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Solutions Manual for Reliability Engineering by Singiresu S. Rao 0136015727

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*** YOU ARE BUYING the Solution Manual for Reliability Engineering by Singiresu S. Rao 0136015727

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ISBN-10 ‏ : ‎ 9780136015727
ISBN-13 ‏ : ‎ 978-0136015727
Author: Rao

Reliability Engineering is intended for use as an introduction to reliability engineering, including the aspects analysis, design, testing, production and quality control of engineering components and systems.

Numerous analytical and numerical examples and problems are used to illustrate the principles and concepts. Expanded explanations of the fundamental concepts are given throughout the book, with emphasis on the physical significance of the ideas. The mathematical background necessary in the area of probability and statistics is covered briefly to make the presentation complete and self-contained. Solving probability and reliability problems using MATLAB and Excel is also presented.

Table of contents:

Chapter 1 Introduction
What You Will Learn
1.1 Uncertainty in Engineering
1.2 Definition of Reliability
1.3 Importance of Reliability
1.4 Pattern of Failures
1.4.1 Component Failures
Solution:
Solution:
1.4.2 Mechanical and Structural Failures
1.5 Factor of Safety and Reliability
1.6 Reliability Analysis Procedure
1.7 Reliability Management
1.8 History of Reliability Engineering
1.9 Some Examples of System Failures
1.9.1 Collapse of Tacoma Narrows Bridge in 1940
1.9.2 Crash of El Al Boeing 747-200 in 1992
1.9.3 Disaster of Space Shuttle Challenger in 1986
1.9.4 Chernobyl Nuclear Power Plant Accident in 1986
1.9.5 Mississippi River Bridge 9340 Collapse in 2007
1.9.6 Fukushima Nuclear Accident in 2011
1.9.7 Explosion of the First Jet Airplane Comet
1.9.8 Breaking of the Tanker S. S. Schenectady
1.9.9 Crash of the Supersonic Aircraft Concorde
1.10 Numerical Solutions Using MATLAB and Excel
Solution:
Solution:
1.11 Reliability Literature
References and Bibliography
Review Questions
Problems
Solutions using MATLAB and Excel
Chapter 2 Basic Probability Theory
What You Will Learn
2.1 Introduction
2.2 Mutually Exclusive Events
2.3 Set Theory
2.4 Sample Points and Sample Space
Solution:
Solution:
2.5 Definition of Probability
2.6 Laws of Probability
2.6.1 Union and Intersection of Two Events
2.6.2 Mutually Exclusive Events
Solution:
Solution:
Solution:
2.6.3 Complementary Events
Solution:
Solution:
Solution:
2.6.4 Conditional Probability
Solution:
2.6.5 Statistically Independent Events
2.6.6 General Laws
2.7 Total Probability Theorem
Solution:
Solution:
Solution:
Solution:
Solution:
2.8 Bayes’ Rule
Solution:
Solution:
References and Bibliography
Review Questions
Problems
Chapter 3 Random Variables and Probability Distributions
What You Will Learn
3.1 Introduction
3.2 Probability Mass Function for Discrete Random Variables
3.3 Cumulative Distribution Function for Discrete Random Variables
Solution:
Solution:
3.4 Probability Density Function for Continuous Random Variables
Solution:
Solution:
Solution:
3.5 Mean, Mode, and Median
3.5.1 Mean
Discrete Case.
Continuous Case.
Solution:
Solution:
3.5.2 Mode
Discrete Case.
Continuous Case.
3.5.3 Median
Discrete Case.
Continuous Case.
Solution:
3.6 Standard Deviation and Skewness Coefficient
3.6.1 Standard Deviation
Solution:
Solution:
Solution:
3.6.2 Skewness Coefficient
Solution:
3.7 Moments of Random Variables
3.8 Importance of Moment Functions—Chebyshev Inequality
Solution:
3.9 Jointly Distributed Random Variables
3.9.1 Joint Density and Distribution Functions
3.9.2 Obtaining the Marginal or Individual Density Function from the Joint Density Function
Solution:
3.10 Moments of Jointly Distributed Random Variables
3.11 Probability Distributions
3.11.1 Binomial Distribution
Solution:
Solution:
3.11.2 Poisson Distribution
Solution:
Solution:
3.11.3 Normal Distribution
Standard Normal Distribution.
Solution:
Solution:
3.11.3 Lognormal Distribution
Solution:
Solution:
3.12 Central Limit Theorem
3.13 Normal Approximation to Binomial Distribution
3.14 Numerical Solutions Using MATLAB and Excel
3.14.1 MATLAB Functions for Discrete and Continuous Probability Distributions
Solution:
Solution:
Solution:
Solution:
Solution:
3.14.2 Random Numbers, Fitting Data to Distributions and Confidence Intervals9
Solution:
Solution:
Solution:
3.14.3 Solutions using Excel
Solution:
Solution:
References and Bibliography
Review Questions
Problems
MATLAB and Excel Problems
Chapter 4 Extremal Distributions
What You Will Learn
4.1 Introduction
4.2 Extreme Value Distributions in Terms of Parent Distribution
4.3 Asymptotic Distributions
4.4 Type-I Asymptotic Distributions
4.4.1 Maximum Value
4.4.2 Smallest Value
4.5 Type-II Asymptotic Distributions
4.5.1 Maximum Value
4.5.2 Smallest Value
4.6 Type-III Asymptotic Distributions
4.6.1 Maximum Value
4.6.2 Smallest Value
4.7 Return Period
Solution:
4.8 Characteristic Value
4.9 Fitting Extremal Distributions to Experimental Data
4.9.1 Least-squares Fit
Solution:
4.10 Generalized Extreme Value Distribution
4.11 Numerical Solutions Using MATLAB and Excel
Solution:
Solution:
Solution:
Solution:
Solution:
References and Bibliography
Review Questions
Problems
MATLAB and Excel Problems
Chapter 5 Functions of Random Variables
What You Will Learn
5.1 Introduction
5.2 Functions of a Single Random Variable
Solution:
Solution:
Solution:
Solution:
5.3 Functions of Two Random Variables
5.3.1 Sum of Two Random Variables
Solution:
Solution:
5.3.2 Product of Two Random Variables
5.3.3 Quotient of Two Random Variables
Solution:
5.4 Function of Several Random Variables
5.5 Moments of a Function of Several Random Variables
5.5.1 Mean and Variance of a Linear Function
5.5.2 Mean and Variance of Sum of Two Random Variables
5.5.3 Mean and Variance of Product of Two Random Variables
5.5.4 Mean and Variance of Quotient of Two Random Variables
5.5.5 Mean and Variance of a General Nonlinear Function of Several Random Variables
Solution:
5.6 Moment-Generating Function
5.6.1 Moments of Normally Distributed Variables
Solution:
5.7 Functions of Several Random Variables
Solution:
5.8 Numerical Solutions Using MATLAB
Solution:
Solution:
References and Bibliography
Review Questions
Problems
MATLAB Problems
Chapter 6 Time-Dependent Reliability of Components and Systems
What You Will Learn
6.1 Introduction
6.2 Failure Rate versus Time Curve
6.3 Reliability and Hazard Functions
Solution:
6.4 Modeling of Failure Rates
6.5 Estimation of Failure Rate from Empirical Data
Solution:
6.6 Mean Time to Failure (MTTF)
Solution:
6.7 Reliability and Hazard Functions for Different Distributions
6.7.1 Exponential Distribution
Solution:
Solution:
6.7.2 Normal Distribution
Solution:
6.7.3 Lognormal Distribution
Solution:
Solution:
6.7.4 Weibull Distribution
Solution:
Solution:
Solution:
6.7.5 Gamma Distribution
6.7.6 Rayleigh Distribution
Solution:
6.7.7 Uniform Distribution
6.8 Expected Residual Life
Solution:
Solution:
6.9 Series Systems
6.9.1 Failure Rate of the System
6.9.2 MTBF of the System
Solution:
6.10 Parallel Systems
Solution:
6.10.1 Failure Rate of the System
6.10.2 MTBF of the System
6.11 (k, n) Systems
6.11.1 MTBF of the System
6.12 Mixed Series and Parallel Systems
6.13 Complex Systems
6.13.1 Enumeration Method
Solution:
6.13.2 Conditional Probability Method
Solution:
6.13.3 Cut-set Method
Solution:
6.14 Reliability Enhancement
6.14.1 Series System
With no constraint.
With constraint.
6.14.2 Parallel System
With no constraint.
With constraint.
6.15 Reliability Allocation—AGREE Method
Solution:
6.16 Numerical Solutions Using MATLAB and Excel
Solution:
Solution:
Solution:
References and Bibliography
Review Questions
Problems
MATLAB and Excel Problems
Chapter 7 Modeling of Geometry, Material Strength, and Loads
What You Will Learn
7.1 Introduction
7.2 Modeling of Geometry
7.2.1 Tolerances on Finished Metal Products
7.2.2 Assembly of Components
Solution:
Solution:
7.3 Modeling of Material Strength
7.3.1 Statistics of Elastic Properties
7.3.2 Statistical Models for Material Strength
7.3.3 Model for Brittle Materials
7.3.4 Model for Plastic Materials
7.3.5 Model for Fiber Bundles
7.4 Fatigue Strength
7.4.1 Constant-Amplitude Fatigue Strength
7.4.2 Variable-Amplitude Fatigue Strength
7.5 Modeling of Loads
7.5.1 Introduction
7.5.2 Dead Loads
7.5.3 Live Loads
Solution:
7.5.4 Wind Loads
Solution:
Solution:
Variation with Height.
Solution:
Determination of Wind Load.
7.5.5 Earthquake Loads
Response Spectrum.
Solution:
Earthquake Loads.
Power Spectrum of Ground Acceleration.
7.6 Numerical Solutions Using MATLAB and Excel
Solution:
Solution:
References and Bibliography
Review Questions
Problems
MATLAB and Excel Problems
Chapter 8 Strength-Based Reliability
What You Will Learn
8.1 Introduction
8.2 General Expression for Reliability
8.3 Expression for Probability of Failure
8.4 General Interpretation of Strength and Load
8.5 Reliability for Known Probability Distributions of S and L
8.5.1 Reliability When S and L Follow Normal Distribution
8.5.2 Approximate Expressions of Reliability for Normal Distribution
Solution:
Solution:
Solution:
8.5.3 Reliability When S and L Follow Lognormal Distribution
Solution:
8.5.4 Reliability When S and L Follow Exponential Distribution
Solution:
8.5.5 Reliability When S and L Follow Extreme Value Distributions
8.5.6 When S and L Follow Type-III Extremal Distributions
8.5.7 Reliability in Terms of Experimentally Determined Distributions of S and L
Solution:
8.6 Factor of Safety Corresponding to a Given Reliability
Solution:
8.7 Reliability of Systems Involving More Than Two Random Parameters
Solution:
Solution:
8.8 First-Order Second-Moment (FOSM) Method
Solution:
Solution:
8.9 Hasofer-Lind Reliability Index with Two Normally Distributed Variables
8.10 Hasofer-Lind Reliability Index with Several Normally Distributed Variables
8.11 Reliability of Weakest-Link and Fail-Safe Systems
8.11.1 Introduction
8.11.2 Reliability of the Fundamental Problem
Bounds on the Probability of Failure.
Solution:
8.11.3 Reliability of Weakest-Link (or Series) Systems4
Simple Bounds on the Probability of Failure.
Ditlevsen Bounds on the Probability of Failure.
Solution:
8.11.4 Reliability Analysis of Fail-Safe (or Parallel) Systems
Probability of Failure.
Bounds on the Probability of Failure.
8.12 Numerical Solutions Using MATALB and Excel
Solution:
Solution:
Solution:
Solution:
Solution:
Solution:
References and Bibliography
Review Questions
Problems
MATLAB and Excel Problems
Chapter 9 Design of Mechanical Components and Systems
What You Will Learn
9.1 Introduction
9.2 Design of Mechanical Components
Solution:
Solution:
Solution:
9.3 Fatigue Design
9.3.1 Deterministic Design Procedure
Solution:
9.3.2 Probabilistic Design Procedure
Solution:
Solution:
9.4 Design of Mechanical Systems
9.4.1 Reliability-Based Design of Gear Trains
Introduction.
Assumptions.
Design Equations.
Mean and Standard Deviations of Induced Stresses.
Probabilistic Model.
Design Procedure.
Numerical Results.
9.5 Reliability Analysis of Mechanical Systems
9.5.1 Cam-Follower Systems
Introduction.
Kinematic Response of the Cam-Follower System.
Mean and Standard Deviation of the Kinematic Response.
Numerical Results.
9.5.2 Four-Bar Mechanisms
Deterministic Analysis.
Probabilistic Analysis.
Numerical Results.
9.6 Numerical Solutions Using MATLAB and Excel
Solution:
Solution:
References and Bibliography
Review Questions
Problems
MATLAB and Excel Problems
Chapter 10 Monte Carlo Simulation
What You Will Learn
10.1 Introduction
10.2 Generation of Random Numbers
10.2.1 Generation of Random Numbers Following Standard Uniform Distribution
10.2.2 Random Variables with Nonuniform Distribution
Solution:
Solution:
Solution:
Solution:
Solution:
10.2.3 Generation of Discrete Random Variables
Solution:
Solution:
10.3 Generation of Jointly Distributed Random Numbers
10.3.1 Independent Random Variables
10.3.2 Dependent Random Variables
Solution:
10.3.3 Generation of Correlated Normal Random Variables
Solution:
10.4 Computation of Reliability
10.4.1 Sample Size and Error in Simulation
10.4.2 Example: Reliability Analysis of a Straight-Line Mechanism
10.5 Numerical Solutions Using MATLAB and Excel
Solution:
Solution:
References and Bibliography
Review Questions
Problems
MATLAB and Excel Problems
Chapter 11 Reliability-Based Optimum Design
What You Will Learn
11.1 Introduction
11.2 Optimization Problem
11.3 Formulation of Optimization Problems
11.3.1 Reliability Allocation Problems
Solution:
Solution:
Solution:
11.3.2 Structural and Mechanical Design Problems
Solution:
Solution:
11.4 Solution Techniques
11.4.1 Graphical-Optimization Method
Solution:
11.4.2 Lagrange Multiplier Method
Solution:
Solution:
11.4.3 Penalty Function Method (SUMT)
Unconstrained Minimization.
One-dimensional Minimization.
Solution:
Solution:
Deterministic Formulation.
Probabilistic Formulation.
11.4.4 Dynamic Programming
Solution:
11.5 Numerical Solutions Using MATLAB
Solution:
Solution:
Solution:
References and Bibliography
Review Questions
Problems
MATLAB Problems
Chapter 12 Failure Modes, Event-Tree, and Fault-Tree Analyses
What You Will Learn
12.1 Introduction
12.2 System-Safety Analysis
12.3 Failure Modes and Effects Analysis (FMEA)
12.4 Event-Tree Analysis
Solution:
Solution:
Solution:
12.5 Fault-Tree Analysis (FTA)
12.5.1 Concept
12.5.2 Procedure
Solution:
Solution:
Solution:
Solution:
12.6 Minimal Cut-Sets
Solution:
12.6.1 Probability of the TOP Event
Solution:
Solution:
References and Bibliography
Review Questions
Problems
Chapter 13 Reliability Testing
What You Will Learn
13.1 Introduction
13.1.1 Objectives of Reliability Tests
13.1.2 Details of a Reliability Test
13.2 Analysis of Failure Time
13.2.1 Analysis of Individual Failure Data
Solution:
13.2.2 Analysis of Grouped Failure Data
13.3 Accelerated Life Testing
13.3.1 Testing Until Partial Failure
13.3.2 Magnified Loading
13.3.3 Sudden-death Testing
Solution:
13.4 Sequential Life Testing
13.5 Statistical Inference and Parameter Estimation
13.5.1 Maximum-likelihood Method
Solution:
Solution:
13.6 Confidence Intervals
13.6.1 Confidence Interval on the Mean of a Normal Random Variable of Known Standard Deviation
Solution:
13.6.2 Confidence Interval on the Mean of a Normal Random Variable of Unknown Standard Deviation
Solution:
13.6.3 Confidence Interval on the Standard Deviation of a Normal Random Variable with Unknown Mean
Solution:
13.7 Plotting of Reliability Data
13.7.1 Least-Squares Technique
13.7.2 Linear Rectification
13.7.3 Plotting Positions
13.7.4 Exponential Distribution
Solution:
13.7.5 Normal Distribution
Solution:
13.7.6 Lognormal Distribution
13.7.7 Weibull Distribution
Solution:
13.8 Numerical Solutions Using MATLAB
13.8.1 Parameter Estimation and Confidence Intervals
Solution:
Solution:
Solution:
13.8.2 Plotting of Data
Solution:
Solution:
References and Bibliography
Review Questions
Problems
MATLAB Problems
Chapter 14 Quality Control and Reliability
What You Will Learn
14.1 Introduction
14.2 Importance of Controlling Dimensions of Products
Solution:
Solution:
14.3 Important Discrete Probability Distributions
14.3.1 Binomial Distribution
Solution:
14.3.2 Hypergeometric Distribution
Solution:
Solution:
14.3.3 Poisson Distribution
Solution:
14.3.4 Relationship Between Poisson and Exponential Distributions
14.4 Six Sigma Approach and Reliability
Solution:
Solution:
Solution:
14.5 Acceptance Sampling
14.6 Process Capability
Solution:
Solution:
14.7 Quality Control Charts
14.7.1 The p-Chart
Solution:
14.7.2 The X ¯ -Chart
Solution:
14.7.3 The R-Chart
Solution:
14.7.4 The c-Chart
Solution:
14.8 Risks
14.9 Operating Characteristic (OC) Curve
14.9.1 OC Curve
14.9.2 Construction of OC Curve
Solution:
14.9.3 Designing a Single Sampling Plan with a Specified OC Curve
14.10 Taguchi Method
14.10.1 Basic Concept
14.10.2 Loss Function
Solution:
14.10.3 Noise Factors
14.10.4 On-Line Versus Off-Line Quality Control
14.10.5 Three-Step Design Approach
Concept Design.
Parameter Design.
Tolerance Design.
14.10.6 Experimental Design
Orthogonal Arrays.
Solution:
14.10.7 Signal-To-Noise Ratio
14.10.8 Experimental Design in the Presence of Noise Factors
Solution:
14.11 Numerical Solutions Using MATLAB
Solution:
References and Bibliography
Review Questions
Problems
MATLAB Problem
Chapter 15 Maintainability and Availability
What You Will Learn
15.1 Introduction
15.2 Maintainability
15.2.1 Overview
15.2.2 Preventive Maintenance
Solution:
Without Repair.
With Repair.
Solution:
Solution:
15.2.3 Imperfect Maintenance
Solution:
15.2.4 Repair-time Distributions
When Time to Repair Follows Exponential Distribution.
When Time to Repair Follows Lognormal Distribution.
Solution:
Solution:
Solution:
15.2.5 Unrepaired Failures
Solution:
15.2.6 Optimal Replacement Strategy
15.2.7 Spare Parts Requirement
Solution:
15.3 Availability
15.3.1 Definitions [15.1, 15.3]
15.3.2 Availability Analysis
15.3.3 Development of the Model
15.3.4 Systems with a Single Component
Solution:
15.3.5 Series Systems
One Repair Person.
Two Repair Persons.
15.3.6 Parallel Systems
One Repair Person.
Two Repair Persons.
15.4 Optimization Approaches
15.5 Numerical Solutions Using MATLAB and Excel
Solution:
Solution:
References and Bibliography
Review Questions
Problems
MATLAB and Excel Problems
Chapter 16 Warranties
What You Will Learn
16.1 Introduction
16.2 Types of Warranties
16.3 Warranty Costs Based on a Single Failure During the Warranty Period
16.3.1 Free Replacement Warranty
Solution:
16.3.2 Pro-rata Warranty
Solution:
16.3.3 Combined Free Replacement Warranty and Pro-rata Warranty (FRW/PRW) Policy
Solution:
16.3.4 FRW Policy Equivalent to a FRW/PRW Policy
Solution:
16.3.5 Lump-sum Payment Type of Warranty
Solution:
16.4 Warranty Costs Considering the Time Value of Money
16.4.1 FRW Policy
Solution:
16.4.2 PRW Policy
Solution:
16.5 Warranty Reserve Fund Considering the Time Value of Money and Future Changes in the Price of the Product
Solution:
16.6 Warranty Analysis Considering Multiple Failures During the Warranty Period
16.6.1 Renewal Process
16.6.2 Computation and Use of Renewal Functions
16.7 Optimum Warranty Period
16.8 Two-dimensional Warranties
16.9 Numerical Solutions Using MATLAB
Solution:
Solution:
References and Bibliography
Review Questions
Problems
MATLAB Problems
Appendix A Standard Normal Distribution Function
Appendix B Values of tα, n for Specific Values of α and n of t-Distribution
Appendix C Values of χ2n, α Corresponding to Specific Values of α and n of χ2-Distribution
Appendix D Product Liability
D.1 Basic Concept
D.2 Definitions
D.3 Theories of Product Liability
D.4 Prevention of Product Liability
Guidelines to Prevent Design Defects
Guidelines to Prevent Manufacturing Defects
References and Bibliography
Answers to Selected Problems