Flaw statistics

FRACTURE AND FLAW STATISTICS OF A TYPICAL COMMERCIAL SILICON NITRIDE... 

It should be obvious from Equation 9-1 that the criterion for failure is that Flaws, Statistics of Fracture, and Measurement Techniques... 

Many distribution functions can be apphed to strength data of ceramics but the function that has been most widely apphed is the WeibuU function, which is based on the concept of failure at the weakest link in a body under simple tension. A normal distribution is inappropriate for ceramic strengths because extreme values of the flaw distribution, not the central tendency of the flaw distribution, determine the strength. One implication of WeibuU statistics is that large bodies are weaker than small bodies because the number of flaws a body contains is proportional to its volume. 

An eminently practical, if less physical, approach to inherent flaw-dependent fracture was proposed by Weibull (1939) in which specific characteristics of the flaws were left unspecified. Fractures activate at flaws distributed randomly throughout the body according to a Poisson point process, and the statistical mean number of active flaws n in a unit volume was assumed to increase with tensile stress a through some empirical relations such as a two-parameter power law... 

Another important aspect of the fatigue of all materials is the statistical nature of the failure process and the scatter which this can cause in the results. In a particular sample of plastic there is a random distribution of microcracks, internal flaws and localised residual stresses. These defects may arise due to structural imperfections (for example, molecular weight variations) or as a result of the fabrication method used for the material. There is no doubt that failure... 

Even plastics with fairly linear stress-strain curves to failure, for example short-fiber reinforced TSs (RPs), usually display moduli of rupture values that are higher than the tensile strength obtained in uniaxial tests wood behaves much the same. Qualitatively, this can be explained from statistically considering flaws and fractures and the fracture energy available in flexural samples under a constant rate of deflection as compared to tensile samples under the same load conditions. These differences become less as the... 

Fan, J., Chen, C., Statistical simulation of low-speed unidirectional flaws in transitional... 

Th/232ih However, this paired isochron approach has an inherent statistical flaw. 

Durbin-Watson statistic Works Objective Is statistically testable Can be computerized Has fatal flaw Requires large number of samples Low statistical power... 

This test thus shares several characteristics with the Durbin-Watson test. It is based on well-known and rigorously sound statistics. It is amenable to automated computerized calculation, and suitable for automatic operation in an automated process situation. It does not have the fatal flaw of the Durbin-Watson Statistic. 

For highly fluid coatings that have to solidify rapidly, obviously fast cross-linkings by thermal or radiation activation are effective. A characteristic susceptibility of fibers to fracture with increasing length, because of the statistics of flaw distribution and the many ways in which these flaws can be induced, such as by chance particles, inhomogeneous qualities of the coating, etc., demand unprecedented precision in polymer film formation. However, there are additional factors, such as... 

Campbell, S.K. (1974), Flaws and Fallacies in Statistical Thinking, Prentice-Hall, Englewood Cliffs, NJ. 

There are two goals for significance testing. The first is to estimate ttie number of clusters in the data and the second is to identify the amount of overlap between ttie various clusters. Unfortunately, no completely satisfactory statistical test exists. One is faced with a difficult decision, either to ignore the problem or to make do with available testing methods. The simplest, most straight-forward test is chosen for this study, the sum of squares ratio test. Even though the test method may be flawed, it is necessary to underscore the importance and usefulness of statistical measures of cluster separation. 

The Marian Diamond studies are not without controversy. For example. Dr. Lucy Rorke, a neuropathologist in Philadelphia, feels that the number of glial cells was in fact normal, but she was impressed that the brain showed none of the usual degenerative changes one sees in older people. Rorke said it looks like the brain of a young person. Terence Hines of Pace University has also pointed out that the Diamond work may have statistical flaws in its analysis of Einstein s brain, so the debate continues. 

Adar, R K. A Flaw in a Universal Mntoi, ScL Arnet.. 50 (February 1988). Ahimony, A.. The Reality of the Quantum Woild, Sri Arner., 46 (January 1988). Batalin, I.A, Isham, C..T., and G A. Vileovisky, Editors Quantum Field Theory find Quantum Statistics, Hilger, Bristol, U.K, 1987 Canrighr, G S. and S.M. Girvin Fractional Statistics Quantum Possibilities in Two Dimensions, Science, 1197 (March 9, 1990). 

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