Showing papers in "Technometrics in 2012"

Some Comments on Cp

Abstract: I study the typical configuration of a Cp plot when the number of variables in the regression problem is large and there are many weak effects. I show that a particular configuration that is very commonly seen can arise in a simple way. I give a formula by means of which the risk incurred by the “minimum CP ” rule can be estimated.

Time Series: Theory and Methods (2nd ed,)

Abstract: (1992). Time Series: Theory and Methods (2nd ed,) Technometrics: Vol. 34, No. 3, pp. 371-371.

A Three-Stage Iterative Procedure for Space-Time Modeling Phillip

Abstract: A three-stage iterative procedure for building space-time models is presented. These models fall into the general class of STARIMA models and are characterized by autoregressive and moving average terms lagged in both time and space. This model class collapses into the ARIMA model class in the absence of spatial correlation. The theoretical properties of STARIMA models are presented and the model building procedure is described and illustrated by a substantive example.

Gaussian Process Single-Index Models as Emulators for Computer Experiments.

Abstract: A single-index model (SIM) provides for parsimonious multidimensional nonlinear regression by combining parametric (linear) projection with univariate nonparametric (nonlinear) regression models. We show that a particular Gaussian process (GP) formulation is simple to work with and ideal as an emulator for some types of computer experiment as it can outperform the canonical separable GP regression model commonly used in this setting. Our contribution focuses on drastically simplifying, reinterpreting, and then generalizing a recently proposed fully Bayesian GP-SIM combination. Favorable performance is illustrated on synthetic data and a real-data computer experiment. Two R packages, both released on CRAN, have been augmented to facilitate inference under our proposed model(s).

Supplement to Degradation-Based Burn-In Planning Under Competing Risks

Abstract: In this supplementary document, the authors describe how to solve the chance constraint problem by combining the bootstrap method and some derivative-free optimization technique and present proofs.

Degradation-based burn-in planning under competing risks

Abstract: Motivated by two real-life examples, this article develops a burn-in planning framework with competing risks. Existing approaches to planning burn-in tests are confined to a single failure mode based on the assumption that this failure mode is subject to infant mortality. Considering the prevalence of competing risks and the high reliability of modern products, our framework differentiates between normal and infant mortality failure modes and recommends degradation-based burn-in approaches. This framework is employed to guide the burn-in planning for an electronic device subject to both a degradation-threshold failure, which is an infant mortality mode and can be modeled by a gamma process with random effect, and a catastrophic mode, which is normal and can be represented with a conventional reliability model. Three degradation-based burn-in models are built and the optimal cutoff degradation levels are derived. Their validity is demonstrated by an electronic device example. We also propose three approach...

Noncollapsing Space-Filling Designs for Bounded Nonrectangular Regions

Abstract: Many researchers use computer simulators as experimental tools, especially when physical experiments are infeasible. When computer codes are computationally intensive, nonparametric predictors can be fitted to training data for detailed exploration of the input–output relationship. The accuracy of such flexible predictors is enhanced by taking training inputs to be “space-filling.” If there are inputs that have little or no effect on the response, it is desirable that the design be “noncollapsing” in the sense of having space-filling lower dimensional projections. This article describes an algorithm for constructing noncollapsing space-filling designs for bounded input regions that are of possibly high dimension. Online supplementary materials provide the code for the algorithm, examples of its use, and show its performance in multiple settings.

Outlier Detection in Functional Observations With Applications to Profile Monitoring

Abstract: The presence of outliers has serious adverse effects on the modeling and forecasting of functional data. Therefore, outlier detection, aiming at identifying abnormal functional curves from a dataset, is quite important. This article proposes a new testing procedure based on functional principal component analysis. Under mild conditions, the null distribution of the test statistic is shown to be asymptotically pivotal with a well-known asymptotic distribution. Simulation results demonstrate good finite-sample performance of the asymptotic test and detection procedure. Finally, by illustrating the connection between profile monitoring in statistical process control and outlier detection in functional data, we apply the proposed approach to a real-data example from a manufacturing process and show that it performs quite well in detecting outlying profiles. Supplementary Material for this article is posted online on the journal web site.

Two-Stage Sensitivity-Based Group Screening in Computer Experiments

Abstract: Sophisticated computer codes that implement mathematical models of physical processes can involve large numbers of inputs, and screening to determine the most active inputs is critical for understanding the input-output relationship. This article presents a new two-stage group screening methodology for identifying active inputs. In Stage 1, groups of inputs showing low activity are screened out; in Stage 2, individual inputs from the active groups are identified. Inputs are evaluated through their estimated total (effect) sensitivity indices (TSIs), which are compared with a benchmark null TSI distribution created from added low noise inputs. Examples show that, compared with other procedures, the proposed method provides more consistent and accurate results for high-dimensional screening. Additional details and computer code are provided in supplementary materials available online.

Planning of Accelerated Life Tests With Dependent Failure Modes Based on a Gamma Frailty Model

Abstract: Accelerated life tests (ALT) provide timely information on product reliability. As product complexity increases, ALT often generate multiple dependent failure modes. However, the planning of an ALT with dependent failure modes has not been well studied in the literature. This article investigates the statistical modeling and planning of ALT with multiple dependent failure modes. An ALT model is constructed. Associated with each failure mode there is a latent lifetime described by a log-location-scale distribution, and the statistical dependence between different failure modes is described by a Gamma frailty model. The proposed model incorporates the ALT model with independent failure modes as a special limiting case. We obtain the c-optimal test plans by minimizing the large-sample approximate variance of the maximum likelihood estimator of a certain life quantile at use condition. The method is illustrated by developing ALT plans for field-effect transistors with competing gate oxide breakdown. A sensiti...

A Robust Standard Deviation Control Chart

Abstract: This article studies the robustness of Phase I estimators for the standard deviation control chart. A Phase I estimator should be efficient in the absence of contaminations and resistant to disturbances. Most of the robust estimators proposed in the literature are robust against either diffuse disturbances, that is, outliers spread over the subgroups, or localized disturbances, which affect an entire subgroup. In this article, we compare various robust standard deviation estimators and propose an algorithm that is robust against both types of disturbances. The algorithm is intuitive and is the best estimator in terms of overall performance. We also study the effect of using robust estimators from Phase I on Phase II control chart performance. Additional results for this article are available online as Supplementary Material.

Clustering Random Curves Under Spatial Interdependence With Application to Service Accessibility

Abstract: Service accessibility is defined as the access of a community to the nearby site locations in a service network consisting of multiple geographically distributed service sites. Leveraging new statistical methods, this article estimates and classifies service accessibility patterns varying over a large geographic area (Georgia) and over a period of 16 years. The focus of this study is on financial services but it generally applies to any other service operation. To this end, we introduce a model-based method for clustering random time-varying functions that are spatially interdependent. The underlying clustering model is nonparametric with spatially correlated errors. We also assume that the clustering membership is a realization from a Markov random field. Under these model assumptions, we borrow information across functions corresponding to nearby spatial locations resulting in enhanced estimation accuracy of the cluster effects and of the cluster membership as shown in a simulation study. Supplementary ...

Variable Selection in Additive Models Using P-Splines

Abstract: This article extends the nonnegative garrote method to a component selection method in a nonparametric additive model in which each univariate function is estimated with P-splines. We also establish the consistency of the procedure. An advantage of P-splines is that the fitted function is represented in a rather small basis of B-splines. A numerical study illustrates the finite-sample performance of the method and includes a comparison with other methods. The nonnegative garrote method with P-splines has the advantage of being computationally fast and performs, with an appropriate parameter selection procedure implemented, overall very well. Real data analysis leads to interesting findings. Supplementary materials for this article (technical proofs, additional numerical results, R code) are available online.

An Improved Bayesian Information Criterion for Multiple Change-Point Models

Abstract: In multiple change-point analysis, inferring the number of change points is often achieved by minimizing a selection criterion that trades off data fidelity with complexity. We address the open problem of defining a selection criterion adapted to the context of multiple change-point analysis. Our approach is inspired by the Schwarz seminal formulation of the Bayesian information criterion (BIC): similarly, we introduce priors—here describing the occurrence of change points—and we use the Laplace approximation to derive a closed-form expression of the criterion. Differently from this previous work, we take advantage of the a priori information introduced, instead of asymptotically eliminating the dependence on priors. Results obtained on simulated series show a substantial gain in performance versus recent alternative criteria used in multiple change-point analysis. Results also show that the a priori information introduced in our criterion on the regularity of interevent times is the main driver of this s...

A Bayesian Approach for Interpreting Mean Shifts in Multivariate Quality Control

Abstract: Multivariate quality characteristics are often monitored using a single statistic or a few statistics. However, it is difficult to determine the causes of an out-of-control signal based on a few summary statistics. Therefore, if a control chart for the mean detects a change in the mean, the quality engineer needs to determine which means shifted and the directions of the shifts to facilitate identification of root causes. We propose a Bayesian approach that gives a direct answer to this question. For each mean, an indicator variable that indicates whether the mean shifted upward, shifted downward, or remained unchanged is introduced. Prior distributions for the means and indicators capture prior knowledge about mean shifts and allow for asymmetry in upward and downward shifts. The mode of the posterior distribution of the vector of indicators or the mode of the marginal posterior distribution of each indicator gives the most likely scenario for each mean. Evaluation of the posterior probabilities of all p...

Robust Design Optimization With Quadratic Loss Derived From Gaussian Process Models

Abstract: Gaussian process models, which include the class of linear models, are widely employed for modeling responses as a function of control or noise factors. Using these models, the average loss at control factor settings can be estimated and compared. However, robust design optimization is often performed based on the expected quadratic loss computed as if the posterior mean were the true response function. This can give very misleading results. We propose an expected quadratic loss criterion derived by taking expectation with respect to the noise factors and the posterior predictive process. Approximate but highly accurate credible intervals for the average quadratic loss are constructed via the numerical inversion of the Lugannani–Rice saddlepoint approximation. The accuracy of the Lugannani–Rice intervals is compared with intervals constructed via moment-matching techniques on real data. This article has supplementary materials that are available online.

Rejoinder on "Clustering Random Curves Under Spatial Interdependence With Application to Service Accessibility"

Abstract: The authors of "Clustering Random Curves Under Spatial Interdependence With Application to Service Accessibility" provide their reactions to each of the five discussions presented in the May 2012 issue of Technometrics.

A General Strategy for Analyzing Data From Split-Plot and Multistratum Experimental Designs

Abstract: Increasingly, industrial experiments use multistratum designs, such as split-plot and strip-plot designs. Often, these experiments span more than one processing stage. The challenge is to identify an appropriate multistratum design, along with an appropriate statistical model. In this article, we introduce Hasse diagrams in the response surface context as a tool to visualize the unit structure of the experimental design, the randomization and sampling approaches used, the stratum in which each experimental factor is applied, and the degrees of freedom available in each stratum to estimate main effects, interactions, and variance components. We illustrate their use on several responses measured in a large study of the adhesion properties of coatings to polypropylene. We discuss quantitative, binary, and ordered categorical responses, for designs ranging from a simple split-plot to a strip-plot that involves repeated measurements of the response. The datasets discussed in this article are available online a...

Posterior Distribution Charts: A Bayesian Approach for Graphically Exploring a Process Mean

Abstract: We develop a Bayesian approach for monitoring and graphically exploring a process mean and informing decisions related to process adjustment. We assume a rather general model, in which the observations are represented as a process mean plus a random error term. In contrast to previous work on Bayesian methods for monitoring a mean, we allow any Markov model for the mean. This includes a mean that wanders slowly, that is constant over periods of time with occasional random jumps or combinations thereof. The approach also allows for any distribution for the random errors, although we focus on the normal error case. We use numerical integration to update relevant posterior distributions (e.g., for the current mean or for future observations), as each new observation is obtained, in a computationally inexpensive manner. Using an example from automobile body assembly, we illustrate how the approach can inform decisions regarding whether to adjust a process. Supplementary Materials for this article, including c...

Rejoinder: Bayesian Computation Using Design of Experiments-Based Interpolation Technique

Abstract: Comment on discussions provided for "Bayesian Computation Using Design of Experiments-Based Interpolation Technique," which have compared the DoIt approximation to several alternative methods for Bayesian computation.

Bayesian Computation Using Design of Experiments-Based Interpolation Technique

Abstract: In this article, a new deterministic approximation method for Bayesian computation, known as design of experiments-based interpolation technique (DoIt), is proposed. The method works by sampling points from the parameter space using an experimental design and then fitting a kriging model to interpolate the unnormalized posterior. The approximated posterior density is a weighted average of normal densities, and therefore, most of the posterior quantities can be easily computed. DoIt is a general computing technique that is easy to implement and can be applied to many complex Bayesian problems. Moreover, it does not suffer from the curse of dimensionality as much as some quadrature methods. It can work using fewer posterior evaluations, which is a great advantage over the Monte Carlo and Markov chain Monte Carlo methods, especially when dealing with computationally expensive posteriors. This article has supplementary material that is available online.

Gaussian Surrogates for Computer Models With Time-Varying Inputs and Outputs.

Abstract: Computer models of dynamic systems produce outputs that are functions of time; models that solve systems of differential equations often have this character. In many cases, time series output can be usefully reduced via principal components to simplify analysis. Time-indexed inputs, such as the functions that describe time-varying boundary conditions, are also common with such models. However, inputs that are functions of time often do not have one or a few “characteristic shapes” that are more common with output functions, and so, principal component representation has less potential for reducing the dimension of input functions. In this article, Gaussian process surrogates are described for models with inputs and outputs that are both functions of time. The focus is on construction of an appropriate covariance structure for such surrogates, some experimental design issues, and an application to a model of marrow cell dynamics.

Bayesian scale space analysis of differences in images

Abstract: This article considers the detection of image features in different spatial scales. The main focus is on capturing the scale-dependent differences in a pair of noisy images, but the technique developed can also be applied to the analysis of single images. The approach proposed uses Bayesian statistical modeling and simulation-based inference, and it can be viewed as a further development of SiZer technology, originally designed for nonparametric curve fitting. Numerical examples include artificial test images and a preliminary analysis of a pair of Landsat images used in satellite-based forest inventory. This article has supplementary material online.

Model-Robust Two-Level Designs Using Coordinate Exchange Algorithms and a Maximin Criterion

Abstract: We propose a candidate-list-free exchange algorithm that facilitates construction of exact, model-robust, two-level experiment designs. In particular, we investigate two model spaces previously considered in the literature. The first assumes that all main effects and an unknown subset of two-factor interactions are active, but that the experimenter knows the number of active interactions. The second assumes that an unknown subset of the main effects, and all associated two-factor interactions, are active. Previous literature uses two criteria for design construction: first, maximize the number of estimable models; then, differentiate between designs equivalent in estimability by choosing the design with the highest average -efficiency. We adopt a similar strategy, but (1) do not impose orthogonality or factor level balance constraints, resulting in generally equal or larger numbers of estimable models, and (2) use a flexible secondary criterion that maximizes the minimum -efficiency. We provide results fo...