Stephen B. Vardeman

Average Run Lengths for CUSUM Schemes When Observations Are Exponentially Distributed

Page (1954) originally noted that it is possible to find an integral equation whose solution gives average run lengths for one-sided CUSUM schemes. Lucas and Crosier (1982), for the case of normally distributed observations, have obtained numerical solutions to Pages integral equation and used these in their study of so called fast-initial-response CUSUM charts. In this article we show that for the case of exponentially distributed observations, the Page equation can be solved without resorting to approximations. We then provide some tables of average run lengths for the exponential case and comment on an application of exponential CUSUM charts to controlling the intensity of a Poisson process.

Contextual classification of multispectral image data

Abstract Compound decision theory is invoked to develop a method for classifying image data using spatial context. Methods for characterizing contextual information in an image are proposed and tested. Experimental results based on both simulated and real multispectral remote sensing data demonstrate the effectiveness of the contextual classifier. A number of practical problems associated with this approach are discussed and possible solutions are explored.

What about the other Intervals

Abstract For a variety of introductory audiences, there are strong practical and pedagogical reasons for the early teaching of statistical interval methods that are often treated as “advanced” topics, if at all. There are also simple, effective ways of making this early introduction. This expository article discusses the elementary teaching of one-sided statistical intervals, prediction intervals, and tolerance intervals for both (one-sample) nonparametric and (general) normal theory contexts.

Two-way random-effects analyses and gauge R&R studies

An important prerequisite of any sensible data-based engineering study is the quantification of the precision of gauges or measuring equipment to be used in data collection. It has long been understood that in the event that more than one individual will use a particular gauge, “measurement variation” for that gauge can include not only a kind of “pure error” component but an “operator” or “technician” component as well. Furthermore, it is well known that the two-way random-effects model provides a natural framework for quantifying the different components of measurement variation. Some parts of standard practice in the “gauge R&R studies” aimed at quantifying measurement precision, however, are unfortunately at odds with what makes sense under this model. Thus, the purpose of this primarily expository article is to explain in elementary terms the use of a two-way random-effects model for gauge R&R studies, to critique current practice, and to point out some simple improvements that can follow from more c...

Optimal Adjustment in the Presence of Deterministic Process Drift and Random Adjustment Error

A state-space process-control model involving adjustment error and deterministic drift of the process mean is presented. The optimal adjustment policy is developed by dynamic programming. This policy calls for a particular adjustment when a Kalman-filter estimator is outside a deadband defined by upper and lower action limits. The effects of adjustment cost, adjustment variance, and drift rate on the optimal policy are discussed. The optimal adjustment policy is computed for a real machining process, and a simulation study is presented that compares the optimal policy to two sensible suboptimal policies.

The Legitimate Role of Inspection in Modern SQC

Abstract For many years there has been much discussion regarding the appropriateness of “inspection” and “acceptance sampling” as tools for quality and productivity. This expository article collects and attempts to put into perspective some of the main points of controversy regarding these techniques.

Estimation of Context for Statistical Classification of Multispectral Image Data

Recent investigations have demonstrated the effectiveness of a contextual classifier that combines spatial and spectral information employing a general statistical approach [1], [2]. This statistical classification algorithm exploits the tendency of certain ground-cover classes to occur more frequently in some spatial contexts than in others. Indeed, a key input to this algorithm is a statistical characterization of the context: the context function. Here we discuss an unbiased estimator of the context function which, besides having the advantage of statistical unbiasedness, has the additional advantage over other estimation techniques of being amenable to an adaptive implementation in which the context-function estimate varies according to local contextual information. Results from applying the unbiased estimator to the contextual classification of three real Landsat data sets are presented and contrasted with results from noncontextual classifications and from contextual classifications utilizing other context-function estimation techniques.

Interval Estimation of a Normal Process Mean from Rounded Data

Standard statistical methods are based on an implicit assumption that numerical data are exact. But in truth, all real data are rounded to some smallest unit of measure related to the precision of the device used to produce them. When the degree of rounding is severe, ignoring the rounding produces statistical methods with operating characteristics far from nominal. We discuss the interval estimation of the parameter μ when rounded data come from the N(μ,σ2) distribution.

Modeling and Inference for Measured Crystal Orientations and a Tractable Class of Symmetric Distributions for Rotations in Three Dimensions

Electron backscatter diffraction (EBSD) is a technique used in materials science to study the microtexture of metals, producing data that measure the orientations of crystals in a specimen. We examine the precision of such data based on a useful class of distributions on orientations in three dimensions (as represented by 3×3 orthogonal matrices with positive determinants). Although such modeling has received attention in the statistical literature, the approach taken typically has been based on general “special manifold” considerations, and the resulting methodology may not be easily accessible to nonspecialists. We take a more direct modeling approach, beginning from a simple, intuitively appealing mechanism for generating random orientations specifically in three-dimensional space. The resulting class of distributions has many desirable properties, including directly interpretable parameters and relatively simple theory. We investigate the basic properties of the entire class and one-sample quasi-likelihood–based inference for one member of the model class, producing a new statistical methodology that is practically useful in the analysis of EBSD data. This article has supplementary material online.

Bayes one-sample and one-way random effects analyses for 3-D orientations with application to materials science

We consider Bayes inference for a class of distributions on orien- tations in 3 dimensions described by 3 3 rotation matrices. Non-informative priors are identied and Metropolis-Hastings within Gibbs algorithms are used to generate samples from posterior distributions in one-sample and one-way random eects models. A simulation study investigates the performance of Bayes analyses based on non-informative priors in the one-sample case, making comparisons to quasi-likelihood inference. A second simulation study investigates the behavior of posteriors for some informative priors. Bayes one-way random eect analyses of orientation matrix data are then developed and the Bayes methods are illustrated in a materials science application.