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statistical distribution

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Series: ASM Technical Books
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.tb.sfa.t52780157
EISBN: 978-1-62708-268-6
... Abstract Failure analysis can sometimes involve considerations of statistics and probability. This chapter reviews some of the basic types of statistical distributions in order to understand some basic principles in their use. The main focus is on the uses of the normal distribution, which...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 November 2019
DOI: 10.31399/asm.tb.mfadr7.t91110666
EISBN: 978-1-62708-247-1
... along with an example. The chapter then discusses the purposes of reliability engineering and introduces four basic statistical distribution functions useful in reliability engineering, namely normal, lognormal, exponential, and Weibull. It also provides information on three fundamental acceleration...
Image
Published: 01 December 1995
Fig. 16-11 Histogram and statistically determined distribution curve of actual casting dimensions held on dimension B of the bearing retainer pictured. The pattern was pine, mounted on cope and drag boards. More
Series: ASM Technical Books
Publisher: ASM International
Published: 01 March 2006
DOI: 10.31399/asm.tb.pht2.t51440243
EISBN: 978-1-62708-262-4
.... In applying statistical analysis, the assumption is implicit that the data analyzed are random; that is, the data tend to scatter around some average value. The pattern of variation or frequency distribution typically found when data are taken from some natural or artificial process is called a normal...
Image
Published: 01 October 2012
Fig. 10.11 Statistical aspects of material design. (a) Weibull plot for reaction-bonded silicon nitride. (b) Improved Weibull distributions. (c) Modification of normal distribution by proof testing. Source: Ref 10.9 More
Image
Published: 01 November 2013
Fig. 14 Schematic representation of particle patterns in a powder mixture. (a) Ordered. (b) Agglomerated. (c) Statistical (random) distribution. (d) Demixed or segregated. Source: Ref 6 More
Series: ASM Technical Books
Publisher: ASM International
Published: 01 December 1995
DOI: 10.31399/asm.tb.sch6.t68200206
EISBN: 978-1-62708-354-6
... of the graphical techniques ( 7 ) to observe serious departures from a normal distribution. Where there is a critical application, more sophisticated tests of normality are available ( 8 , 9 ). Most statistical computer programs provide measures for evaluating the fit of data to normal distributions...
Series: ASM Technical Books
Publisher: ASM International
Published: 30 April 2024
DOI: 10.31399/asm.tb.phtpp.t59380163
EISBN: 978-1-62708-456-7
... In-process inspection and testing Final testing If these factors are incorporated into the heat treating operation, together with proper methods of statistical analysis of evaluation, quality can be ensured. Hardness Tests Hardness is the most widely used test to control heat treatment...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 December 1995
DOI: 10.31399/asm.tb.sch6.t68200220
EISBN: 978-1-62708-354-6
... that is being used by steel foundries to improve quality by improving the process is the use of designed experiment techniques. Rather than making changes to the process in an intuitive, on line way, this method allows changes to be tested off line in a planned, statistically valid way. Several variables can...
Book Chapter

Series: ASM Technical Books
Publisher: ASM International
Published: 01 April 2013
DOI: 10.31399/asm.tb.imub.t53720293
EISBN: 978-1-62708-305-8
..., indicate that casting performance in service will be affected. Equally important are the size, location, and distribution of these discontinuities. Those discontinuities that are small and located near the center of the casting have little effect, while those located at or near the surface of the casting...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.tb.scm.t52870351
EISBN: 978-1-62708-314-0
... assume a normal distribution, although other types of statistical distributions are available and are used. Three types of design allowables are considered: A-basis, B-basis, and S-basis. A-basis and B-basis allowables are calculated using the following formulas: (Eq 13.2) σ A = σ...
Book Chapter

Series: ASM Technical Books
Publisher: ASM International
Published: 01 September 2005
DOI: 10.31399/asm.tb.gmpm.t51250311
EISBN: 978-1-62708-345-4
... in the fundamental stress formulas for contact and bending to address overload, gear dynamics, size, load distribution, surface condition (contact only), and rim thickness (bending only). Design-allowable stress numbers are modified by further factors that address intended life, operating temperature, reliability...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 December 1984
DOI: 10.31399/asm.tb.mpp.t67850410
EISBN: 978-1-62708-260-0
... Abstract This chapter covers the emerging practice of quantitative microscopy and its application in the study of the microstructure of metals. It describes the methods used to quantify structural gradients, volume fraction, grain size and distribution, and other features of interest...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 November 2019
DOI: 10.31399/asm.tb.mfadr7.t91110506
EISBN: 978-1-62708-247-1
... to add a limited amount of cost to production test in order to make yield enhancement more efficient through statistical data collection. Several other areas of data sampling may be added. For example, a limit on the total test time overhead added by the data collection is useful. The data collection...
Book Chapter

Series: ASM Technical Books
Publisher: ASM International
Published: 01 October 2012
DOI: 10.31399/asm.tb.lmub.t53550511
EISBN: 978-1-62708-307-2
... to the random distribution of flaws in ceramics, there is a variation of strengths for various elements of a part. Thus, the strength of the various elements can be considered to have a statistical distribution with values above and below some characteristic strength. If an element is subjected to some value...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 October 2021
DOI: 10.31399/asm.tb.ciktmse.t56020013
EISBN: 978-1-62708-389-8
...: Statistical Distribution of Particles on a Plane Given a plane of area A with N particles distributed randomly on the surface, show that the probability distribution function P ( r ) of the nearest neighbor distance r between any two particles is given by: P ( r ) = 2 π a r...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 December 2004
DOI: 10.31399/asm.tb.tt2.t51060163
EISBN: 978-1-62708-355-3
... for fractographic analysis are outlined in ASTM C 1322, “Standard Practice for Fractography and Characterization of Fracture Origins in Advanced Ceramics.” Many data-analysis procedures for characterizing strength distributions can be found in the applied mathematics and statistics literature. Commercial...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.tb.tm.t52320013
EISBN: 978-1-62708-357-7
.... Fig. 2.9 Various factors to increase entropy 2.2.3 Maxwell-Boltzmann Distribution Law (M-B Statistics) The number of methods ( W ) of distributing N 0 balls to two boxes by N 1 and N 2 = N 0 – N 1 is expressed by (Eq 2.37) W ( N 1 , N 2 ) = N...
Book Chapter

Series: ASM Technical Books
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.tb.sfa.t52780081
EISBN: 978-1-62708-268-6
... not been observed or noted in the past. Sometimes, this occurs when a new inspector is assigned to an area. Such a situation is disconcerting, because it suggests that failures have occurred in the past and were not detected. Perhaps the failure is occurring as the result of normal statistical variation...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 November 2019
DOI: 10.31399/asm.tb.mfadr7.t91110613
EISBN: 978-1-62708-247-1
... timing failures fall into two classes: (1) intrinsic ICs (free of defects), and (2) extrinsic ICs (presence of defects). Intrinsic ICs can fail due to an unfortunate distribution of circuit statistics and/or environmental conditions. An extrinsic IC may have subtle imperfections in vias or contacts...