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statistical distribution
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Book Chapter
Book: Systems Failure Analysis
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...
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 is the most commonly used statistical distribution. The chapter also includes a section discussing the reliability and probability of passing.
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...
Abstract
This chapter surveys both basic quality and basic reliability concepts as an introduction to the failure analysis professional. It begins with a section describing the distinction between quality and reliability and moves on to provide an overview of the concept of experiment design 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 models used by reliability engineers: Arrhenius, Eyring, and power law models. The chapter concludes with information on failure rates and mechanisms and the two techniques for uncovering reliability issues, namely burn-in and outlier screening.
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.
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Book Chapter
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...
Abstract
A successful heat treating operation is determined by the ability to satisfy the customer's quality requirements consistently and economically. This chapter reviews the steps that are important to produce quality parts in heat treating with a brief practical explanation of each. The steps include selecting proper material and design of the part being treated; determining whether the process is capable of heat treatment; using statistical process control, control charting, and in-process inspection and testing; and applying statistical quality control and final testing (sampling) to verify the results.
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
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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
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Book Chapter
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...
Abstract
Users of steel castings establish performance requirements for specific characteristics of the castings based on the planned use. They express tolerance for variation in those characteristics to the producer of the castings. One issue which should never be taken for granted in considering capability and tolerances is the ability to measure with accuracy and precision (repeatability and reproducibility). This chapter discusses the methods for measuring accuracy and precision. It describes the variation of process characteristics, capability indices in general use, and factors related to process performance and tolerance specification.
Book Chapter
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...
Abstract
This chapter covers the steps and tests that are important to produce quality parts in heat treating. The quality tests discussed include hardness tests, such as Brinell, Rockwell, and microhardness tests. The chapter also examines tensile testing, toughness testing, optical metallography, and nondestructive testing. The chapter concludes by discussing in-process inspections and the final inspection.
Book Chapter
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...
Abstract
The inspection of castings normally involves checking for shape and dimensions, coupled with aided and unaided visual inspection for external discontinuities and surface quality. This chapter discusses methods for determining surface quality, internal discontinuities, and dimensional inspection. Casting defects including porosity, oxide films, inclusions, hot tears, metal penetration, and surface defects are reviewed. Liquid penetrant inspection, magnetic particle inspection, eddy current inspection, radiographic inspection, ultrasonic inspection, and leak testing for castings are discussed. The chapter provides information on the procedures involved in the inspection of castings that are limited to visual and dimensional inspections, weight testing, and hardness testing. It also discusses the use of computer equipment in foundry inspection operations.
Book Chapter
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...
Abstract
This chapter discusses composite testing procedures, including tension, compression, shear, flexure, and fracture toughness testing as well as adhesive shear, peel, and honeycomb flatwise tension testing. It also discusses specimen preparation, environmental conditioning, and data analysis.
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...
Abstract
Mechanical tests are performed to evaluate the durability of gears under load. The chapter first discusses the processes involved in the computations of stress for test parameters of gear. Next, the chapter reviews the four areas of specimen characterization of a test program, namely dimensional, surface finish texture, metallurgical, and residual stress. The following section presents the tests that simulate gear action, namely the rolling contact fatigue test, the single-tooth fatigue test, the single-tooth single-overload test, and the single-tooth impact test. Finally, the chapter describes the test procedures for surface durability (pitting), root strength (bending), and scoring (or scuffing) testing.
Book Chapter
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...
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. It provides examples showing how the various features appear, how they are measured, and how the resulting data are converted into usable form. The chapter also discusses the quantification of fracture morphology and its correlation with material properties and behaviors.
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...
Abstract
Semiconductor memories are superb drivers for process yield and reliability improvement because of their highly structured architecture and use of aggressive layout rules. This combination provides outstanding failure signature analysis possibilities for the entire design, manufacturing, and test process. This article discusses five key disciplines of the signature analysis process that need to be orchestrated within the organization: design for test practices, test floor data collection methodology, post-test data analysis tools, root cause theorization, and physical failure analysis strategies.
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...
Abstract
Ceramics normally have high melting temperatures, excellent chemical stability and, due to the absence of conduction electrons, tend to be good electrical and thermal insulators. They are also inherently hard and brittle, and when loaded in tension, have almost no tolerance for flaws. This chapter describes the applications, properties, and behaviors of some of the more widely used structural ceramics, including alumina, aluminum titanate, silicon carbide, silicon nitride, zirconia, zirconia-toughened alumina (ZTA), magnesia-partially stabilized zirconia (Mg-PSZ), and yttria-tetragonal zirconia polycrystalline (Y-TZP). It also provides information on materials selection, design optimization, and joining methods, and covers every step of the ceramic production process.
Book Chapter
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...
Abstract
This chapter provides readers with worked solutions to more than 25 problems related to compositional impurities and structural defects. The problems deal with important issues and challenges such as the design of low-density steels, the causes and effects of distortion in different crystal structures, the ability to predict the movement of dislocations, the influence of impurities on defects, the relationship between gain size and material properties, the identification of specific types of defects, the selection of compatible metals for vacuum environments, and the effect of twinning planes on stacking sequences. The chapter also includes problems on how the formation of precipitates can produce slip planes and how grain boundaries can act as obstacles to dislocation motion.
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...
Abstract
This chapter describes tensile testing of advanced ceramic materials, a category that includes both noncomposite, or monolithic, ceramics and ceramic-matrix composites (CMCs). The chapter presents four key considerations that must be considered when carrying out tensile tests on advanced monolithic ceramics and CMCs. These include effects of flaw type and location on tensile tests, separation of flaw populations, design strength and scale effects, and lifetime predictions and environmental effects. The chapter discusses the advantages, problems, and complications of four basic categories of tensile testing techniques as applied to ceramics and CMCs. These categories are true direct uniaxial tensile tests at ambient temperatures, indirect tensile tests, tests where failure is presumed to result from tensile stresses, and high-temperature tensile tests.
Book Chapter
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...
Abstract
This chapter describes the basics of energy and entropy and “free energy.” Fundamentals of internal energy U , the enthalpy H , entropy S , free energies G , and F of a substance are presented. The chapter also presents the thermal vibration model to promote a better understanding of the U , S , and F of the crystal. It covers basic concepts of thermodynamics of magnetic transition and discusses the role and the meaning of magnetic transition in iron and steel. The chapter concludes with a general discussion on an amorphous phase from a thermodynamic viewpoint.
Book Chapter
Book: Systems Failure Analysis
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...
Abstract
This chapter targets areas that determine if a change occurred and if the change induced the failure: change or what's different analysis. It describes the different sources of changes that induce process deficiencies: design, process, test and inspection, environmental, supplier lot, aging, and supplier changes. The chapter presents an example of a cluster bomb failure to explain how the failure analysis team found and corrected the failure cause.
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...
Abstract
Electronics spans a number of devices, their configurations, and properties. A challenge is to identify those electronic subjects essential for failure analysis. This article reviews the normal operation and terminal characteristics of MOSFET. It describes the electronic behavior of bridges, opens, and parametric delay defects, which is essential for understanding the symptoms of a failing IC. These electronic principles are then applied to a CMOS failure analysis technique using a power supply signature analysis.
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