Statistical aspects

The first of these points will be commented upon subsequently in connection with an interpretation of the statistical variability of fracture events. To answer this and the second question the highly developed tools of statistical analysis (e.g., 1—2) are available their application forms a backbone of industrial quality control and material design. Understandably, the complex input (mechanical, thermal, and environmental attack) acting upon a complex system (e. g., a highly structured polymer) has a complex, non-deterministic output. The determination and evaluation of only a small number of different data will necessarily reveal only a partial aspect of the fracture process. For this reason the questions as to cause and kinetics of fracture development can rarely be answered unambiguously. Any mathematical interrelations established between variables (e.g., time and stress) are valid for extrapolation only if the basis does not change. 

In this chapter an overview of conceptually different fracture theories is presented which have in common that they do not make explicite reference to the characteristic properties of the molecular chains, their configurational and super-molecular order and their thermal and mechanical interaction. This will be seen to apply to the classical failure criteria and general continuum mechanical models. Rate process fracture theories take into consideration the viscoelastic behavior of polymeric materials but do not derive their fracture criteria from detailed morphological analysis. These basic theories are invaluable, however, to elucidate statistical, non-morphological, or continuum mechanical aspects of the fracture process. 

From a statistical standpoint, the variability of a material property, e.g., fracture strength, is explained by referring to one or more of the following three arguments  

The beginning of fracture is a statistical event, the occurrence of which is described by probability laws. 

Apparently identical specimens of a set are inherently different, e.g., they contain a large number of flaws of different size or severeness and the most severe of these flaws determines the fracture strength. 

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Master equation methods are not tire only option for calculating tire kinetics of energy transfer and analytic approaches in general have certain drawbacks in not reflecting, for example, certain statistical aspects of coupled systems. Alternative approaches to tire calculation of energy migration dynamics in molecular ensembles are Monte Carlo calculations [18,19 and 20] and probability matrix iteration [21, 22], amongst otliers. 

The usual practice in these appHcations is to concentrate on model development and computation rather than on statistical aspects. In general, nonlinear regression should be appHed only to problems in which there is a weU-defined, clear association between the independent and dependent variables. The generalization of statistics to the associated confidence intervals for nonlinear coefficients is not well developed. 

Rice, R. C. 1997 Statistical Aspects of Design. In ASM International, ASM Handbook No. 20 - Materials Selection and Design, 10th Edition. OH ASM International. 

ASTM Special Technical Publication No. 91 discusses in detail the important ramifications to be considered in the various statistical aspects of fatigue testing. Most often, the fatigue curves as well as the tabulated values... 

This chapter provides a complementary perspective to that provided by Kramer and Mah (1994). Whereas they emphasize the statistical aspects of the three primary process monitoring tasks, data rectification, fault detection, and fault diagnosis, we focus on the theory, development, and performance of approaches that combine data analysis and data interpretation into an automated mechanism via feature extraction and label assignment. 

In recent years pharmaceutical scientists have participated in lively discussions about how present methods of bioequivalency determination might legitimately and advantageously be modified. For example, the question of whether it is necessary to always take plasma samples so that AUC at the end of the test is at least 90% of AUC at time infinity has been explored [7,8], Statistical aspects of this and other possible methods of modifying protocol design are covered in a most useful book published in 1999 and in several papers [8-10,22],... 

O Saito. Statistical aspects of infinite network formations. Polym Eng Sci 19 234-235, 1979. 

Scargle, J. D. (1982). Studies in astronomical time series analysis. II. Statistical aspects of spectral analysis of unevenly spaced data. Astroph. J., 263, 835-53. 

Food and Drug Administration (FDA) (2001). Guidance for Industry Statistical Aspects of the Design, Analysis and Interpretation of Chronic Rodent Carcinogenicity Studies of Pharmaceuticals. USDHEW, Washington, D.C. 

Mantel, N. and Haenszel, W. (1952) Statistical aspects of the analysis of data from the retrospective studies of disease, J. Nat. Cancer Inst., 22 719-748. 

For the reader who would like to further explore experimental design, there are a number of more detailed texts available which include more extensive treatments of the statistical aspects of experimental design (Cochran and Cox, 1975 Diamond, 1981 Federer, 1955 Hicks, 1982 Kraemer and Thiemann, 1987 and Myers, 1972). 

The comparison of time profiles involves many statistical aspects, some of which were touched upon in the previous discussion, where appropriate. In particular, it was stressed that, with the Moore-Flanner index f2 as the sole exception, statistical comparisons are generally made in terms of... 

Statistics plays a crucial role in any data analysis, and accordingly, the statistical aspects are mentioned and appropriate equations/code are supplied. E.g. examples are given for the least-squares analysis of data with white noise as well as y2-analyses for data with non-uniformly distributed noise. However, the statistical background for the appropriate choice of the two methods and more importantly, the effects of wrong assumptions about the noise structure are not included. 

Difficulties in both the chemical and statistical aspects of the problem have been found to be enormous in utilizing such a... 

Apart from the atomistics of charge exchange, especially electron capture, there is also a statistical aspect which has been studied extensively within a classical approach [51] which appears adequate for gases but less obvious for penetration through solids [63]. 

Many of the important statistical aspects of clinical trials design are dealt with in detail in Chapter 6 of this volume (Nigel Baber and John Sweatman) and so here only specific statistical aspects are discussed. 

Mantel N, Haenszel W. Statistical aspects of data from retrospective studies of disease. / Natl Cancer Inst 1959 22 719 8. 

Finally most therapeutic specific guidelines contain recommendations that directly impact on statistical considerations, for example in terms of the definition of endpoints, the requirement for more than one primary endpoint, the definition of analysis sets and the choice of A. In a particular therapeutic setting it is self-evident that the requisite guidelines should be studied carefully in order to extract relevant information for statistical aspects of design and analysis. 

The nobler the metal is, the more easily the cation can pick up the electron from the azide ion and be reduced (Ref 5, p 145) Under the title "Statistical Aspects of Sensitivity , Dunkle gives a resume of a lecture presented by Mr A. Bulfinch at PicArsn on 6 Jan, 1958 (Ref 5, pp 148-50)... 

Simon R, Altman DG. Statistical aspects of prognostic factor studies in oncology. Br J Cancer 1994 69 979-985. 

Finally, in the third section, readers will find four chapters that address the role of pharmacogenomics in drug development in oncology, including an industry perspective on this subject, as well as statistical aspects related to the discovery of pharmacogenomic biomarkers during drug development. 

Furthermore, significant industry and FDA resources are spent debating issues related to acceptable variability, need for additional in-process testing and how specification acceptance limits should be established. Often these debates are focused on acceptance limits or the statistical aspects. In these debates a proportionate focus on the underlying manufacturing science is often missing. For example ... 

ISO (2003), Statistical aspects of sampling from bulk materials—Part 1 General principles, 11648-1 (Geneva International Organization for Standardization). 

In the consideration of the statistical aspects of turbulence it was found to be of utility (B6, K4, Rl) to establish the correlation in time (B6) of the velocity vectors as a function of the distance between two points in the turbulent stream. The correlation coefficient is defined by... 

The observations of wave and particle behaviour, and the statistical aspects of the quantum theory, are among the problems which may still leave the reader puzzled. This is an appropriate reaction, as some of the best brains of the twentieth century have grappled with such issues, and have failed to find a totally satisfactory explanation. 

Since the start of validation in the late 1970s, there has been little published on the statistical aspects of conducting a successful process validation. What follows are some of the statistical techniques that have been either suggested in... 

BROWN, C.C. (1978). Statistical aspects of extrapolation of dichotomous dose-response data, J. Natl. Cancer Inst. 60, 101-108. 

TYoe, J. (1992). Statistical aspects of ion-molecule reactions, in State-Selected and State-to-State Ion-Molecule Reaction Dynamics, Part 2 Theory, ed. M. Baer and C.Y. Ng (Wiley, New York). 

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