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B-1 Appendix B Taylor Series Expansion Appendix B Taylor Series Expansion ……………………………………………………………………………….……1 Problem B-1. cos( ) !! …….xxx   124 24 For h = 0.1 x = x0 + h = 0 + 0.1 = 0.1 The following table […]

1-1 CHAPTER 1. INTRODUCTION CHAPTER 1. INTRODUCTION ………………………………………………………………………………………….1 1.2 to 1.5. Ignorance and Uncertainty …………………………………………………………………………….…..1 1.6. Introduction to Simulation ………………………………………………………………………………….……….3 The following table provides a summary of the problems with their appropriate sections: Section Problems 1.2 to 1.5. Ignorance and […]

10-1 CHAPTER 10. ANALYSIS OF VARIANCE CHAPTER 10. ANALYSIS OF VARIANCE …………………………………………………………………………1 10.1. Introduction ……………………………………………………………………………………………..……………..1 10.2. General Procedure ……………………………………………………………………………………………………1 10.3. Multiple Comparisons in the ANOVA Test …………………………………………………………………4 The following table provides a summary of the problems with their appropriate sections: […]

11-1 CHAPTER 11. CONFIDENCE INTERVALS AND SAMPLE SIZE DETERMINATION CHAPTER 11. CONFIDENCE INTERVALS AND SAMPLE SIZE DETERMINATION ………….1 11.1. Introduction ……………………………………………………………………………………………..……………..1 11.2. General Procedure ……………………………………………………………………………………………………1 The following table provides a summary of the problems with their appropriate sections: Section Problems […]

CHAPTER 12. REGRESSION ANALYSIS Chapter 12. Regression Analysis ………………………….……………………………………………………………….1 12.1. Introduction ……………………………………………………………………………………………..……………..1 12.2. Correlation Analysis …………………………………………………………………………………………………1 12.3. Introduction to Regression ………………………………………………………………………………………17 12.4. Principle of Least Squares ……………………………………………………………………………………….19 12.5. Reliability of the Regression Equation ………………………………………………………………………23 12.6. Reliability of Point Estimates of […]

12-20 a. Y=0.08046+0.97126X 6 8 10 Y Observed data Regression line b. Y=1.39080+0.07471X 0 2 4 6 0246810 X Y Regression line 8 10 Observed data General observations: xOne point that is an outlier can significantly change the model and […]

13-1 CHAPTER 13. MULTIPLE AND NONLINEAR REGRESSION ANALYSIS Chapter 13. Multiple and Nonlinear Regression Analysis ………………………………………………………..1 13.1. Introduction …………………………………………………………………………………………………………….1 13.2. Correlation Analysis …………………………………………………………………………………………………1 13.3. Multiple Regression Analysis…………………………………………………………………………………….3 13.4 and 13.5. Regression Analysis of Polynomial and Power Models ………………………………….15 The following […]

13-17 Slope 0.686053651 8 10 12 Y Predicted Y For the quadratic model, the following table will be used: X1 = X X2 = X2Y 0.8 0.64 2.8 1.6 2.56 4.9 3.1 9.61 6.5 4.4 19.36 8.1 6.3 39.69 8.8 […]

14-1 CHAPTER 14. RELIABILITY ANALYSIS OF COMPONENTS CHAPTER 14. RELIABILITY ANALYSIS OF COMPONENTS ……………………………………………1 14.1. Introduction …………………………………………………………………………………………………………….1 14.2. Time to Failure ………………………………………………………………………………………………………..1 14.3. Reliability of Components …………………………………………………………………………………………1 14.4. to 14.6. Reliability Assessments Methods (FORM, ASM, and Simulation) ……………………..1 14.7. Reliability-Based […]

14-21 Iteration Random variable Mean for equivalent normal Standard deviation for equivalent normal Partial derivative Directional cosine New design point H 3.84051404 0.453491803 -0.076865 -0.6837712 3.035248 Lognormal Distribution, fx Lognormal Cumulative, Fx )-1(Fx(x*)) Px N Vx N 0.18211672 0.037890514 -1.775707 […]

14-33 T=9 H=? L=1 Random variable Mean Value Mean for equivalent Normal Standard Deviation Standard Deviation of Equivalent Normal Coefficient of Variation Py H 3.15 3.08685171 0.4725 0.4698741 0.15 1.136277 L 1 0.80077681 0.1 0.0997513 0.1 -0.004975 T 9 Vy […]

15-1 CHAPTER 15. RELIABILITY AND RISK ANALYSIS OF SYSTEMS CHAPTER 15. RELIABILITY AND RISK ANALYSIS OF SYSTEMS ……….………………………….1 15.1. Reliability of Systems……………………………………………………………………………………..………..1 15.2. and 15.3 Risk Analysis and Risk-Based Decision Analysis …………………………………………..5 The following table provides a summary of the […]

16-1 CHAPTER 16. BAYESIAN METHODS CHAPTER 16. BAYESIAN METHODS …………………………….…………………………………………………1 16.1. Introduction ……………………………………………………………………………………………..……………..1 16.2. Bayesian Probabilities …………………………………………………………………………………….………..1 16.3. Bayesian Estimation of Parameters …………………………………………………………………………….8 16.4. Bayesian Statistics ……………………………………………………………………………………….…………..8 The following table provides a summary of the problems with their appropriate sections: […]

2-17 6 100-125 7 125-150 8 150-175 9 175-200 10 200-225 Problem 2-25. The data vary. In the first interval, the measured frequencies are more numerous than the simulated data; but in the later intervals, the simulated data have generally […]

2-1 CHAPTER 2. DATA DESCRIPTION AND TREATMENT CHAPTER 2. DATA DESCRIPTION AND TREATMENT ……………………………………………………1 2.2. Classification of Data …………………………………………………………………………………………………1 2.3. Graphical Description of Data ……………………………………………………………………………….…….2 2.4. Histograms and Frequency Diagrams …………………………………………………………………………15 2.6. Descriptive Measures ……………………………………………………………………………………….………24 The following table provides a […]

3-1 CHAPTER 3. FUNDAMENTALS OF PROBABILITY CHAPTER 3. FUNDAMENTALS OF PROBABILITY ………………………………………………………….1 3.1. Introduction ……………………………………………………………………………………………….……………..1 3.2. Sample Space, Sets, and Events ……………………………………………………………………………….….1 3.3. Mathematics of Probability …………………………………………………………………………………..…….6 3.4./3.5. Random Variables and Their Probability Distributions/Moments …………………………….12 3.7. Simulation and Probability Distributions […]

0 0.2 0.4 0123 x function value FX(x) 0.6 0.8 1 fX(x) Problem 3-41. To be legitimate pdf, (ܲሺെ൏ܺ൏൅ሻൌ׬݂௫ሺݔሻ݀ݔൌͳ ା ି ͳൌනʹ݁ି௞௫݀ݔൌ ା ଴ʹන݁ି௞௫݀ݔ ା ଴ න݁ ି௞௫݀ݔൌ ା ଴ͲǤͷൌቈ݁ି௞௫ െ݇ ቉ȁ଴  െͲǤͷ݇ൌ݁ିെ݁଴ൌͲെͳ ࢑ൌ૛ Density function: ݂௫ሺݔሻൌ൜ʹ݁ିଶ௫ǡͲ൑ݔ൑ Ͳǡ݋ݐ݄݁ݎݓ݅ݏ݁ Cumulative […]

4-1 CHAPTER 4. PROBABILITY DISTRIBUTIONS FOR DISCRETE RANDOM VARIABLES CHAPTER 4. PROBABILITY DISTRIBUTIONS FOR DISCRETE RANDOM VARIABLES ….1 4.1. Introduction ………………………………………………………………………………………………………………1 4.2. to 4.7. All Distributions ………………………………………………………………………………………………1 4.9. Simulation and Probability Distributions …………………………………………………………………….14 The following table provides a summary of […]

5-1 CHAPTER 5. PROBABILITY DISTRIBUTIONS FOR CONTINUOUS RANDOM VARIABLES CHAPTER 5. PROBABILITY DISTRIBUTIONS FOR CONTINUOUS RANDOM VARIABLES …………………………………………………………………………………………………………………….. 1 5.1. Introduction ………………………………………………………………………………………………………………1 5.2. Uniform Distributions ………………………………………………………………………………………………..1 5.3. Normal Distributions ………………………………………………………………………………………………….2 5.4. Lognormal Distributions ……………………………………………………………………………………..……..4 The following table provides a summary […]

6-1 CHAPTER 6. MULTIPLE RANDOM VARIABLES CHAPTER 6. MULTIPLE RANDOM VARIABLES ……………………………………………………………..1 6.1. Introduction ………………………………………………………………………………………………………………1 6.2. Joint Random Variables and Their Probability Distributions …………………………………………..1 6.3. Functions of Random Variables …………………………………………………………………………………..8 6.5. Multivariable Simulation …………………………………………………………………………………………..14 The following table provides a summary […]

7-1 CHAPTER 7. SIMULATION CHAPTER 7. SIMULATION …………………………………..………………………………………………………….1 7.1. Introduction ………………………………………………………………………………………………………………1 7.2. Monte Carlo Simulation ……………………………..………………………………………………………………1 7.3. Random Numbers ………………………………………………………………………………………………………1 7.4. Generation of Random Variables …………………………………………………………………………………4 7.5. Generation of Selected Discrete Random Variables ……………………………………………………….5 7.6. Generation of Selected Continuous Random […]

CHAPTER 8. FUNDAMENTALS OF STATISTICAL ANALYSIS CHAPTER 8. FUNDAMENTALS OF STATISTICAL ANALYSIS ………………………………………..1 8.1. Introduction ………………………………………………………………………………………………………………1 8.2. Estimation of Parameters …………………………………………………………………………………………….1 8.3. Method of Moments Estimation ………………………..…………………………………………………………3 8.4. Maximum Likelihood Estimation ……………………….……………………………………………………….8 8.5. Sampling Distributions ……………………………………………………………………………………..………..8 The following table provides […]

9.4. Hypothesis Tests of Variances Problem 9-39. X: n = 9; Y: n = 6 82.4%)5( 810.4 )030332.0( )06652.0( : 2 2 2 2 22 z atF S S F H critical y x yxA VV Therefore, the yields are […]

9-1 CHAPTER 9. HYPOTHESIS TESTING CHAPTER 9. HYPOTHESIS TESTING ……………………………………………………………………………….1 9.1. Introduction ………………………………………………………………………………………………………………1 9.2. General Procedure ……………………………………………………………………………………………………..1 9.3. Hypothesis Tests of Means ………………………………………………………………………………………….3 The following table provides a summary of the problems with their appropriate sections: Section Problems 9.1 9.2 […]