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exponential 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 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
... 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 stress-corrosion...
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
... 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 distribution gamma...
Image
Published: 01 January 2000
Fig. 11 Failures as a function of time. The failure percentages follow an exponential distribution with a Weibull slope of unity. More
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
... Abstract This article discusses some of the statistical aspects of design from an engineer's perspective. It reviews the commonly used statistical terms and distributions for providing some guidance on the practical engineering applications of these distributions. The article describes...
Series: ASM Handbook
Volume: 8
Publisher: ASM International
Published: 01 January 2000
DOI: 10.31399/asm.hb.v08.a0009218
EISBN: 978-1-62708-176-4
... Abstract This article presents typical problems encountered in the analysis of experimental creep and creep-rupture data and the possible solutions to these drawbacks. It provides information on planning the test and creep strain/time relationships. The exponential creep equation...
Series: ASM Handbook
Volume: 4C
Publisher: ASM International
Published: 09 June 2014
DOI: 10.31399/asm.hb.v04c.a0005835
EISBN: 978-1-62708-167-2
... because it helps reduce heat losses and increase thermal process effectiveness. However, in the case of heating a workpiece, it is easier to obtain uniform temperature distribution in materials that have high thermal conductivity. Providing the required heat uniformity is important for bar and billet...
Series: ASM Handbook
Volume: 10
Publisher: ASM International
Published: 15 December 2019
DOI: 10.31399/asm.hb.v10.a0006632
EISBN: 978-1-62708-213-6
... stresses present. Corrections for the exponential attenuation of the radiation penetrating the subsurface stress distribution and for relaxation of the stresses present due to layer removal are then necessary, as discussed subsequently. Because the surface is not disturbed in order for the lattice strain...
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
... by using the “algebra of normal distribution functions” as given in Haugen ( Ref 15 ). Distributions There are at least 20 different probability distributions, several of which are very useful in reliability theory and application. Useful life, noted above, uses the (negative) exponential...
Series: ASM Handbook
Volume: 6
Publisher: ASM International
Published: 01 January 1993
DOI: 10.31399/asm.hb.v06.a0001481
EISBN: 978-1-62708-173-3
... heat is deposited internally, rather than as a surface flux, the input energy can be assumed to be deposited within a spheroidal or ellipsoidal region that is similar in shape to the weld puddle. As described by Ref 15 , the heat input can be taken to vary exponentially as a Gaussian distribution...
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
..., 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 sampling...
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
..., depending on parameters Type of extreme value distribution Bounded to the left (cannot be negative) Applications: life of electronic components; material strengths (fracture toughness), time to wear out (bearings, pumps) Exponential Exponential One parameter (sometimes two...
Series: ASM Handbook
Volume: 4A
Publisher: ASM International
Published: 01 August 2013
DOI: 10.31399/asm.hb.v04a.a0005789
EISBN: 978-1-62708-165-8
... on the design of the probe, heat-extraction dynamics, and influence of wetting kinematics. It also includes discussions on the simplified 1-D temperature-distribution model, calculation of the HTC, and the finite-volume method for the heat-conduction equation. finite-volume method hardness heat-transfer...
Series: ASM Handbook
Volume: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.a0005516
EISBN: 978-1-62708-197-9
... toward its core at which the current decreases exponentially to 1/exp its value at the surface. The power density at this distance will decrease to 1/exp 2 its value at the surface. Figure 10 illustrates the skin effect appearance by showing the distribution of current density and power density from...
Series: ASM Handbook
Volume: 4A
Publisher: ASM International
Published: 01 August 2013
DOI: 10.31399/asm.hb.v04a.a0005761
EISBN: 978-1-62708-165-8
... it can vary by a factor of 20. It also is important to be aware that commonly accepted assumptions regarding current and power distribution due to skin effect are not valid for a great majority of induction surface-hardening applications. For example, the widely accepted assumption of exponential...
Series: ASM Handbook
Volume: 8
Publisher: ASM International
Published: 01 January 2000
DOI: 10.31399/asm.hb.v08.a0003291
EISBN: 978-1-62708-176-4
... components and multiaxial testing methods. multiaxial stress creep creep rupture tubular component effective stress effective strain elastic stress distribution steady-state creep stress multiaxial creep ductility multiaxial testing thermal stress DESIGN OF PRESSURIZED COMPONENTS...
Series: ASM Handbook Archive
Volume: 10
Publisher: ASM International
Published: 01 January 1986
DOI: 10.31399/asm.hb.v10.a0001762
EISBN: 978-1-62708-178-8
... Abstract The diffraction pattern of any material contains structural and chemical property information that can be extracted using radial distribution function analysis. This article provides an introduction to the technique and presents several examples highlighting various ways in which...
Series: ASM Handbook
Volume: 6A
Publisher: ASM International
Published: 31 October 2011
DOI: 10.31399/asm.hb.v06a.a0005603
EISBN: 978-1-62708-174-0
... to be a radially symmetric, normally distributed surface flux at any instant in time ( Ref 13 ). The heat flux provided by the source, q , can be expressed conveniently as an exponential, or Gaussian, function, such that: (Eq 1) q ( r ) = ( 3 f Q π r ′ 2 ) exp [ − 3...
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
.... 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 components) can be calculated. Compared...
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
... to vibration response data. The Weibull with a shape factor of 2 is known as a Rayleigh distribution and is the natural result of narrow-band random vibration of a linear system ( Ref 27 ). A squaring phenomenon, such as might result from fluid drag forces, will distort the Rayleigh into an exponential...