probability statistics and reliability for engineers and scientists third editio

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4. https://gioumeh.com/product/probability-statistics-and-reliability-for-engineers-and-scientists-third-edition-solution-manual/https://gioumeh.com/product/probability-statistics-and-reliability-for-engineers-and-scientists-third-edition-solution-manual/ SOLUTIONS MANUAL FOR Probability, Statistics, and Reliability for Engineers and Scientists Third Edition by Bilal M. Ayyub Richard H. McCuen Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group, an informa business

5. https://gioumeh.com/product/probability-statistics-and-reliability-for-engineers-and-scientists-third-edition-solution-manual/https://gioumeh.com/product/probability-statistics-and-reliability-for-engineers-and-scientists-third-edition-solution-manual/ CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2011 by Taylor and Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Printed in the United States of America on acid-free paper 10 9 8 7 6 5 4 3 2 1 International Standard Book Number: 978-1-4398-7646-6 (Paperback) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com

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7. https://gioumeh.com/product/probability-statistics-and-reliability-for-engineers-and-scientists-third-edition-solution-manual/https://gioumeh.com/product/probability-statistics-and-reliability-for-engineers-and-scientists-third-edition-solution-manual/ ACKNOWLEDGEMENT The authors would like to acknowledge the undergraduate students who took the probability and statistics for civil engineering course during the fall semester of 2009 and the teaching assistant, Ms. Che-Yu Chang, for their help in preparing draft solutions of new problems created for the third edition of the textbook. ii

8. https://gioumeh.com/product/probability-statistics-and-reliability-for-engineers-and-scientists-third-edition-solution-manual/https://gioumeh.com/product/probability-statistics-and-reliability-for-engineers-and-scientists-third-edition-solution-manual/ TABLE OF CONTENTS CHAPTER 1. INTRODUCTION ................................................................................................... 1-1 1.2 to 1.5. Ignorance and Uncertainty ....................................................................................... 1-1 1.6. Introduction to Simulation ................................................................................................. 1-3 CHAPTER 2. DATA DESCRIPTION AND TREATMENT ........................................................ 2-1 2.2. Classification of Data ......................................................................................................... 2-1 2.3. Graphical Description of Data ........................................................................................... 2-2 2.4. Histograms and Frequency Diagrams .............................................................................. 2-15 2.6. Descriptive Measures ....................................................................................................... 2-24 CHAPTER 3. FUNDAMENTALS OF PROBABILITY ............................................................... 3-1 3.1. Introduction ........................................................................................................................ 3-1 3.2. Sample Space, Sets, and Events......................................................................................... 3-1 3.3. Mathematics of Probability ................................................................................................ 3-6 3.4./3.5. Random Variables and Their Probability Distributions/Moments ........................... 3-12 3.7. Simulation and Probability Distributions ........................................................................ 3-29 CHAPTER 4. PROBABILITY DISTRIBUTIONS FOR DISCRETE RANDOM VARIABLES .................................................................................................................................. 4-1 4.1. Introduction ........................................................................................................................ 4-1 4.2. to 4.7. All Distributions ..................................................................................................... 4-1 4.9. Simulation and Probability Distributions ........................................................................ 4-14 CHAPTER 5. PROBABILITY DISTRIBUTIONS FOR CONTINUOUS RANDOM VARIABLES .................................................................................................................................. 5-1 5.1. Introduction ........................................................................................................................ 5-1 5.2. Uniform Distributions ........................................................................................................ 5-1 5.3. Normal Distributions ......................................................................................................... 5-2 5.4. Lognormal Distributions .................................................................................................... 5-4 5.5. Exponential Distributions .................................................................................................. 5-6 5.6. Triangular Distributions ..................................................................................................... 5-7 5.8. Raleigh Distributions ......................................................................................................... 5-8 5.9. Statistical Probability Distributions ................................................................................. 5-10 5.10. Extreme Value Distributions ......................................................................................... 5-12 5.13. Simulation and Probability Distributions ...................................................................... 5-13 CHAPTER 6. MULTIPLE RANDOM VARIABLES ................................................................... 6-1 6.1. Introduction ........................................................................................................................ 6-1 6.2. Joint Random Variables and Their Probability Distributions ............................................ 6-1 6.3. Functions of Random Variables ........................................................................................ 6-8 6.5. Multivariable Simulation ................................................................................................. 6-14 CHAPTER 7. SIMULATION ........................................................................................................ 7-1 7.1. Introduction ........................................................................................................................ 7-1 7.2. Monte Carlo Simulation..................................................................................................... 7-1 7.3. Random Numbers .............................................................................................................. 7-1 7.4. Generation of Random Variables ...................................................................................... 7-4 7.5. Generation of Selected Discrete Random Variables .......................................................... 7-5 7.6. Generation of Selected Continuous Random Variables .................................................... 7-8 7.9. Simulation Projects .......................................................................................................... 7-11 CHAPTER 8. FUNDAMENTALS OF STATISTICAL ANALYSIS ........................................... 8-1 8.1. Introduction ........................................................................................................................ 8-1 iii

9. https://gioumeh.com/product/probability-statistics-and-reliability-for-engineers-and-scientists-third-edition-solution-manual/https://gioumeh.com/product/probability-statistics-and-reliability-for-engineers-and-scientists-third-edition-solution-manual/ 8.2. Estimation of Parameters ................................................................................................... 8-1 8.3. Method of Moments Estimation ........................................................................................ 8-3 8.4. Maximum Likelihood Estimation ...................................................................................... 8-8 8.5. Sampling Distributions ...................................................................................................... 8-8 CHAPTER 9. HYPOTHESIS TESTING ....................................................................................... 9-1 9.1. Introduction ........................................................................................................................ 9-1 9.2. General Procedure.............................................................................................................. 9-1 9.3. Hypothesis Tests of Means ................................................................................................ 9-3 9.4. Hypothesis Tests of Variances ......................................................................................... 9-12 9.5. Tests of Distributions ....................................................................................................... 9-15 9.7. Simulation of Hypothesis Test Assumptions ................................................................... 9-21 CHAPTER 10. ANALYSIS OF VARIANCE .............................................................................. 10-1 10.1. Introduction .................................................................................................................... 10-1 10.2. General Procedure.......................................................................................................... 10-1 10.3. Multiple Comparisons in the ANOVA Test .................................................................. 10-4 10.4. Test of Population Variances ....................................................................................... 10-10 10.5. Randomized Block Design .......................................................................................... 10-11 10.6. Two-Way Analysis of Variance .................................................................................. 10-12 CHAPTER 11. CONFIDENCE INTERVALS AND SAMPLE SIZE DETERMINATION ....... 11-1 11.1. Introduction .................................................................................................................... 11-1 11.2. General Procedure.......................................................................................................... 11-1 11.3. Confidence Intervals on Sample Statistics..................................................................... 11-2 11.4. Sample Size Determination ........................................................................................... 11-6 11.5. Relationship Between Decision Parameters and Types I and II Errors ......................... 11-8 CHAPTER 12. REGRESSION ANALYSIS ................................................................................ 12-1 12.1. Introduction .................................................................................................................... 12-1 12.2. Correlation Analysis ...................................................................................................... 12-1 12.3. Introduction to Regression ........................................................................................... 12-17 12.4. Principle of Least Squares ........................................................................................... 12-19 12.5. Reliability of the Regression Equation ........................................................................ 12-23 12.6. Reliability of Point Estimates of the Regression Coefficients ..................................... 12-27 12.7. Confidence Intervals of the Regression Equation........................................................ 12-30 12.8. Correlation Versus Regression .................................................................................... 12-32 12.9. Applications of Bivariate Regression Analysis ........................................................... 12-34 12.10. Simulation and Prediction Models ............................................................................. 12-36 CHAPTER 13. MULTIPLE AND NONLINEAR REGRESSION ANALYSIS ......................... 13-1 13.1. Introduction .................................................................................................................... 13-1 13.2. Correlation Analysis ...................................................................................................... 13-1 13.3. Multiple Regression Analysis ........................................................................................ 13-3 13.4 and 13.5. Regression Analysis of Polynomial and Power Models ............................... 13-15 CHAPTER 14. RELIABILITY ANALYSIS OF COMPONENTS ............................................. 14-1 14.1. Introduction .................................................................................................................... 14-1 14.2. Time to Failure............................................................................................................... 14-1 14.3. Reliability of Components ............................................................................................. 14-1 14.4. to 14.6. Reliability Assessments Methods (FORM, ASM, and Simulation) ................. 14-1 14.7. Reliability-Based Design ............................................................................................. 14-40 CHAPTER 15. RELIABILITY AND RISK ANALYSIS OF SYSTEMS ................................... 15-1 15.1. Reliability of Systems .................................................................................................... 15-1 15.2. and 15.3 Risk Analysis and Risk-Based Decision Analysis .......................................... 15-5 CHAPTER 16. BAYESIAN METHODS ..................................................................................... 16-1 iv

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11. https://gioumeh.com/product/probability-statistics-and-reliability-for-engineers-and-scientists-third-edition-solution-manual/https://gioumeh.com/product/probability-statistics-and-reliability-for-engineers-and-scientists-third-edition-solution-manual/ 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 1.1 and 1.5 1 to 3 1.6 4 to 14 1.2 to 1.5. Ignorance and Uncertainty Problem 1-1. The structural analysis of a reinforced concrete building is used herein to construct different levels of abstractions. It is common in this type of analysis to use a model to describe the structural behavior of the building due to various loads. The model can be viewed as an abstraction of some aspects of the building system. In performing this abstraction, an analyst or engineer must decide which aspects of the system to include and which to leave out. Figure 1-1 shows example abstractions with different types of uncertainty. Therefore depending on the state of knowledge about the system and the background of the analyst or engineer, other aspects of the system might not be known, thus increasing the overall uncertainty of the system. In these three categories, i.e., abstracted, non-abstracted, and unknown aspects of the system, several types of uncertainty can be present. Figure 1-1 provides examples of uncertainties within each category. Uncertainties in this building system are considered to be mainly attributed to ambiguity and vagueness in defining the parameters of the systems and their relations. The ambiguity component is generally due to non-cognitive sources, which include: (1) physical randomness; (2) statistical uncertainty due to the use of limited information to estimate the characteristics of these parameters; and (3) model uncertainties that are due to simplifying assumptions in analytical and prediction models, simplified methods, and idealized representations of real performances. The vagueness-related uncertainty is due to cognitive sources such as: (1) the definition of certain parameters, e.g., structural performance (failure or survival), quality, deterioration, skill and experience of construction workers and engineers, environmental impact of projects, conditions of existing structures; (2) other human factors; and (3) defining the inter-relationships among the parameters of the problems, especially for complex systems.

12. https://gioumeh.com/product/probability-statistics-and-reliability-for-engineers-and-scientists-third-edition-solution-manual/https://gioumeh.com/product/probability-statistics-and-reliability-for-engineers-and-scientists-third-edition-solution-manual/ Real System epistemological levels Abstraction at several A Model of the System Analyst or Engineer Abstracted aspects of system such as Non-abstracted aspects of system such as Unknown aspects of system such as Geometry, Material properties, Boundary and support conditions, Loading conditions, and load combination Fault-soil-structure interaction, some nonlinear aspects of structural response Soil properties, Faults, Extreme loads Construction errors Uncertainty Types Uncertainty Types Uncertainty Types Physical randomness Vaguely defined parameters and relations, Human and organizational errors, Conflict and confusion in information Physical randomness, Vaguely defined parameters and relations, Statistical uncertainty, Human and organizational errors Physical randomness, Lack of knowledge, Human and organizational errors Uncertainty types and their relations to real and abstracted systems Figure 1-1. Uncertainty types for a reinforced concrete building system Problem 1-2. Item Examples Aleatory uncertainty Sea wave elevation Soil shear strength Air quality Traffic volume at selected bridges Residential construction cost per SF Non-reducible * Epistemic uncertainty usually is present at the same time as aleatory uncertainty. Epistemic uncertainty* Occurrence rate of hurricanes in the Gulf of Mexico Sea-level rise in the next 100 years Losses due to flooding of a city Environmental impact of an oil spill Reduction Can be reduced by gathering data and constructing knowledge Problem 1-3. The solution to this problem can be presented in the following format: <Ignorance type> - <example> Conscious Ignorance – DNA provides the genetic make-up of living things, yet we are unable to completely decode its meaning. Inconsistency – analysis using a linear model yet true behavior is nonlinear. 1-2

13. https://gioumeh.com/product/probability-statistics-and-reliability-for-engineers-and-scientists-third-edition-solution-manual/https://gioumeh.com/product/probability-statistics-and-reliability-for-engineers-and-scientists-third-edition-solution-manual/ Confusion – in their attempt to develop explanations of previously unexplained phenomena, young graduate student often lack the understanding to clearly identify the problem. Inaccuracy – design equations often lend much insight into a physical problem, yet most often their results, though may be on the same order of magnitude, are inaccurate. Conflict – light is either particle or energy, but can never be both. Incompleteness – the theory of everything, the unified field theory rather, attempts to link all forces together into a single theory. Though much progress has been made in this field (so we believe), our ideas are still incomplete. Unknowns – solutions to all engineering problems exist, but often someone unknowns must be discovered first. Absence – generalized theories attempt to explain phenomena as applicable to a particular group. However, sometimes these theories do not seem to work for special individuals of that group though there are claims it should. Uncertainty – engineering students often turn in erroneous homework solutions, clearly indicating a lack of sureness of the homework topics. Approximations – most analysis techniques in structural analysis are approximate in nature since they are known not to be able to characterize all aspects of a structure’s behavior. Vagueness – researchers sometimes develop solutions to problems without completely understanding the true nature of the problem. Coarseness – in structural analysis, crude calculations are often made to validate highly complex numerical models. . If the order of magnitude is achieved, the model is assumed valid, yet the trie result may not be real. Simplifications – taking a nonlinear problem and simplifying it enough to justify using linear analysis. Likelihood – if a probability of an event occurring is less than one, the event is inherently uncertain. For example, scientists quote a probability that a given asteroid will hit the earth. Unless such a probability is zero or one, it is uncertain whether or not the event will occur. Since such an event has been unlikely, scientists often ignore these asteroids if their apparent path does not tend towards the earth. Randomness – analyzing structures whose material properties are random. A-basis values are used in analysis since the true value cannot be known without test. Sampling – an assessment on structural strength made by analyzing a small sample of concrete slabs may yield an average strength for the sample, but it is not indicative of the population of all similar concrete slabs. Ambiguity – the problem is not clear, so any proposed solution might not address all aspects of the problem. Blind ignorance – approving the design of a component based on design code standards without considering those failure modes that may not be included in the analysis techniques. Fallacy – pre-Galilean concepts that understood the earth to be the center of the universe (erroneous belief). Unknowable – The behavior of an n-dimensional creature and its way of life (cannot be ascertained by humans). Irrelevance – Some scientists once ignored the behavior and events of planets far distant from Earth, citing these events as irrelevant to the conditions in our solar system. Yet, it has been observed that though distance lessens any effect such an event has on our solar system, the effect is still felt (something believed not relevant so ignored). Untopicality – since the existence of fairy magic is deemed unlikely, researchers will ignore its existence when trying to explain natural phenomena. Undecidability – an approach to solving a problem may not follow the logic of current problem solving methodologies, and it is undecided whether or not the logical approach used is appropriate. Taboo – the supernatural abilities claimed by psychics are often discredited since they often contradict many common religious beliefs. 1.6. Introduction to Simulation Problem 1-4. die 1,1 1,2 1,3 1,4 1,5 1,6 sum 2 3 4 5 6 7 die 2,1 2,2 2,3 2,4 2,5 2,6 sum 3 4 5 6 7 8 die 3,1 3,2 3,3 3,4 3,5 3,6 sum 4 5 6 7 8 9 die 4,1 4,2 4,3 4,4 4,5 4,6 sum 5 6 7 8 9 10 die 5,1 5,2 5,3 5,4 5,5 5,6 sum 6 7 8 9 10 11 die 6,1 6,2 6,3 6,4 6,5 6,6 sum 7 8 9 10 11 12 1-3