Donald W. Marquardt

Computer Analysis of NMR Spectra: Magnetic Equivalence Factoring

An extension of the NMR analysis method of Swalen and Reilly is described. The Hamiltonian matrix is factored to reduce it to minimal dimension by taking advantage of magnetic equivalence. Significant improvements are obtained in computation speed, computer program capacity, and convenience of use. Other extensions of the method provide a thorough statistical assessment of the resulting parameter estimates, and permit a solution even when some of the energy levels do not participate in any of the assigned transitions. The method has been tested by analyzing the 60‐Mc/sec proton resonance spectra of propane (A6B2) and isobutane (A9B). The chemical shifts, downfield from internal tetramethylsilane, and the coupling constants are: CH3CH2CH3; δ(CH3) = 0.912±0.005 ppm, δ(CH2) = 1.350±0.005 ppm, J = 7.35±0.02 cps: (CH3)3CH; δ(CH3) = 0.900±0.005 ppm, δ(CH) = 1.738±0.005 ppm, J = 6.73±0.05 cps.

Test Statistics for Mixture Models

Regression models of the forms proposed by Scheffe and by Becker have been widely and usefully applied to describe the response surfaces of mixture systems. These models do not contain a constant term. It has been common practice to test the statistical significance of these mixture models by the same statistical procedures used for other regression models whose constant term is absent (e.g., because the regression must pass through the origin). In this paper we show that the common practice produces misleading reslllts for mixtures. The mixture models require a different set of F, R 2, and R A 2 statistics. The correct mixture statistics correspond to a physically consistent null hypothesis and are also consistent with the expression of the mixture model in the older “slack-variable” form. An illustrative example is included.

Screening Concepts and Designs for Experiments with Mixtures

A strategy for determining the most important components in a mixture system is developed. The proposed screening designs are usefrd in those situations where the number of candidate components, q, is large. Our simplex screening designs, which contain 2q + 1 or 3q + 1 points, are recommended when it is possible to experiment over the total composition range of all components (0–100%) or the experimental region can be expressed as a simplex in terms of pseudocomponents. We recommend extreme vertices screening designs, which contain approximately q + 10 points, when some or all of the components are subject to upper and lower constraints. Examples are included to illustrate the proposed designs and associated analyses.

The Importance of Statisticians

On reexamine le role du statisticien et on montre comment il est percu et comment il se voit

Statistical Consulting in Industry

Abstract The statistics community is showing increasing interest in consulting in industry. This interest has stimulated questions concerning recognition and job satisfaction, job opportunities, and educational and training needs. These questions are considered in this article. A central theme is that effective statistical consulting requires total involvement in the consulting situation and that good recognition flows naturally from such an approach. This concept is defined in operational terms.

Statistical analysis of NMR spin-lattice relaxation times

Abstract Nuclear magnetic resonance spin-lattice relaxation time data, obtained with the inversion-recovery pulse sequence and subsequent Fourier transformation, are analyzed by various statistical estimation procedures. The different estimation methods often give markedly different T1 estimates. The most reliable method is shown to be iterative nonlinear estimation. Omission of explicit experimental determination of S∞ is feasible with this method. The effect of a misadjusted flip angle on the T1 estimates is discussed for two different estimation methods. A general nonlinear estimation method is developed suitable for the analysis of data from temperature-, frequency-, or pH-dependent T1 studies. This method enables the simultaneous determination of frequency factors τ0, activation energies Ea, spin-rotational coupling constants Crmeff, and chemical shift anisotropies Δσ in a single step. Phosphorus-31 data are used for this study but the conclusions are not restricted to this particular nucleus.

Time Dependence of Mechanical Breakdown in Bundles of Fibers. II. The Infinite Ideal Bundle under Linearly Increasing Loads

This article contains an extension of the theory of the previous paper to the calculation of the behavior of an infinite ideal bundle in a constant rate of loading experiment. It is assumed throughout that the bundle is composed of filaments which have been randomly selected from a first‐order ensemble for which the average lifetime under separate dead loads is an exponential function of the applied load. The differential equation which describes the breakdown of such a bundle has been numerically investigated with a CPC digital computer using a fourth‐order Runge‐Kutta method. It has been found that, throughout the practical range in rates of loading, the bundles tensile strength (units of force at break per initial unit area) is about 90% of the strength of the individual filaments. It also was found that the strength of the bundle is approximately an increasing linear function of the logarithm of the rate of loading.

Comment: Collinearity Diagnostics Depend on the Domain of Prediction, the Model, and the Data

The issue of mean-centering has generated a lot of discussion. The point of view described by Belsley in his current article and in Belsley, Kuh, and Welsch (1980), in contrast with Marquardt and Snee (1975), Marquardt (1980), and Montgomery and Peck (1982), retraces much of the same ground as does the earlier debate between Smith and Campbell (1980) and Marquardt (1980). As often happens with extended discussions of this type, the resolution turns out to depend upon the somewhat different premises from which the parties have operated. We will attempt to be more explicit about our views than in the past, and to relate them to Belsleys position.

New Technical and Educational Directions for Managing Product Quality

Abstract Product quality has high visibility in todays economic environment. It is now widely acknowledged that most quality problems are “management” or “systems” problems requiring “statistics” in their solution. This article explores the respective roles of • business philosophy • management systems • technology systems in the attainment of consistently high product quality. To meet todays needs, greater attention will have to be given to the balance and the interrelationships of these three facets. The quality technology systems require new directions and new emphases in statistics, software engineering, and other disciplines in order to be cost-effective. Most important is widespread education in the statistical tools needed for these new directions—education by industry, universities, and technical societies. For the universities there is the promise of increased student enrollments because of the recognized economic importance of quality management and the promise of challenging research problems...

Criteria for Evaluating the Performance of Statistical Consultants in Industry

Abstract In a recent paper on statistical consulting (Marquardt 1979), an operational approach called total involvement was advocated. This paper continues that discussion, but focuses on the criteria for evaluating a consultants effectiveness, whatever the operational approach. A related goal is to characterize sources of data to evaluate performance. Interrelationships with the consulting environment and the evaluation viewpoint are explored. The total involvement approach is found to produce not only maximum consulting effectiveness, but also a clear definition of what is expected of a statistical consultant, and a wealth of performance evaluation data as by-products.