Weibull parameters

The price of flexibility comes in the difficulty of mathematical manipulation of such distributions. For example, the 3-parameter Weibull distribution is intractable mathematically except by numerical estimation when used in probabilistic calculations. However, it is still regarded as a most valuable distribution (Bompas-Smith, 1973). If an improved estimate for the mean and standard deviation of a set of data is the goal, it has been cited that determining the Weibull parameters and then converting to Normal parameters using suitable transformation equations is recommended (Mischke, 1989). Similar estimates for the mean and standard deviation can be found from any initial distribution type by using the equations given in Appendix IX. 

Figure 4.16 Short-term tensile strength Weibull parameters for an alloy steel at various temperatures (Upson eta/., 1967)...

A 3-parameter Weibull approximates to a Normal distribution when (3 = 3.44, and so we ean eonvert the Normal stress to Weibull parameters by using ... 

Mischke, C. R. 1989 Stochastic Methods in Mechanical Design Part 1 property data and Weibull parameters. In Proceedings 8th Biannual Conference on Failure Prevention and Reliability, Design Engineering of ASME, Montreal, Canada, 1-10 Sept. 

A, the fitted Weibull parameters listed in Table 2 and the remaining model parameters as listed in Figure 4 (panel a) or the assumed zero order release rates of 4%, 5%, and 6.7% per hour (panel b). 

Table 2 Fitted Weibull Parameters for the Three In Vitro Drug-Release Profiles Shown in Figure 3...

Interface properties of carbon fiber-epoxy matrix composites and Weibull parameters of carbon fibers"... 

Note that /3 and /4 are stress components in the plane of isotropy and, therefore, have the same Weibull parameters. The parameters i and /3i would be obtained from uniaxial tensile experiments along the material orientation direction, dt. The parameters a2 and /Efe would be obtained from torsional experiments of thin-walled tubular specimens where the shear stress is applied across the material orientation direction. The final two parameters, a3 and /33, would be obtained from uniaxial tensile experiments transverse to the material orientation direction. 

Fig. 11.2 Typical family of reliability contours. Weibull parameters, < i = 15,...

This technique was employed in calculating the reliability contours depicted in Fig. 11.4. The reliability contours represent a homogeneously stressed material element, and for dimensionless , the Weibull parameter /3 has units of stress (volume)1/a. Here a, = 5, j3, = 0.2, ac = 35, /3C = 2, abc — 35, and f bc = 2.32. The three surfaces correspond to 0tj = 0.95, 0.5, and 0.05. Note that the reliability contours retain the general behavior of the deterministic failure surface from which they were generated. In general, as the a values increase, the spacing between contours diminishes. Eventually the contours would not be distinct and they would effectively map out a... 

Regarding the distribution (2.19), two remarks can be made. First, it is not possible to get it straightforwardly from the second choice for the function C n) given by (2.15). Secondly, the constant If is practically equal to the most probable failure current if the Weibull parameter is large enough (for example, if m is larger than 5). 

Physically the Weibull parameters and are constants, unlike the median strain for fibril breakdown which depends on the size of the sample tested. The size effect... 

It is possible to make models which give microscopic meaning to the Weibull parameter 8 of the statistical description of fibril breakdown given in Eq. (31), or the related fibril stability — e. The necessary inputs are values for Pg CSi) which is defined as the P at a craze stress corresponding to a plastic strain e = 1. Modi-... 

Rosa V. Effect of ion exchange on Weibull parameters, subcritical crack growth and R-curve behavior of a dental porcelain. Master thesis. University of Sao Paulo 2007. 

An important feature of the above strength analysis is that a large number of test specimens need to be broken before the Weibull parameters can be known with any accuracy. For example, one often needs to break at least 30 specimens before m is known within 20% and strength testing program. 

When performing strength testing, it is critical that the flaws leading to failure in the test specimens are the same as those that cause failure in service. Spurious results will be obtained, for example, if flaws are produced in the machining of test specimens. Additionally, flaws in the component may appear during service (e.g., by oxidation or corrosion) and these may be different than those in test specimens. In some cases, several types of flaws may be present in the same specimen and this leads to non-linearities in the Weibull plots. Techniques have been put forward for extracting the Weibull parameters from such plots. In many situations, Weibull plots need to be extrapolated to failure probability values well... 

Determine the Weibull parameters in the active environment at one stressing rate. (This involves breaking at least 20 specimens.)... 

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