摘要:

A number of difficult problems in experimental design and analysis were afforded by an experiment to evaluate the precision and accuracy of a new facility for calibrating cryogenic flow meters. Time order was an important variable, but could not be economically randomized. The design space was not rectangular and two important variables were intrinsically highly correlated. The resulting data had outliers, cycles, unexpected shifts and other dilticultics. This report chronicals the evolution of the design of the experiments and the analysis of the results.

ISSN:0040-1706    

DOI:10.1080/00401706.1977.10489576

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

This paper is concerned with the optimum allocation of test units to overstress conditions when it is desired to estimate the survival probability at a design condition with a low expected failure probability. The criterion is that of minimizing the large sample variance: a logistic model is assumed. Expressions and charts for allocating test units to the accelerated stresses are provided and procedures for determining the stresses when these are not all specified are given. The gain in efficiency from using these plans versus testing exclusively at the design condition is analyzed. The requirement for some testing at the design stress and at an intermediate stress is also considered.

ISSN:0040-1706    

DOI:10.1080/00401706.1977.10489577

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

Drs. Meeker and Hahn have presented useful optimum overstress tests, based on the logistic model. This discussion centers on some of the practical problems associated with overstress plans in general, and on the implications of these for optimal experimental design.

ISSN:0040-1706    

DOI:10.1080/00401706.1977.10489578

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

Attribute responses are often elicited by the simultaneous action of two or more variables. Experimental design and parameter estimation schemes, analogous to the familiar univariate plans, are developed here for the bivariate case. Using general exponential distributions of the formP(U= I) = exp (−γ). where γ is a suitably defined function, the elements of the information matrix are derived explicitly. Minimizing the determinant of this matrix. which is equivalent to minimizing the generalized variance. leads to optimal experimental designs. Explicit derivations are presented for univariate and bivariate exponential and Weibull distributions. The conditions are detined under which sequential optimal designs based on these results can be used.

ISSN:0040-1706    

DOI:10.1080/00401706.1977.10489579

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

ISSN:0040-1706    

DOI:10.1080/00401706.1977.10489580

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

Methods to determine the validity of regression models include comparison of model predictions and coefficients with theory, collection of new data to check model predictions. comparison of results with theoretical model calculations, and data splitting or cross-validation in which a portion of the data is used toestimatethe model coefficients, and the remainder of the data is used to measure thepredictionaccuracy of the model. An expository review of these methods is presented. It is concluded that data splitting is an effective method of model validation when it is not practical to collect new data to test the model. The DUPLEX algorithm, developed by R. W. Kennard, is recommended for dividing the data into the estimation set and prediction set when there is no obvious variable such as time to use as a basis to split the data. Several examples are included to illustrate the various methods of model validation.

ISSN:0040-1706    

DOI:10.1080/00401706.1977.10489581

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

For testing general linear hypotheses in multiple regression models. it is shown that non-stochastically shrunken ridge estimators yield the same centralF-ratios andt-statistics as does the least squares estimator. Thus although ridge regression does produce biased point estimates which deviate from the least squares solution, ridge techniques do not generally yield “new” normal theory statistical inferences: in particular, ridging does not necessarily produce “shifted” confidence regions. A concept, the ASSOCIATFD PROBABILITY of a ridge estimate, is defined using the usual, hyperellipsoidal confidence region centered at the least squares estimator, and it is argued that ridge estimates are of relatively little interest when they are so “extreme” that they lie outside of the least squares region of say 90 percent confidence.

ISSN:0040-1706    

DOI:10.1080/00401706.1977.10489582

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

In continuation of the study of [10] and [5], designs for quadratic regression are considered when the possible values of the controlable variable aremixturesx= (x1,x2, …,xq+ 1) of nonnegative componentsxiwith Σq+ 11xi= I. The “all-boas” design of Box and Draper [1] for guarding against cubic bias, and the design that is optimum with respect to theD-optimality criterion ignoring the posaibility of such bias, are compared in terms of the average and the maximum of the variance and bias functions of the fitted repression. TheD-optimum design performs well in terms of the Box-Draper criterion unless the sample size is fairly large, and is superior in terms of maximum variance and bias.

ISSN:0040-1706    

DOI:10.1080/00401706.1977.10489583

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

Designs for quadratic regression are considered when the possible values of the controlable variable are mixturesx= (x1,x2, …,xq+ 1) of nonnegative componentsxiwith Σq+ 11xi= 1. The designs that are optimum with respect to theD-,A-, andE-optimality criteria are compared in their performance relative to these and other criteria. Computational routines for obtaining these designs are developed, and the geometry of optimum structures is discussed. Except whenq= 2, theA-optimum design is supported by the vertices and midpoints of edges of the simplex, as is the case for the previously knownD-optimum design. Although theE-optimum design requires more observation points, it is more robust in its efficiency, under variation of criterion: but all three designs perform reasonably well in this sense.

ISSN:0040-1706    

DOI:10.1080/00401706.1977.10489584

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

In certain exponential life-testing models, the optimal number of replacements is a function of the unknown parameter which is being estimated. Two procedures are proposed in this paper to overcome this dificulty by sequentially estimating the parameter and redesigning the experiment in a model similar to that considered by Blight [1]. Monte Carlo studies indicate that such an approach yields results which are almost as good as the optimal design which depends on the unknown parameter. Life-test data on semiconductor devices is used for the purpose of illustrating the proposed procedures.

ISSN:0040-1706    

DOI:10.1080/00401706.1977.10489585

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor