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log normal distribution

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Image
Published: 01 January 2000
Fig. 5 Schematic S / N diagram showing log normal distribution of lives at various stress levels More
Image
Published: 01 January 1997
Fig. 13 Density function for a log-normal distribution More
Series: ASM Handbook
Volume: 8
Publisher: ASM International
Published: 01 January 2000
DOI: 10.31399/asm.hb.v08.a0009213
EISBN: 978-1-62708-176-4
...Abstract Abstract The six types of statistical distributions are normal distribution, log normal distribution, Weibull distribution, exponential distribution, binomial distribution, and Poisson distribution. This article discusses the applicability of each distribution, providing information...
Series: ASM Handbook
Volume: 13A
Publisher: ASM International
Published: 01 January 2003
DOI: 10.31399/asm.hb.v13a.a0003641
EISBN: 978-1-62708-182-5
... the main characteristics of probability distributions, such as normal distribution, log-normal distribution, exponential distribution, Poisson distribution, and extreme-value distribution. It also provides information on the statistical concepts to produce effective test programs. susceptibility...
Image
Published: 01 January 1997
Fig. 6 Cumulative distribution function for fatigue data from Table 1 based on an assumed log-normal distribution. More
Image
Published: 30 September 2015
Fig. 4 Log-normal plots of cumulative undersized particle size distributions of water-atomized (80Ni-20Cr and type 316L) metal powders. Source: Ref 1 More
Book Chapter

By P.S. Grant
Book: Casting
Series: ASM Handbook
Volume: 15
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.hb.v15.a0005225
EISBN: 978-1-62708-187-0
..., stochastic process that always produces a wide range of droplet diameters. The article schematically illustrates a typical log-normal droplet diameter probability density distribution on a mass or volume basis obtained by gas atomization. It also explains the changes in solid fraction during the spray...
Series: ASM Handbook
Volume: 20
Publisher: ASM International
Published: 01 January 1997
DOI: 10.31399/asm.hb.v20.a0002431
EISBN: 978-1-62708-194-8
... well be log normal. Fig. 6 Cumulative distribution function for fatigue data from Table 1 based on an assumed log-normal distribution. Two statistical data points of significance can be drawn from Fig. 6 . First, an estimate of the geometric average value of the sample can be obtained...
Series: ASM Handbook
Volume: 8
Publisher: ASM International
Published: 01 January 2000
DOI: 10.31399/asm.hb.v08.a0009219
EISBN: 978-1-62708-176-4
... , 16 ). If the logarithms of the fatigue lives are assumed to be normally distributed about the mean line, and the scatter in log lives is assumed constant over the range of stress levels being considered, then log N can be considered the dependent variable in the analysis. Stress or strain...
Image
Published: 01 December 2009
Fig. 13 Estimated distribution for fraction of grains with cracks that reach a length three times mean grain size (40 μm) as a function of applied loading cycles (lower right) for multiple statistical realizations of equiaxed polycrystalline IN 100 microstructures with log normal grain size More
Series: ASM Handbook
Volume: 19
Publisher: ASM International
Published: 01 January 1996
DOI: 10.31399/asm.hb.v19.a0002369
EISBN: 978-1-62708-193-1
... people have their favorite distribution type: some like log-normal, which results from normally distributed logarithms of the data, and some prefer Weibull, which is a natural form for fatigue data because it was originally derived as a model of “weakest link” behavior for fatigue applications. Both...
Book Chapter

Series: ASM Desk Editions
Publisher: ASM International
Published: 01 December 1998
DOI: 10.31399/asm.hb.mhde2.a0003088
EISBN: 978-1-62708-199-3
..., to classify and quantify their possible causes with their associated probability of occurrence, and to evaluate their impact on the overall system performance. Failure mode and effect analysis normally is implemented as part of a comprehensive reliability program. The analysis is performed at increasing...
Series: ASM Handbook
Volume: 11
Publisher: ASM International
Published: 15 January 2021
DOI: 10.31399/asm.hb.v11.a0006767
EISBN: 978-1-62708-295-2
... situation, including the loads and the distribution of stresses within the configuration. Is there an additional load/stress that was not included in the analysis, which changes the stress distribution? Or is the stress analysis incorrect? In many cases, however, stress analysis alone is not sufficient...
Series: ASM Handbook
Volume: 1A
Publisher: ASM International
Published: 31 August 2017
DOI: 10.31399/asm.hb.v01a.a0006314
EISBN: 978-1-62708-179-5
... of the alloy or in the superheated liquid. Therefore, it may be more appropriate to use a log-normal distribution such as ( Ref 37 , 38 ): (Eq 20) N max ( Δ T ) = N o σ 1 2 π ∫ − ∞ ln   Δ T exp ( − ( x − m 1 ) 2 2 σ 1 2...
Series: ASM Handbook
Volume: 17
Publisher: ASM International
Published: 01 August 2018
DOI: 10.31399/asm.hb.v17.a0006463
EISBN: 978-1-62708-190-0
... (known as “ a -hat,” or â , versus a data). The review of the data collected by these systems showed that the data generally were linear on a log-log scale, with variance normally distributed around the mean, independent of crack size ( Fig. 4 ). Fig. 4 Illustration of the linear relationship...
Series: ASM Handbook
Volume: 4A
Publisher: ASM International
Published: 01 August 2013
DOI: 10.31399/asm.hb.v04a.a0005790
EISBN: 978-1-62708-165-8
... temperatures of plain carbon, low-alloy and high-alloy steels and temperature-time relations of subcritical annealing. Practical implications for induction annealing and induction normalizing are included. The article concludes by describing induction softening, which softens the threaded area on carburized...
Series: ASM Handbook
Volume: 21
Publisher: ASM International
Published: 01 January 2001
DOI: 10.31399/asm.hb.v21.a0003382
EISBN: 978-1-62708-195-5
... with Spatial Reference to the Normal, the Log Normal, and the Weibull Distributions,” FOA Report D 20045-DB, Defense Research Institute, Stockholm, 1977 17. Talreja R. , “Estimation of Weibull Parameters for Composite Materials Strength and Fatigue Life Data,” STP 723, American Society...
Series: ASM Handbook
Volume: 7
Publisher: ASM International
Published: 30 September 2015
DOI: 10.31399/asm.hb.v07.a0006065
EISBN: 978-1-62708-175-7
.... ( Ref 19 ) found that to be true with wax powders atomized in air. These powders have a tighter size distribution represented by the Rosin-Ramler law as opposed to the log-normal law that generally applies to atomized metal powders. Particle Size Distribution When various mechanisms operate...
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003514
EISBN: 978-1-62708-180-1
... has its own notation, Φ( z ), that is, F Z ( z ) = P ( Z ≤ z ) = Φ( z ). Lognormal Distribution Let X be a random variable. If Y = log X is normally distributed, then X is said to be lognormally distributed. To compute probabilities when X is lognormal: P ( X ≤ x...
Series: ASM Handbook
Volume: 24
Publisher: ASM International
Published: 15 June 2020
DOI: 10.31399/asm.hb.v24.a0006567
EISBN: 978-1-62708-290-7
... for understanding the size of a particular powder sample. Figure 6 shows the count- and volume-based PSDs for two samples of aluminum alloy powder feedstock for laser powder-bed fusion sourced from different vendors. Typical PSDs of feedstock for additive manufacturing are log-normally distributed in the volume...