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Summary
by Xiaobin Le
Reliability-Based Mechanical Design, Volume 1
Preface
Introduction to Reliability in Mechanical Design
Engineering Design Process
Phase One: Needs Assessment
Phase Two: Design Specifications
Phase Three: Conceptual Design
Phase Four: Detailed Design
Phase Five: Implementation
Failures in Engineering Design
Uncertainty in Engineering
Definition of Reliability
Importance of Reliability
Reliability History
Reliability vs. Factor of Safety
Summary
References
Exercises
Fundamental Reliability Mathematics
Introduction
Experiment, Outcome, Sample Space, and Event
Set Theory
Definition of Probability
Relative Frequency
Axiomatic Definition
Some Basic Operations of Probability
Probability of Mutually Exclusive Events
Probability of an Event in a Finite Sample Space
Probability of Union and Intersection of Two Events
Probability of a Complementary Event
Probability of Statistically Independent Events
Conditional Probability
Total Probability Theorem
Bayes' Rule
Random Variable
Mean, Standard Deviation, and Coefficient of Variance
Histogram
Definition of a Histogram
Histogram by Excel and MATLAB
Probability Functions
Probability Functions of a Continuous Random Variable
Probability Functions of a Discrete Random Variable
Mean of a Random Variable
Standard Deviation and Coefficient of Variance
Some Typical Probability Distributions
Binomial Distribution
Poisson Distribution
Uniform Distribution
Normal Distribution (1/2)
Normal Distribution (2/2)
Log-Normal Distribution
Weibull Distribution
Exponential Distribution
Goodness-of-Fit Test: 2 Test
Introduction
The Chi-Square Test (1/2)
The Chi-Square Test (2/2)
The Chi-Square (2) Goodness-of-Fit Test by the Matlab Program
References
Exercises (1/3)
Exercises (2/3)
Exercises (3/3)
Computational Methods for the Reliability of a Component
Introduction
Limit State Function
Reliability of a Component with Two Random Variables
Interference Method
Computation of Reliability When Both are Normal Distributions
Computation of Reliability When Both are Log-normal Distributions
Computation of Reliability When Both are Exponential Distributions
Reliability Index
The First-Order Second-Moment (FOSM) Method
The FOSM Method for a Linear Limit State Function
The FOSM Method for a Nonlinear State Function
The Hasofer–Lind (H-L) Method (1/2)
The Hasofer–Lind (H-L) Method (2/2)
The Rackwitz and Fiessler (R-F) method (1/2)
The Rackwitz and Fiessler (R-F) method (2/2)
The Monte Carlo Method (1/2)
The Monte Carlo Method (2/2)
Summary
References
Exercises
Reliability of a Component under Static Load
Introduction
Geometric Dimension as a Random Variable
Static Loading as a Random Variable
Mechanical Properties of Materials as Random Variables
Estimation of Some Design Parameters (1/2)
Estimation of Some Design Parameters (2/2)
Reliability of a Rod under Axial Loading
Reliability of a Rod under Axial Loading for a Strength Issue
Reliability of a Rod under Axial Loading for a Deformation Issue (1/2)
Reliability of a Rod under Axial Loading for a Deformation Issue (2/2)
Reliability of a Component under Direct Shearing
Reliability of a Shaft under Torsion
Reliability of a Shaft under Torsion for a Strength Issue
Reliability of a Shaft under Torsion for a Deformation Issue
Reliability of a Beam under Bending Moment
Reliability of a Beam under Bending for a Strength Issue
Reliability of a Beam under Bending for a Deflection Issue
Reliability of a Component under Combined Stresses
Reliability of a Component of Ductile Material under Combined Stresses
Reliability of a Component of Brittle Material under Combined Stresses (1/2)
Reliability of a Component of Brittle Material under Combined Stresses (2/2)
Summary
References
Exercises
Samples of MATLAB®Programs
The H-L Method for Example 3.11
The R-F Method for Example 3.13
The Monte Carlo Method for Example 3.14
Author's Biography
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The Monte Carlo Method (2/2)
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References
3.8.
T
HE
MON
TE
CARLO
METHOD
155
End
F
igure
3.9:
e
flowchart
of
a
MA
TLAB
program
for
the
Monte
Car
lo
method.
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