Peter A. Parker

A change point method for linear profile data

We propose a change point approach based on the segmented regression technique for testing the constancy of the regression parameters in a linear profile data set. Each sample collected over time in the historical data set consists of several bivariate observations for which a simple linear regression model is appropriate. The change point approach is based on the likelihood ratio test for a change in one or more regression parameters. We compare the performance of this method to that of the most effective Phase I linear profile control chart approaches using a simulation study. The advantages of the change point method over the existing methods are greatly improved detection of sustained step changes in the process parameters and improved diagnostic tools to determine the sources of profile variation and the location(s) of the change point(s). Also, we give an approximation for appropriate thresholds for the test statistic. The use of the change point method is demonstrated using a data set from a calibration application at the National Aeronautics and Space Administration (NASA) Langley Research Center. Copyright

Construction of Balanced Equivalent Estimation Second-Order Split-Plot Designs

Practical restrictions on randomization are commonplace in industrial experiments due to the presence of hard-to-change or costly-to-change factors. Using a split-plot design (SPD) structure reduces the number of times that these hard-to-change factors are reset during the experiment. A class of second-order response surface SPDs has been proposed in which the ordinary least squares estimates of the model are equivalent to the generalized least squares estimates. Equivalent estimation designs provide best linear unbiased estimates that are independent of the variance components and can be obtained with standard statistical software. Moreover, design selection is robust to model misspecification and does not require previous knowledge of the variance components. This article expands the conditions to obtain equivalent estimation designs and outlines two systematic design construction techniques for building balanced versions of the central composite design. In addition, it presents an approach to generating equivalent estimation D-optimal designs. By applying these design construction techniques, a catalog of designs is generated. These methods provide practitioners with the necessary tools to build equivalent estimation SPDs for a wide variety of applications.

Tutorial: Industrial Split-plot Experiments

ABSTRACT Many industrial experiments involve two types of factors: those that are hard-to-change and those that are easy-to-change (ETC). Hard-to-change (HTC) factors have levels that are difficult and/or expensive to change. As a result, the experimenter would prefer to run the experiment in such a manner as to minimize the number of times that he/she must change the levels of these factors. Unfortunately, it is precisely the changing of these levels that provides the information about the effects of the HTC factors. Consequently, when we minimize the number of times we change the levels of these factors, we also minimize the relevant information about their effects. This paper summarizes the structure and the analysis of industrial split-plot experiments. The purpose of this article is to teach practitioners how to identify split-plot experimental conditions, how to run the experiment efficiently, and then how to analyze the results. The article illustrates both first-order and second-order experiments. The first four sections provide a basic background on experimental design and an introduction to first-order split-plot experiments. The remainder of this article contains more advanced topics dealing with second-order, split-plot experiments.

Classes of Split-Plot Response Surface Designs for Equivalent Estimation

When planning an experimental investigation, we are frequently faced with factors that are difficult or time consuming to manipulate, thereby making complete randomization impractical. A split-plot structure differentiates between the experimental units associated with these hard-to-change factors and those that are relatively easy-to-change. Furthermore, it provides an efficient strategy that integrates the restrictions imposed by the experimental apparatus into the design structure. In this paper, several industrial and scientific examples are presented to highlight design considerations when a restriction on randomization is encountered. We propose classes of split-plot response designs that provide an intuitive and natural extension from the completely randomized context. For these designs, the ordinary least-squares estimates of the model are equivalent to the generalized least-squares estimates. This property provides best linear unbiased estimators and simplifies model estimation. The design conditions that provide equivalent estimation are presented and lead to design construction strategies to transform completely randomized Box–Behnken, equiradial and small composite designs into a split-plot structure. Published in 2006 by John Wiley & Sons, Ltd.

Response Surface Methods for Efficient Complex Aircraft Configuration Aerodynamic Characterization

A response surface methodology approach to wind-tunnel testing of aircraft with complex configurations is being investigated at the Langley full-scale tunnel as part of a series of tests using design of experiments. An exploratory study was conducted using response surface methodology and a 5% scale blended-wing-body model in an effort to efficiently characterize aerodynamic behavior as a function of attitude and multiple control surface inputs. This paper provides a direct comparison of the design of experiments/response surface methodology and one factor at a time methods for a low-speed wind-tunnel test of a blended-wing-body aircraft configuration with 11 actuated control surfaces. A modified fractional factorial design, augmented with center points and axial points, produced regression models for the characteristic aerodynamic forces and moments over a representative design space as a function of model attitude and control surface inputs. Model adequacy and uncertainty levels were described using robust statistical methods inherent to the response surface methodology practice. Experimental goals included the capture of fundamental stability and control data for simulation models and comparisons to baseline data from recent one factor at a time tests. Optimization is demonstrated for control surface allocation for a desired response. A discussion of highlights and problems associated with the test is included.

Statistical Engineering — Forming the Foundations

Editors: Christine M. Anderson-Cook, Lu Lu, Panelists: Gordon Clark, Stephanie P. DeHart, Roger Hoerl, Bradley Jones, R. Jock MacKay, Douglas Montgomery, Peter A. Parker, James Simpson, Ronald Snee, Stefan H. Steiner, Jennifer Van Mullekom, G. Geoff Vining, Alyson G. Wilson Los Alamos National Laboratory, Los Alamos, New Mexico Ohio State University, Columbus, Ohio DuPont, Roanoke, Virginia GE Global Research, Schenectady, New York SAS, Cary, North Carolina University of Waterloo, Waterloo, Ontario, Canada Arizona State University, Tempe, Arizona NASA, Langley, Virginia Eglin Air Force Base, Valparaiso, Florida Snee Associates, Newark, Delaware DuPont, Richmond, Virginia Virginia Tech, Blacksburg, Virginia Institute for Defense Analyses, Washington, DC INTRODUCTION

Robust split‐plot designs

In many experimental situations, practitioners are confronted with costly, time consuming, or hard-to-change (HTC) factors. These practical or economic restrictions on randomization can be accommodated with a split-plot design structure that minimizes the manipulation of the HTC factors. Selecting a good design is a challenging task and requires knowledge of the opportunities and restrictions imposed by the experimental apparatus and an evaluation of statistical performance among competing designs. Building on the well-established evaluation criteria for the completely randomized context, we emphasize the unique qualitative and quantitative evaluation criteria for split-plot designs. An example from hypersonic propulsion research is used to demonstrate the consideration of multiple design evaluation criteria. Published in 2007 by John Wiley & Sons, Ltd.

Comparing computer experiments for fitting high-order polynomial metamodels

The use of simulation as a modeling and analysis tool is wide spread. Simulation is an enabling tool for experimenting virtually on a validated computer environment. Often the underlying function for a computer experiment result has too much curvature to be adequately modeled by a low-order polynomial. In such cases, finding an appropriate experimental design is not easy. We evaluate several computer experiments assuming the modeler is interested in fitting a high-order polynomial to the response data considering both optimal and space-filling designs. We also introduce a new class of hybrid designs that can be used for deterministic or stochastic simulation models.

Wind-Tunnel Balance Characterization for Hypersonic Research Applications

Wind-tunnel research was recently conducted at the NASA Langley Research Center s 31-Inch Mach 10 Hypersonic Facility in support of the Mars Science Laboratory s aerodynamic program. Researchers were interested in understanding the interaction between the freestream flow and the reaction control system onboard the entry vehicle. A five-component balance, designed for hypersonic testing with pressurized flow-through capability, was used. In addition to the aerodynamic forces, the balance was exposed to both thermal gradients and varying internal cavity pressures. Historically, the effect of these environmental conditions on the response of the balance have not been fully characterized due to the limitations in the calibration facilities. Through statistical design of experiments, thermal and pressure effects were strategically and efficiently integrated into the calibration of the balance. As a result of this new approach, researchers were able to use the balance continuously throughout the wide range of temperatures and pressures and obtain real-time results. Although this work focused on a specific application, the methodology shown can be applied more generally to any force measurement system calibration.

Statistical Engineering—Roles for Statisticians and the Path Forward

Experts from diverse areas of industry, government, and academia are asked about the changing roles for statisticians in the SE workplace and discuss some of the opportunities and challenges for the future.