Reliability Engineering

Transcription

1 Reliability Engineering

2 Alessandro Birolini Reliability Engineering Theory and Practice 8th Edition With 210 Figures, 60 Tables, 140 Examples, and 80 Problems for Homework

3 Prof. Dr. Alessandro Birolini * Centro Storico Bargello Firenze Tuscany, Italy birolini@emeritus.ethz.ch * Ingénieur et penseur, Ph.D., Professor Emeritus of Reliability Eng. at the Swiss Federal Institute of Technology (ETH), Zurich ISBN DOI / ISBN (ebook) Library of Congress Control Number: Springer-Verlag GmbH Deutschland 1994, 1997, 1999, 2004, 2007, 2010, 2014, 2017 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer-Verlag GmbH Germany The registered company address is: Heidelberger Platz 3, Berlin, Germany

4 "La chance vient à l'esprit qui est prêt à la recevoir." 1) Louis Pasteur "Quand on aperçoit combien la somme de nos ignorances dépasse celle de nos connaissances, on se sent peu porté à conclure trop vite." 2) Louis de Broglie "Prima di essere ingenieri voi siete uomini." 3) Francesco de Sanctis "One has to learn to consider causes rather than symptoms of undesirable events and avoid hypocritical attitudes." Alessandro Birolini "Freedom is to be fulfilled while respecting others." Alessandro Birolini "It is time to remember that humankind needs nature, but nature does not need humankind." Alessandro Birolini "It is time to recognize the necessity to extend the Declaration on the Right of Peoples to Peace to a Universal Declaration of People's Rights, and to move so toward a world wide Confederation of Democratic Republics." Alessandro Birolini 1) "Opportunity comes to the intellect which is ready to receive it." 2) "When one recognizes how much the sum of our ignorance exceeds that of our knowledge, one is less ready to draw rapid conclusions." 3) "Before being engineers you are men."

5 Preface to the 8 th Edition This book shows how to build in and assess reliability, availability, maintainability, and safety (RAMS) of components, equipment & systems. It presents the state-of-the-art of reliability (RAMS) engineering, in theory & practice, and is based on over 30 years author's experience in this field, half in industry and half as Professor of Reliability Engineering at the ETH, Zurich. The request for a Chinese translation of this book and the very high ebook requirements were the motivation for this final edition, the 13 th since 1985, including German editions [6.5] *. Extended and carefully reviewed to improve accuracy, it represents the continuous improvement effort to satisfy the reader's needs & confidence, and is more worthy now of appreciation's expressed in the book reviews mentioned on the book cover [1.17, 1.0]. It remains the author's aim, to concentrate research results in a book, to facilitate consultation and reduce publications flow. The launching of the 6 th English Edition was celebrated with a special Session at the 12 th Int. Conference on Quality and Dependability CCF 2010 held in Sinaia, Sept [1.0 (2010)]. The structure of the book has been maintained through all editions, with main Chapters 1 to 8 and Appendices A1 to A11 (A10 & A11 since the 5 th Edition 2007). Chapters 2, 4 & 6 (230 pp.) deal carefully with analytical investigations, Chapter 5 (25 pp.) with design guidelines, Chapters 3 and 7 (90 pp.) with tests, and Chapter 8 (15 pp.) with assurance activities during the production phase. Appendix A1 (15 pp.) defines and fully comments on the terms commonly used in reliability (RAMS) engineering. Appendices A2 - A5 (30 pp.) have been added to Chapter 1 (25 pp.) to support managers in answering the question of how to specify & achieve high reliability (RAMS) targets for complex equipment & systems. Appendices A6 - A8 (150 pp.) are a careful introduction to probability theory, stochastic processes, and mathematical statistics, as necessary for Chapters 2, 4, 6, and 7, consistent from a mathematical point of view but still with reliability engineering applications in mind (demonstration of established theorems is referred, and for all other propositions or equations, sufficient details for a complete demonstration are given). Appendices A9 - A11 (20 pp.) include statistical tables, Laplace transforms, probability charts, basic technological component's properties, and problems for homework. This book structure allows rapid access to practical results. Methods and tools are given in a way that they can be tailored to cover different reliability (RAMS) requirement levels, and be used for risk management analyses too. Thanks to Appendices A6 - A8 the book is mathematically self contained, and can be used as text book or as desktop reference with a large number of tables (60), figures (210), and examples / exercises (220, of which 80 as problems for homework). Writing and rewriting was necessary in some places, so as to improve readability and coherence. The book has grown from 420 to 650 pages (incl. References & Index), with important extensions, in particular, since the 4 th Edition (2004): 4 th Edition: Introduction to imperfect switching, incomplete coverage, fault tolerant reconfigurable systems (time & failure censoring), items with more than two states, Monte Carlo approach for rare events, nonhomogeneous Poisson processes with applications to reliability tests. 5 th Edition: Introduction to common cause failures, Petri nets, dynamic FTA, availability tests for continuous operation, trend tests, particular nonregenerative processes, homework problems. 6 th Edition: Proof of Eqs. (6.88) & (6.94), introduction to network reliability, event trees & binary decision diagrams, extension of maintenance strategies & incomplete coverage, conditions to have t1= A t2 in accelerated tests, refinements for complex systems & approx. expressions. 7 th Edition: Strategy to mitigate incomplete coverage, introduction to human reliability with design guidelines & new models, refinement of reliability allocation & design guidelines for maintainability, and writing relevant statements and rules italics and centered on the text.

6 VIII Preface New in this 8 th and final edition are, in particular : an introduction to risk management and to the concept of mean time to accident with structurally new models based on a novel subclass of semi-markov processes, introduced for investigations on human reliability in Section 6.10 of the 7 th Edition, and further refined (pp ); reliability & availability calculation of a k -out-of- n redundancy for n- k=2, constant failure & arbitrary repair rates, only one repair crew, and no further failures at system down (pp ); refinement of compound failure rate models for multiple failure mechanisms (pp , ); refinement of spare parts provisioning (pp ); refinement of necessary & sufficient conditions to have a regeneration point at the end of a repair, with respect to the state considered (pp. 386, , 353, 393, 522 & 526, footnote on p. 220); improved discussions / refinements on the: procedure for calculating MTTFS & PAS= AAS of large complex systems (pp ); models building / verification (pp. 102, 168, 220, , 252, , 363, 368, 406, 536); use of MTBF 1/l (pp. 6, 40, ), R ( t1, t2 ) for interval reliability (not for reliability, pp. 40, 179, 397), and l( x ) for nonrepairable & repairable items (as necessary for investigations on repairable systems, pp. 5, ), as well as comments to l( x), MTBF, MTTF (pp ); distinction between MTTRS and MDTS (footnote on p. 121, pp , 200, 217, 279, 394); distinction between MTBF, MTTF, MUT S (pp. 6, , 217, 279, , ); advantage of only one repair crew at system level (pp. 171 & 240, footnotes on pp. 386, 204, 121); influence of a repair priority (footnote on p. 220), and of a series element (footnote on p. 221); acceleration factor for assemblies, e. g. populated PCBs (p. 376); approximate expressions for imperfect switching & incomplete coverage (pp ); memoryless property (pp. 40, 179, ; p. 220 for repair priority, p. 138 for minimal repair); question catalogues for design reviews (pp. 79, 120, 423, 424); comments to a skillful, allegorical story of reliability (p. 406); removal of some minor shortcomings. Furthermore, considering that reliability, maintainability, safety, and software quality have to be built into complex equipment & systems, particular attention has been paid, since the first edition of this book, to the: selection of design guidelines for reliability, maintainability, and software quality (Chapter 5), as well as to practical aspects in a great number of examples, figures & tables, in Chapters 1, 3, 8 & Appendices A1 - A5, and in Chapters 2, 4, 6, 7 whenever dealing with const. failure & repair rates; investigation of causes limiting redundancy efficacy (like imperfect switching, incomplete coverage, common cause / mode failures, and multiple failure mechanisms); clear formulation and critical validation of models used, to identify their possibilities and limits, as well as elaboration of analytical solutions to allow trade off studies; specification of the item's (system's) state at t = 0, often tacitly assumed new or as-good-as-new in practical applications, which has great influence on its reliability and availability if the involved failure and / or repair rates are time dependent (to satisfy this necessity, reliability figures at system level have in this book indices Si, where S stands for system (the highest integration level of the item considered) and i for the state entered at t = 0, i = 0 for system new or as-good-as-new); development of powerful and practically oriented tools for the investigation of large series-parallel structures with constant failure & repair rates (macro structures), and of complex structures (key item, totally independent elements, models based on Markov or semi-regenerative processes); generalization of repair time distributions, and as far as possible of failure-free time distributions, step by step up to the case in which the process involved remains regenerative with a minimum number of regeneration states, to show capability and limits of models involved, evaluate the influence of distribution function shapes on final results, and provide approximate expressions useful for practical applications;

7 Preface IX central role of software quality assurance for complex equipment & systems, by considering that software problems are quality problems which have to be solved with quality assurance tools; prerequisites for accelerated tests, in particular in transferring an acceleration factor A from the MTTF to the (random) failure-free time t ; consequent use of failure-free time for failure-free operating time, MTBF for 1/l (at equipment & system level, as usual in practical applications), repair for restoration (by neglecting logistic & administrative delays), and interarrival times starting by x = 0 at each occurrence of the event considered (necessary when investigating repairable systems; in this context, the assumption asgood-as-new after repair is critically discussed wherever necessary, and the historical distinction between non-repairable and repairable items (systems) is scaled down); use of the memoryless property wherever possible to simplify calculations and considerations; however, taking care that it applies only with exponentially distributed random times, in particular thus only with constant failure and / or repair rates; use of independent for mutually, statistically, stochastically independent (as generally occurs in practical reliability applications), mean for expected value, and asymptotic & steady-state for stationary (by assuming irreducible embedded chains, for availability considerations); careful definition and comment on terms used in RAMS engineering (Appendix A1), as well as distinction between basically different quantities (e. g. between l( t) and f (), t z (), t h (), t m()). t The book were used for over 15 years at the ETH Zurich (for an introductory course at undergraduate level and for postgraduate courses), as well as for a large number of seminars in industry. Reliability (RAMS) engineering is a key for future reliable, safe, sustainable & long life products. It is thus to be regretted that at the author retirement, some "Colleagues" found it correct to transfer the Reliability Laboratory of the ETH to the EMPA. The few practitioners which consider this book too theoretically oriented, overlook the strong practically oriented Chapters 1, 3, 5, 8 & Appendices A1 - A5, as well as that investigations in Chapter 6 are necessary to assess factors affecting redundancy efficacy (e. g. incomplete coverage) & influence of repair time distribution function shapes on final results, and that Appendices A6 - A8 are useful to make the book mathematically self contained. Modeling is important in engineering sciences to investigate and predict item's behavior (e. g. in relation to performance, reliability & safety); oversimplified models should be avoided, and validation of model assumptions (physical & statistical aspects) should precede any data analysis (of course, approach for lifeless or living entities / systems is quite different). This final edition extends and replaces all previous editions. The agreeable cooperation with Springer-Verlag is gratefully acknowledged. Looking back to all editions (1 st German 1985 [6.5]), thanks are due, in particular, to K. P. LaSala for reviewing the 4 th & 6 th Editions [1.17], I. C. Bacivarov for reviewing the 6 th Edition [1.0], book reviewers of German editions, P. Franken & I. Kovalenko for commenting Appendices A6 - A8 (1990 & 1996), W. Luithardt for commenting Section 5.3 (2016), A. Bobbio, F. Bonzanigo & M. Held for supporting numerical evaluations, J. Thalhammer for the final edition of all figures, and L. Lambert for reading final manuscripts. On the front-page, four new sentences have been added to the three given since the 4 th Edition; these seven sentences, centered on generosity, modesty, ethics, responsibility, liberty, sustainability and people rights, should help, in particular young people, to make the world a better place (see also [1.2 (2010), 1.0 (2016)]). Zurich and Florence, September 13, 2017 Alessandro Birolini * For [...], see References at the end of the book.

8 Contents 1 Basic Concepts, Quality & Reliability (RAMS) Assurance of Complex Equip. & Systems Introduction Basic Concepts Reliability Failure Failure Rate, MTTF, MTBF Maintenance, Maintainability Logistic Support Availability Safety, Risk, Risk Acceptance Quality Cost and System Effectiveness Product Liability Historical Development Basic Tasks & Rules for Quality & Rel. (RAMS) Assurance of Complex Eq. & Systems Quality and Reliability (RAMS) Assurance Tasks Basic Quality and Reliability (RAMS) Assurance Rules Elements of a Quality Assurance System Motivation and Training Reliability Analysis During the Design Phase (Nonrepairable Elements up to System Failure) Introduction Predicted Reliability of Equipment and Systems with Simple Structure Required Function Reliability Block Diagram Operating Conditions at Component Level, Stress Factors Failure Rate of Electronic Components Reliability of One-Item Structures Reliability of Series-Parallel Structures with Independent Elements Systems without Redundancy (series models) Concept of Redundancy Parallel Models Series - Parallel Structures with Independent Elements Majority Redundancy Part Count Method Reliability of Systems with Complex Structure Key Item Method Bridge Structure Rel. Block Diagram in which Elements Appear More than Once Successful Path Method State Space Method Boolean Function Method Parallel Models with Constant Failure Rates and Load Sharing Elements with more than one Failure Mechanism or one Failure Mode Basic Considerations on Fault Tolerant Structures Reliability Allocation and Optimization

9 XII Contents 2.5 Mechanical Reliability, Drift Failures Failure Modes Analyses Reliability Aspects in Design Reviews Qualification Tests for Components and Assemblies Basic Selection Criteria for Electronic Components Environment Performance Parameters Technology Manufacturing Quality Long-Term Behavior of Performance Parameters Reliability Qualification Tests for Complex Electronic Components Electrical Test of Complex ICs Characterization of Complex ICs Environmental and Special Tests of Complex ICs Reliability Tests Failure Modes, Mechanisms, and Analysis of Electronic Components Failure Modes of Electronic Components Failure Mechanisms of Electronic Components Failure Analysis of Electronic Components Present VLSI Production-Related Reliability Problems Qualification Tests for Electronic Assemblies Maintainability Analysis Maintenance, Maintainability Maintenance Concept Equipment and Systems Partitioning Fault Detection (Recognition) and Localization User Documentation Training of Operation and Maintenance Personnel User Logistic Support Maintainability Aspects in Design Reviews Predicted Maintainability Calculation of MTTR S & MDT S Calculation of Mean Time to Preventive Maintenance Basic Models for Spare Parts Provisioning Centralized Logistic Support, Nonrepairable Spare Parts Decentralized Logistic Support, Nonrepairable Spare Parts Repairable Spare Parts Maintenance Strategies Complete renewal at each maintenance action Block replacement with minimal repair at failure Further considerations on maintenance strategies Basic Cost Considerations Design Guidelines for Reliability, Maintainability, and Software Quality Design Guidelines for Reliability Derating

10 Contents XIII Cooling Moisture Electromagnetic Compatibility, ESD Protection Components and Assemblies Component Selection Component Use PCB and Assembly Design PCB and Assembly Manufacturing Storage and Transportation Particular Guidelines for IC Design and Manufacturing Design Guidelines for Maintainability General Guidelines Testability Connections, Accessibility, Exchangeability Adjustment Human, Ergonomic, and Safety Aspects Design Guidelines for Software Quality Guidelines for Software Defect Prevention Configuration Management Guidelines for Software Testing Software Quality Growth Models Reliability and Availability of Repairable Systems Introduction, General Assumptions, Conclusions One-Item Structure One-Item Structure New at Time t = Reliability Function Point Availability Average Availability Interval Reliability Special Kinds of Availability One-Item Structure New at Time t = 0 and with Constant Failure Rate λ One-Item Structure with Arbitrary Conditions at t = Asymptotic Behavior Steady-State Behavior Systems without Redundancy Series Structure with Constant Failure and Repair Rates Series Structure with Constant Failure and Arbitrary Repair Rates Series Structure with Arbitrary Failure and Repair Rates out-of-2 Redundancy (Warm, one Repair Crew) out-of-2 Redundancy with Constant Failure and Repair Rates out-of-2 Redundancy with Constant Failure and Arbitrary Rep. Rates out-of-2 Red. with Const. Failure Rate in Reserve State & Arbitr. Rep. Rates k-out-of-n Redundancy (Warm, Identical Elements, one Repair Crew) k-out-of-n Redundancy with Constant Failure and Repair Rates k-out-of-n Redundancy with Constant Failure and Arbitrary Repair Rates Simple Series - Parallel Structures (one Repair Crew) Approximate Expressions for Large Series - Parallel Structures Introduction Application to a Practical Example

11 XIV Contents 6.8 Systems with Complex Structure (one Repair Crew) General Considerations Preventive Maintenance Imperfect Switching Incomplete Coverage Elements with more than two States or one Failure Mode Fault Tolerant Reconfigurable Systems Ideal Case Time Censored Reconfiguration (Phased-Mission Systems) Failure Censored Reconfiguration Reward and Frequency / Duration Aspects Systems with Common Cause Failures Basic Considerations on Network-Reliability General Procedure for Modeling Complex Systems Alternative Investigation Methods Systems with Totally Independent Elements Static and Dynamic Fault Trees Binary Decision Diagrams Event Trees Petri Nets Numerical Reliability and Availability Computation Numerical Computation of System's Reliability and Availability Monte Carlo Simulations Approximate expressions for Large, Complex Systems Human Reliability Risk Management for repairable Systems Introduction Risk Modeling, S ( t ), MTTFA Risk Avoidance and Risk Mitigation Statistical Quality Control and Reliability (RAMS) Tests Statistical Quality Control Estimation of a Defective Probability p Simple Two-sided Sampling Plans for Demonstration of a Def. Probability p Simple Two-sided Sampling Plan Sequential Test One-sided Sampling Plans for the Demonstration of a Def. Probability p Statistical Reliability (RAMS) Tests Reliability and Availability Estimation & Demon. for a given (fixed) Mission Availability Estimation & Demonstration for Continuous Operation (steady-state) Availability Estimation (Erlangian Failure-Free and/or Repair Times) Availability Demonstration (Erlangian Failure-Free and/or Repair Times) Further Availability Evaluation Methods for Continuous Operation Estimation and Demonstration of a Const. Failure Rate λ (or of MTBF 1/ λ ) Estimation of a Constant Failure Rate λ Simple Two-sided Test for the Demonstration of λ Simple One-sided Test for the Demonstration of λ Estimation and Demonstration of an MTTR Estimation of an MTTR Demonstration of an MTTR Accelerated Testing

12 Contents XV 7.5 Goodness-of-fit Tests Kolmogorov-Smirnov Test Chi-square Test Statistical Analysis of General Reliability Data General considerations Tests for Nonhomogeneous Poisson Processes Trend Tests Tests of a HPP versus a NHPP with increasing intensity Tests of a HPP versus a NHPP with decreasing intensity Heuristic Tests to distinguish between HPP and Monotonic Trend Reliability Growth Quality & Reliability Assurance During the Production Phase (Basic Considerations) Basic Activities Testing and Screening of Electronic Components Testing of Electronic Components Screening of Electronic Components Testing and Screening of Electronic Assemblies Test and Screening Strategies, Economic Aspects Basic Considerations Quality Cost Optimization at Incoming Inspection Level Procedure to handle first deliveries Appendices (A1 - A11) A1 Terms and Definitions A2 Quality and Reliability (RAMS) Standards, Story of Reliability Engineering A2.1 Introduction A2.2 General Requirements in the Industrial Field A2.3 Requirements in the Aerospace, Railway, Defense, and Nuclear Fields A2.4 A Skillful, Allegorical Story of Reliability A3 Definition and Realization of Quality & Reliability (RAMS) Requirements A3.1 Definition of Quality and Reliability (RAMS) Requirements A3.2 Realization of Quality & Reliability (RAMS) Requirements for Complex Eq. & Syst A3.3 Elements of a Quality and Reliability (RAMS) Assurance Program A3.3.1 Project Organization, Planning, and Scheduling A3.3.2 Quality and Reliability (RAMS) Requirements A3.3.3 Reliability, Maintainability, and Safety Analyses A3.3.4 Selection & Qualification of Components, Materials, Manuf. Processes A3.3.5 Software Quality Assurance A3.3.6 Configuration Management A3.3.7 Quality Tests A3.3.8 Quality Data Reporting System A4 Checklists for Design Reviews A4.1 System Design Review A4.2 Preliminary Design Reviews A4.3 Critical Design Review (System Level) A5 Requirements for a Quality Data Reporting System

13 XVI Contents A6 Basic Probability Theory A6.1 Field of Events A6.2 Concept of Probability A6.3 Conditional Probability, Independence A6.4 Fundamental Rules of Probability Theory A6.4.1 Addition Theorem for Mutually Exclusive Events A6.4.2 Multiplication Theorem for Two Independent Events A6.4.3 Multiplication Theorem for Arbitrary Events A6.4.4 Addition Theorem for Arbitrary Events A6.4.5 Theorem of Total Probability A6.5 Random Variables, Distribution Functions A6.6 Numerical Parameters of Random Variables A6.6.1 Expected Value (Mean) A6.6.2 Variance A6.6.3 Modal Value, Quantile, Median A6.7 Multidimensional Random Variables, Conditional Distributions A6.8 Numerical Parameters of Random Vectors A6.8.1 Covariance Matrix, Correlation Coefficient A6.8.2 Further Properties of Expected Value and Variance A6.9 Distribution of the Sum of Indep. Positive Random Variables and of τ min, τ max A6.10 Distribution Functions used in Reliability Analysis A Exponential Distribution A Weibull Distribution A Gamma Distribution, Erlangian Distribution, and χ 2 Distribution A Normal Distribution A Lognormal Distribution A Uniform Distribution A Binomial Distribution A Poisson Distribution A Geometric Distribution A Hypergeometric Distribution A6.11 Limit Theorems A Laws of Large Numbers A Central Limit Theorem A7 Basic Stochastic-Processes Theory A7.1 Introduction A7.2 Renewal Processes A7.2.1 Renewal Function, Renewal Density A7.2.2 Recurrence Times A7.2.3 Asymptotic Behavior A7.2.4 Stationary Renewal Processes A7.2.5 Homogeneous Poisson Processes (HPP) A7.3 Alternating Renewal Processes A7.4 Regenerative Processes with a Finite Number of States A7.5 Markov Processes with a Finite Number of States A7.5.1 Markov Chains with a Finite Number of States A7.5.2 Markov Processes with a Finite Number of States A7.5.3 State Probabilities and Stay Times in a Given Class of States A Method of Differential Equations A Method of Integral Equations A Stationary State and Asymptotic Behavior

14 Contents XVII A7.5.4 Frequency / Duration and Reward Aspects A Frequency / Duration A Reward A7.5.5 Birth and Death Process A7.6 Semi-Markov Processes with a Finite Number of States A7.7 Semi-regenerative Processes with a Finite Number of States A7.8 Nonregenerative Stochastic Processes with a Countable Number of States A7.8.1 General Considerations A7.8.2 Nonhomogeneous Poisson Processes (NHPP) A7.8.3 Superimposed Renewal Processes A7.8.4 Cumulative Processes A7.8.5 General Point Processes A8 Basic Mathematical Statistics A8.1 Empirical Methods A8.1.1 Empirical Distribution Function A8.1.2 Empirical Moments and Quantiles A8.1.3 Further Applications of the Empirical Distribution Function A8.2 Parameter Estimation A8.2.1 Point Estimation A8.2.2 Interval Estimation A Estimation of an Unknown Probability p A Estimation of Param. λ for Exp. Distrib.: Fixed T, instant. repl A Estimation of Param. λ for Exp. Distrib.: Fixed n, no repl A Availability Estimation (Erlangian Failure-Free and/or Repair Times) 561 A8.3 Testing Statistical Hypotheses A8.3.1 Testing an Unknown Probability p A Simple Two-sided Sampling Plan A Sequential Test A Simple One-sided Sampling Plan A Availability Demonstr. (Erlangian Failure-Free and/or Rep. Times) A8.3.2 Goodness-of-fit Tests for Completely Specified F 0( t ) A8.3.3 Goodness-of-fit Tests for F 0( t ) with Unknown Parameters A9 Tables and Charts A9.1 Standard Normal Distribution A9.2 χ 2 - Distribution (Chi-Square Distribution) A9.3 t - Distribution (Student distribution) A9.4 F - Distribution (Fisher distribution) A9.5 Table for the Kolmogorov-Smirnov Test A9.6 Gamma Function A9.7 Laplace Transform A9.8 Probability Charts (Probability Plot Papers) A9.8.1 Lognormal Probability Chart A9.8.2 Weibull Probability Chart A9.8.3 Normal Probability Chart A10 Basic Technological Component's Properties A11 Problems for Homework Acronyms References Index