is more precise and is based on a new parameterization of the canonical form.

In performing random simulations using CEA models, the method of sampling is important. It effects the accuracy and the convergence speed of the mean and standard deviation estimates. This presentation discusses one special case: sampling of spot welding location from potentially thousands of spot welds on a vehicle body. This study is prompted by the need of evaluating the effect of missing or low quality welds on the structural integrity of the body, identifying critical welds, and optimizing weld locations. A random sampling method based on the principle of Latin-Hypercube sampling is developed for this special application, which also accommodates GM's internal specifications on welding quality. We'll also present a case study in which the efficiency of three different sampling methods is compared. The new method, called Balanced Latin-Hypercube Sampling (BLHS), has shown significant improvements over the other two. Further applications of the method will also be discussed.

In this article a brick wall model is developed to describe the relationship between the minimum intergranular corrosion (IGC) path length and the aspect ratio of grains of high strength wrought aluminum alloy. We study the distribution of the horizontal distance that a corrosion path will travel in the metal and fit the model to an actual corrosion data set using the method of moments. The distribution of the horizontal distance of a corrosion path along a given grain is assumed to be uniformly distributed given the length of the grain, which is itself modeled by a gamma distribution. A modified brick wall model is proposed that imposes a distribution on the vertical distance traveled by the corrosion path as well. We use computer simulation to evaluate the fit of these models.

Accelerated life tests are commonly used to assess the reliability of materials, components, and subsystems. A frequently asked question is "what do these test results say about performance in the field." Laboratory tests are carefully controlled whereas the field environment is highly variable. Products in the field see, for example, different use rates. If detailed information on the distribution of use rates in the field is available, it is possible to use laboratory test results to predict the failure time distribution in the field. Often such information is not available. If both life test data and field data (e.g., from Warranty returns) are available, focusing on one or more failure modes, it is possible to fit a physically-motivated transfer function to relate the two data sets. Under a reasonable set of practical assumptions, this transfer function can then be used to predict the failure time distribution for a future component or product operating in the same use environment. This talk will describe a model and methods for fitting such a transfer function model. The methods will be illustrated with an example in which the transfer function was used to predict the failure time distribution of a turbine device that had two different failure modes.