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Weibull distribution

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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: 18
Publisher: ASM International
Published: 31 December 2017
DOI: 10.31399/asm.hb.v18.a0006402
EISBN: 978-1-62708-192-4
... between wear and reliability in terms of exponential distribution, Weibull distribution, and gamma distribution. It concludes with information on the effects of interaction on failure probability. friction wear tribological testing tribographs transition diagrams tribomaps reliability Weibull...
Series: ASM Handbook
Volume: 20
Publisher: ASM International
Published: 01 January 1997
DOI: 10.31399/asm.hb.v20.a0002476
EISBN: 978-1-62708-194-8
... concepts and models associated with performing time-independent and time-dependent reliability analyses for brittle materials exhibiting scatter in ultimate strength. The article discusses the two-parameter and three-parameter Weibull distribution for representing the underlying probability density...
Series: ASM Handbook
Volume: 19
Publisher: ASM International
Published: 01 January 1996
DOI: 10.31399/asm.hb.v19.a0002415
EISBN: 978-1-62708-193-1
... debonding. It discusses the fatigue behavior of composite laminates in the form of a relation between applied maximum fatigue stress and fatigue life. The article explains Weibull distribution and parameters estimation for fatigue data analysis and life prediction of composite laminates. It analyzes...
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
... be normally distributed (Gaussian distribution), while high-COV quantities are often modeled by Weibull and other one-sided distributions, as discussed below. Uncertainty in <italic>S</italic>-<italic>N</italic> Data As mentioned above, dividing a problem into constituent (albeit sometimes arbitrary...
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
..., such as Weibull probability paper. Although not statistically rigorous, plotting of CDFs on different types of probability paper can be very helpful in evaluating whether or not it is reasonable to assume a particular statistical distribution. Sample versus Population Parameters When performing...
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
... identical conditions produces a high degree of scatter, in comparison with metals. Thus, statistical treatment of the fatigue data is of particular interest. The distribution of static strength and fatigue life can be described mathematically by a two-parameter Weibull function ( Ref 16 ). A two- parameter...
Series: ASM Handbook
Volume: 11A
Publisher: ASM International
Published: 30 August 2021
DOI: 10.31399/asm.hb.v11A.a0006803
EISBN: 978-1-62708-329-4
... method, and the most frequently used simulation methods, standard Monte Carlo sampling, Latin hypercube sampling, and discrete probability distribution sampling. Further, the article discusses methods developed to analyze the results of probabilistic methods and covers the use of epistemic and aleatory...
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
... at the same level of confidence. Fig. 9 One-sided tolerance limits on data The tolerance limit defined in Eq 18 is only valid if the stated assumptions are not violated. In some situations, the underlying distribution cannot be assumed, or evidence may suggest a Weibull, rather than log normal...
Series: ASM Handbook
Volume: 19
Publisher: ASM International
Published: 01 January 1996
DOI: 10.31399/asm.hb.v19.a0002373
EISBN: 978-1-62708-193-1
... distribution is used in statistical analysis of bearing-life tests. A typical bearing-life Weibull plot is shown in Fig. 10 ( Ref 12 ). Fig. 10 Weibull plot of ball-bearing lives distribution. Source: Ref 12 Two life values in the distribution are shown. The L 10 life, or the life at which...
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
.... Mathematics Any function that is strictly positive and for which the area is unity qualifies for a PDF, but there are standard functions, or distributions, that are commonly used in engineering practice. Some of these are the normal, lognormal, extreme value, and Weibull distributions. The PDF and CDF...
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
... and for discontinuities in the material. In the probabilistic approach, each design parameter is accorded a statistical distribution of values. From these distributions and from an allowable limit on probability of failure, minimum acceptable dimensions in critical areas (or minimum strength levels for critical...
Series: ASM Handbook
Volume: 21
Publisher: ASM International
Published: 01 January 2001
DOI: 10.31399/asm.hb.v21.a0003393
EISBN: 978-1-62708-195-5
... distribution, the population may be better described by a Weibull or lognormal distribution, or if it fits none of these, a nonparametric calculation is used ( Fig. 5 ). The B - basis value can be determined from the formulas given in MIL-HDBK-17 section 8.3 for each type of distribution. Fig. 5 Common...
Series: ASM Handbook
Volume: 20
Publisher: ASM International
Published: 01 January 1997
DOI: 10.31399/asm.hb.v20.a0002432
EISBN: 978-1-62708-194-8
... distribution, which has a single parameter. Also as noted above, the binomial and Poisson distributions are very useful in certain situations. The Poisson distribution has a single parameter while the binomial distribution has two parameters. The Weibull distribution was developed in the late 1940s...
Series: ASM Handbook
Volume: 13C
Publisher: ASM International
Published: 01 January 2006
DOI: 10.31399/asm.hb.v13c.a0004128
EISBN: 978-1-62708-184-9
... then be repeated for various stress levels. This analysis was conducted for 7075-T6 specimens with an open-hole ( K t =3) geometry without corrosion as well as with superimposed initial flaw sizes corresponding to the characteristic, 5th and 95th percentile values for the Weibull distribution of the pit...
Series: ASM Desk Editions
Publisher: ASM International
Published: 01 November 1995
DOI: 10.31399/asm.hb.emde.a0003060
EISBN: 978-1-62708-200-6
... engine parts. Fig. 11 Weibull distribution of SN235 at 950 °C (1740 °F). Weibull modulus, 18.4; maximum strength, 870 MPa (125 ksi); minimum strength, 610 MPa (88 ksi); average strength, 760 MPa (110 ksi); number of specimens, 112 Fig. 12 Analytical vs. experimental test results...
Series: ASM Handbook
Volume: 20
Publisher: ASM International
Published: 01 January 1997
DOI: 10.31399/asm.hb.v20.a0002490
EISBN: 978-1-62708-194-8
... in flaw population, and part design to be iterated to a successful design in terms of the stresses calculated by finite element analysis. The finite element net is combined with the known statistical failure behavior (flaw distribution) of the ceramic. This protocol is most frequently based on Weibull...
Series: ASM Handbook
Volume: 5
Publisher: ASM International
Published: 01 January 1994
DOI: 10.31399/asm.hb.v05.a0005586
EISBN: 978-1-62708-170-2
...) LT long transverse (direction) m meter m constant shear, or frictional factor; Weibull slope, for reliability above 90%; Weibull distribution; dispersion parameter; molecular weight mA milliampere MAS Microbeam Analysis Society MBE molecular-beam epitaxy...
Series: ASM Handbook
Volume: 19
Publisher: ASM International
Published: 01 January 1996
DOI: 10.31399/asm.hb.v19.a0002376
EISBN: 978-1-62708-193-1
... , June 1972 36. Tallian T.E. , Weibull Distribution of Rolling Contact Fatigue Life and Deviations Therefrom , ASLE Trans. , Vol 5 , 1962 , p 183 – 196 10.1080/05698196208972465 37. Zaretsky E.V. , Ed., STLE Life Factors for Rolling Bearings , STLE SP-34, 1992 38...
Series: ASM Handbook
Volume: 18
Publisher: ASM International
Published: 31 December 2017
DOI: 10.31399/asm.hb.v18.a0006426
EISBN: 978-1-62708-192-4
... and the reliability and lifetime expressions from Weibull and Palmgren led to the first bearing ratings and life theories and various fatigue and material constants. This led to methods on computing stresses for basic bearing geometries and considerable fatigue testing. Following the work of Grubin in 1949 ( Ref 2...