Multistate Analysis and Design

Download Multistate Analysis and Design PDF Online Free

Author :
Publisher :
ISBN 13 :
Total Pages : 230 pages
Book Rating : 4.:/5 (768 download)

DOWNLOAD NOW!


Book Synopsis Multistate Analysis and Design by : Jeremy Sundermeyer Agte

Download or read book Multistate Analysis and Design written by Jeremy Sundermeyer Agte and published by . This book was released on 2011 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: This research contributes to the field of aerospace engineering by proposing and demonstrating an integrated process for the early-stage, multistate design of aerospace systems. The process takes into early consideration the many partially degraded states that real-world systems experience throughout their operation. Despite advancing efforts aimed at maintaining operation in a state of optimum performance, most systems spend very substantial amounts of time operating in degraded or off-nominal states (e.g. Hubble space telescope, Mars Spirit rover, or aircraft flying under minimum-equipment-list restrictions). There exist relatively few methods and tools to address this at the beginning of the design process. At one end of the spectrum is design optimization, but this typically concentrates on the system in its nominal state of operation, only infrequently considering failure states through piecemeal application of constraints. There is reliability analysis, which focuses on component failure rates and the benefits of redundancy but does not consider how well or poorly the system performs with partial failures. Finally, there is controls theory, where control laws are optimized but the plant is typically assumed to be given a priori. The methodology described within this thesis coordinates elements from each of these three areas into an effective integrated framework. It allows the designer deeper insight into the complex problem of designing cost effective systems that must operate for long durations with little or expensive opportunity for repair or intervention. Specific contributions include: 1) the above methodology, which evaluates responses in system expected performance and availability to changes in static design variables (geometry) and component failure rates, accounting for control design variables (gains) where appropriate, 2) the demonstration of the cost and benefits associated with a multistate design approach as compared to reliability analysis and the nominal design approach, and 3) a multilayer extension of Markov analysis, for translating single sortie vehicle level metrics into measures of multistate campaign performance. The process is demonstrated through three application case studies. The first of these establishes the feasibility of the approach through the multistate analysis of performance for an existing twin-engine aircraft. This analysis was enabled through the development of a multidisciplinary simulation based design model for evaluation of multistate aircraft performance. A medium-altitude long endurance unmanned aerial vehicle is designed in the second case study, first from a single-sortie, ultra long endurance perspective and then from a multiple sortie, mission campaign perspective. Finally, the third case study demonstrates applicability of the approach to a lower level subsystem, that of the lubrication system for a geared turbofan engine. Several major findings result from these case studies, including that: 1) multistate performance output spaces have distinctly unique shapes and boundaries, depending on whether formed through variation of component failure rates, static design variables (geometry), or a multistate combination of both, 2) a region of multistate performance results from the combined variation of failure rates and static design variables that is unachievable through the independent variation of either one, 3) small changes in static design variables may be used to significantly improve system availability, and 4) the general multistate design problem is one of competing objectives between system availability, expected performance, nominal performance, and cost.

Fuzzy Multistate System Analysis and Design Using Imprecise Cusomer Information

Download Fuzzy Multistate System Analysis and Design Using Imprecise Cusomer Information PDF Online Free

Author :
Publisher :
ISBN 13 :
Total Pages : 378 pages
Book Rating : 4.:/5 (51 download)

DOWNLOAD NOW!


Book Synopsis Fuzzy Multistate System Analysis and Design Using Imprecise Cusomer Information by : Gopal P. Mohanty

Download or read book Fuzzy Multistate System Analysis and Design Using Imprecise Cusomer Information written by Gopal P. Mohanty and published by . This book was released on 2001 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Computational Protein Design

Download Computational Protein Design PDF Online Free

Author :
Publisher : Humana
ISBN 13 : 9781493966356
Total Pages : 0 pages
Book Rating : 4.9/5 (663 download)

DOWNLOAD NOW!


Book Synopsis Computational Protein Design by : Ilan Samish

Download or read book Computational Protein Design written by Ilan Samish and published by Humana. This book was released on 2016-12-03 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim this volume is to present the methods, challenges, software, and applications of this widespread and yet still evolving and maturing field. Computational Protein Design, the first book with this title, guides readers through computational protein design approaches, software and tailored solutions to specific case-study targets. Written in the highly successful Methods in Molecular Biology series format, chapters include introductions to their respective topics, step-by-step, readily reproducible laboratory protocols, and tips on troubleshooting and avoiding known pitfalls. Authoritative and cutting-edge, Computational Protein Design aims to ensure successful results in the further study of this vital field.

Multi-state System Reliability: Assessment, Optimization And Applications

Download Multi-state System Reliability: Assessment, Optimization And Applications PDF Online Free

Author :
Publisher : World Scientific Publishing Company
ISBN 13 : 981310614X
Total Pages : 375 pages
Book Rating : 4.8/5 (131 download)

DOWNLOAD NOW!


Book Synopsis Multi-state System Reliability: Assessment, Optimization And Applications by : Gregory Levitin

Download or read book Multi-state System Reliability: Assessment, Optimization And Applications written by Gregory Levitin and published by World Scientific Publishing Company. This book was released on 2003-03-12 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most books on reliability theory are devoted to traditional binary reliability models allowing for only two possible states for a system and its components: perfect functionality and complete failure. However, many real-world systems are composed of multi-state components, which have different performance levels and several failure modes with various effects on the entire system performance (degradation). Such systems are called Multi-State Systems (MSS). The examples of MSS are power systems where the component performance is characterized by the generating capacity, computer systems where the component performance is characterized by the data processing speed, communication systems, etc.This book is the first to be devoted to Multi-State System (MSS) reliability analysis and optimization. It provides a historical overview of the field, presents basic concepts of MSS, defines MSS reliability measures, and systematically describes the tools for MSS reliability assessment and optimization. Basic methods for MSS reliability assessment, such as a Boolean methods extension, basic random process methods (both Markov and semi-Markov) and universal generating function models, are systematically studied. A universal genetic algorithm optimization technique and all details of its application are described. All the methods are illustrated by numerical examples. The book also contains many examples of application of reliability assessment and optimization methods to real engineering problems.The aim of this book is to give a comprehensive, up-to-date presentation of MSS reliability theory based on modern advances in this field and provide a theoretical summary and examples of engineering applications to a variety of technical problems. From this point of view the book bridges the gap between theoretical advances and practical reliability engineering.

Multi-State Survival Models for Interval-Censored Data

Download Multi-State Survival Models for Interval-Censored Data PDF Online Free

Author :
Publisher : CRC Press
ISBN 13 : 1315356732
Total Pages : 323 pages
Book Rating : 4.3/5 (153 download)

DOWNLOAD NOW!


Book Synopsis Multi-State Survival Models for Interval-Censored Data by : Ardo van den Hout

Download or read book Multi-State Survival Models for Interval-Censored Data written by Ardo van den Hout and published by CRC Press. This book was released on 2016-11-25 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multi-State Survival Models for Interval-Censored Data introduces methods to describe stochastic processes that consist of transitions between states over time. It is targeted at researchers in medical statistics, epidemiology, demography, and social statistics. One of the applications in the book is a three-state process for dementia and survival in the older population. This process is described by an illness-death model with a dementia-free state, a dementia state, and a dead state. Statistical modelling of a multi-state process can investigate potential associations between the risk of moving to the next state and variables such as age, gender, or education. A model can also be used to predict the multi-state process. The methods are for longitudinal data subject to interval censoring. Depending on the definition of a state, it is possible that the time of the transition into a state is not observed exactly. However, when longitudinal data are available the transition time may be known to lie in the time interval defined by two successive observations. Such an interval-censored observation scheme can be taken into account in the statistical inference. Multi-state modelling is an elegant combination of statistical inference and the theory of stochastic processes. Multi-State Survival Models for Interval-Censored Data shows that the statistical modelling is versatile and allows for a wide range of applications.

Binary Decision Diagrams and Extensions for System Reliability Analysis

Download Binary Decision Diagrams and Extensions for System Reliability Analysis PDF Online Free

Author :
Publisher : John Wiley & Sons
ISBN 13 : 1119178002
Total Pages : 199 pages
Book Rating : 4.1/5 (191 download)

DOWNLOAD NOW!


Book Synopsis Binary Decision Diagrams and Extensions for System Reliability Analysis by : Liudong Xing

Download or read book Binary Decision Diagrams and Extensions for System Reliability Analysis written by Liudong Xing and published by John Wiley & Sons. This book was released on 2015-06-05 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent advances in science and technology have made modern computing and engineering systems more powerful and sophisticated than ever. The increasing complexity and scale imply that system reliability problems not only continue to be a challenge but also require more efficient models and solutions. This is the first book systematically covering the state-of-the-art binary decision diagrams and their extended models, which can provide efficient and exact solutions to reliability analysis of large and complex systems. The book provides both basic concepts and detailed algorithms for modelling and evaluating reliability of a wide range of complex systems, such as multi-state systems, phased-mission systems, fault-tolerant systems with imperfect fault coverage, systems with common-cause failures, systems with disjoint failures, and systems with functional dependent failures. These types of systems abound in safety-critical or mission-critical applications such as aerospace, circuits, power systems, medical systems, telecommunication systems, transmission systems, traffic light systems, data storage systems, and etc. The book provides both small-scale illustrative examples and large-scale benchmark examples to demonstrate broad applications and advantages of different decision diagrams based methods for complex system reliability analysis. Other measures including component importance and failure frequency are also covered. A rich set of references is cited in the book, providing helpful resources for readers to pursue further research and study of the topics. The target audience of the book is reliability and safety engineers or researchers. The book can serve as a textbook on system reliability analysis. It can also serve as a tutorial and reference book on decision diagrams, multi-state systems, phased-mission systems, and imperfect fault coverage models.

Multistate Models for the Analysis of Life History Data

Download Multistate Models for the Analysis of Life History Data PDF Online Free

Author :
Publisher : CRC Press
ISBN 13 : 1351646052
Total Pages : 524 pages
Book Rating : 4.3/5 (516 download)

DOWNLOAD NOW!


Book Synopsis Multistate Models for the Analysis of Life History Data by : Richard J Cook

Download or read book Multistate Models for the Analysis of Life History Data written by Richard J Cook and published by CRC Press. This book was released on 2018-05-15 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multistate Models for the Analysis of Life History Data provides the first comprehensive treatment of multistate modeling and analysis, including parametric, nonparametric and semiparametric methods applicable to many types of life history data. Special models such as illness-death, competing risks and progressive processes are considered, as well as more complex models. The book provides both theoretical development and illustrations of analysis based on data from randomized trials and observational cohort studies in health research. It features: Discusses a wide range of applications of multistate models, Presents methods for both continuously and intermittently observed life history processes, Gives a thorough discussion of conditionally independent censoring and observation processes, Discusses models with random effects and joint models for two or more multistate processes, Discusses and illustrates software for multistate analysis that is available in R, Target audience includes those engaged in research and applications involving multistate models.

Introducing Survival and Event History Analysis

Download Introducing Survival and Event History Analysis PDF Online Free

Author :
Publisher : SAGE
ISBN 13 : 1848601026
Total Pages : 301 pages
Book Rating : 4.8/5 (486 download)

DOWNLOAD NOW!


Book Synopsis Introducing Survival and Event History Analysis by : Melinda Mills

Download or read book Introducing Survival and Event History Analysis written by Melinda Mills and published by SAGE. This book was released on 2011-01-19 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an accessible, practical and comprehensive guide for researchers from multiple disciplines including biomedical, epidemiology, engineering and the social sciences. Written for accessibility, this book will appeal to students and researchers who want to understand the basics of survival and event history analysis and apply these methods without getting entangled in mathematical and theoretical technicalities. Inside, readers are offered a blueprint for their entire research project from data preparation to model selection and diagnostics. Engaging, easy to read, functional and packed with enlightening examples, ‘hands-on’ exercises, conversations with key scholars and resources for both students and instructors, this text allows researchers to quickly master advanced statistical techniques. It is written from the perspective of the ‘user’, making it suitable as both a self-learning tool and graduate-level textbook. Also included are up-to-date innovations in the field, including advancements in the assessment of model fit, unobserved heterogeneity, recurrent events and multilevel event history models. Practical instructions are also included for using the statistical programs of R, STATA and SPSS, enabling readers to replicate the examples described in the text.

RNA Nanotechnology

Download RNA Nanotechnology PDF Online Free

Author :
Publisher : CRC Press
ISBN 13 : 9814411647
Total Pages : 468 pages
Book Rating : 4.8/5 (144 download)

DOWNLOAD NOW!


Book Synopsis RNA Nanotechnology by : Bin Wang

Download or read book RNA Nanotechnology written by Bin Wang and published by CRC Press. This book was released on 2014-04-02 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the past few decades there has been incredible growth in "bionano"-related research, which has been accompanied by numerous publications in this field. Although various compilations address topics related to deoxyribonucleic acid (DNA) and protein, there are few books that focus on determining the structure of ribonucleic acid (RNA) and using RNA as building blocks to construct nanoarchitectures for biomedical and healthcare applications. RNA Nanotechnology is a comprehensive volume that details both the traditional approaches and the latest developments in the field of RNA-related technology. This book targets a wide audience: a broad introduction provides a solid academic background for students, researchers, and scientists who are unfamiliar with the subject, while the in-depth descriptions and discussions are useful for advanced professionals. The book opens with reviews on the basic aspects of RNA biology, computational approaches for predicting RNA structures, and traditional and emerging experimental approaches for probing RNA structures. This section is followed by explorations of the latest research and discoveries in RNA nanotechnology, including the design and construction of RNA-based nanostructures. The final segment of the book includes descriptions and discussions of the potential biological and therapeutic applications of small RNA molecules, such as small/short interfering RNAs (siRNAs), microRNAs (miRNAs), RNA aptamers, and ribozymes.

Nonparametric Models for Longitudinal Data

Download Nonparametric Models for Longitudinal Data PDF Online Free

Author :
Publisher : CRC Press
ISBN 13 : 0429939078
Total Pages : 512 pages
Book Rating : 4.4/5 (299 download)

DOWNLOAD NOW!


Book Synopsis Nonparametric Models for Longitudinal Data by : Colin O. Wu

Download or read book Nonparametric Models for Longitudinal Data written by Colin O. Wu and published by CRC Press. This book was released on 2018-05-23 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonparametric Models for Longitudinal Data with Implementations in R presents a comprehensive summary of major advances in nonparametric models and smoothing methods with longitudinal data. It covers methods, theories, and applications that are particularly useful for biomedical studies in the era of big data and precision medicine. It also provides flexible tools to describe the temporal trends, covariate effects and correlation structures of repeated measurements in longitudinal data. This book is intended for graduate students in statistics, data scientists and statisticians in biomedical sciences and public health. As experts in this area, the authors present extensive materials that are balanced between theoretical and practical topics. The statistical applications in real-life examples lead into meaningful interpretations and inferences. Features: • Provides an overview of parametric and semiparametric methods • Shows smoothing methods for unstructured nonparametric models • Covers structured nonparametric models with time-varying coefficients • Discusses nonparametric shared-parameter and mixed-effects models • Presents nonparametric models for conditional distributions and functionals • Illustrates implementations using R software packages • Includes datasets and code in the authors’ website • Contains asymptotic results and theoretical derivations

Handbook of Performability Engineering

Download Handbook of Performability Engineering PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 1848001312
Total Pages : 1331 pages
Book Rating : 4.8/5 (48 download)

DOWNLOAD NOW!


Book Synopsis Handbook of Performability Engineering by : Krishna B. Misra

Download or read book Handbook of Performability Engineering written by Krishna B. Misra and published by Springer Science & Business Media. This book was released on 2008-08-24 with total page 1331 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dependability and cost effectiveness are primarily seen as instruments for conducting international trade in the free market environment. These factors cannot be considered in isolation of each other. This handbook considers all aspects of performability engineering. The book provides a holistic view of the entire life cycle of activities of the product, along with the associated cost of environmental preservation at each stage, while maximizing the performance.

Models for Multi-State Survival Data

Download Models for Multi-State Survival Data PDF Online Free

Author :
Publisher : CRC Press
ISBN 13 : 0429642261
Total Pages : 293 pages
Book Rating : 4.4/5 (296 download)

DOWNLOAD NOW!


Book Synopsis Models for Multi-State Survival Data by : Per Kragh Andersen

Download or read book Models for Multi-State Survival Data written by Per Kragh Andersen and published by CRC Press. This book was released on 2023-10-11 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multi-state models provide a statistical framework for studying longitudinal data on subjects when focus is on the occurrence of events that the subjects may experience over time. They find application particularly in biostatistics, medicine, and public health. The book includes mathematical detail which can be skipped by readers more interested in the practical examples. It is aimed at biostatisticians and at readers with an interest in the topic having a more applied background, such as epidemiology. This book builds on several courses the authors have taught on the subject. Key Features: · Intensity-based and marginal models. · Survival data, competing risks, illness-death models, recurrent events. · Includes a full chapter on pseudo-values. · Intuitive introductions and mathematical details. · Practical examples of event history data. · Exercises. Software code in R and SAS and the data used in the book can be found on the book’s webpage.

Optimal Reliability Modeling

Download Optimal Reliability Modeling PDF Online Free

Author :
Publisher : John Wiley & Sons
ISBN 13 : 047127545X
Total Pages : 562 pages
Book Rating : 4.4/5 (712 download)

DOWNLOAD NOW!


Book Synopsis Optimal Reliability Modeling by : Way Kuo

Download or read book Optimal Reliability Modeling written by Way Kuo and published by John Wiley & Sons. This book was released on 2003-02-17 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: Promotes better ways to diagnose, maintain, and improve existing systems. Existing reliability evaluation models are examined with respect to today's complicated engineering systems that have hundreds of thousands of integrated component designs.

Regulation Versus Litigation

Download Regulation Versus Litigation PDF Online Free

Author :
Publisher : University of Chicago Press
ISBN 13 : 0226432181
Total Pages : 344 pages
Book Rating : 4.2/5 (264 download)

DOWNLOAD NOW!


Book Synopsis Regulation Versus Litigation by : Daniel P. Kessler

Download or read book Regulation Versus Litigation written by Daniel P. Kessler and published by University of Chicago Press. This book was released on 2011-02 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: The efficacy of various political institutions is the subject of intense debate between proponents of broad legislative standards enforced through litigation and those who prefer regulation by administrative agencies. This book explores the trade-offs between litigation and regulation, the circumstances in which one approach may outperform the other, and the principles that affect the choice between addressing particular economic activities with one system or the other. Combining theoretical analysis with empirical investigation in a range of industries, including public health, financial markets, medical care, and workplace safety, Regulation versus Litigation sheds light on the costs and benefits of two important instruments of economic policy.

Sensitivity Analysis: Matrix Methods in Demography and Ecology

Download Sensitivity Analysis: Matrix Methods in Demography and Ecology PDF Online Free

Author :
Publisher : Springer
ISBN 13 : 3030105342
Total Pages : 308 pages
Book Rating : 4.0/5 (31 download)

DOWNLOAD NOW!


Book Synopsis Sensitivity Analysis: Matrix Methods in Demography and Ecology by : Hal Caswell

Download or read book Sensitivity Analysis: Matrix Methods in Demography and Ecology written by Hal Caswell and published by Springer. This book was released on 2019-04-02 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book shows how to use sensitivity analysis in demography. It presents new methods for individuals, cohorts, and populations, with applications to humans, other animals, and plants. The analyses are based on matrix formulations of age-classified, stage-classified, and multistate population models. Methods are presented for linear and nonlinear, deterministic and stochastic, and time-invariant and time-varying cases. Readers will discover results on the sensitivity of statistics of longevity, life disparity, occupancy times, the net reproductive rate, and statistics of Markov chain models in demography. They will also see applications of sensitivity analysis to population growth rates, stable population structures, reproductive value, equilibria under immigration and nonlinearity, and population cycles. Individual stochasticity is a theme throughout, with a focus that goes beyond expected values to include variances in demographic outcomes. The calculations are easily and accurately implemented in matrix-oriented programming languages such as Matlab or R. Sensitivity analysis will help readers create models to predict the effect of future changes, to evaluate policy effects, and to identify possible evolutionary responses to the environment. Complete with many examples of the application, the book will be of interest to researchers and graduate students in human demography and population biology. The material will also appeal to those in mathematical biology and applied mathematics.

Spacecraft Reliability and Multi-State Failures

Download Spacecraft Reliability and Multi-State Failures PDF Online Free

Author :
Publisher : John Wiley & Sons
ISBN 13 : 1119970075
Total Pages : 201 pages
Book Rating : 4.1/5 (199 download)

DOWNLOAD NOW!


Book Synopsis Spacecraft Reliability and Multi-State Failures by : Joseph Homer Saleh

Download or read book Spacecraft Reliability and Multi-State Failures written by Joseph Homer Saleh and published by John Wiley & Sons. This book was released on 2011-04-22 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: SPACECRAFT RELIABILITY AND MULTI-STATE FAILURES ] SPACECRAFT RELIABILITY AND MULTI-STATE FAILURES A STATISTICAL APPROACH The aerospace community has long recognized and repeatedly emphasizes the importance of reliability for space systems. Despite this, little has been published in book form on the topic. Spacecraft Reliability and Multi-State Failures addresses this gap in the literature, offering a unique focus on spacecraft reliability based on extensive statistical analysis of system and subsystem anomalies and failures. The authors provide new results pertaining to spacecraft reliability based on extensive statistical analysis of on-orbit anomaly and failure data that will be particularly useful to spacecraft manufacturers and designers, for example in guiding satellite (and subsystem) test and screening programs and providing an empirical basis for subsystem redundancy and reliability growth plans. The authors develop nonparametric results and parametric models of spacecraft and spacecraft subsystem reliability and multi-state failures, quantify the relative contribution of each subsystem to the failure of the satellites thus identifying the subsystems that drive spacecraft unreliability, and propose advanced stochastic modeling and analysis tools for the reliability and survivability of spacecraft and space-based networks. Spacecraft Reliability and Multi-State Failures provides new nonparametric results pertaining to spacecraft reliability based on extensive statistical analysis of on-orbit anomaly and failure data develops parametric models of spacecraft and spacecraft subsystem reliability and multi-state failures quantifies the relative contribution of each subsystem to the failure of the satellites proposes advanced stochastic modeling and analysis tools for the reliability and survivability of spacecraft and space-based networks provides a dedicated treatment of the reliability and subsystem anomalies of communication spacecraft in geostationary orbit.

The Universal Generating Function in Reliability Analysis and Optimization

Download The Universal Generating Function in Reliability Analysis and Optimization PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 1846282454
Total Pages : 458 pages
Book Rating : 4.8/5 (462 download)

DOWNLOAD NOW!


Book Synopsis The Universal Generating Function in Reliability Analysis and Optimization by : Gregory Levitin

Download or read book The Universal Generating Function in Reliability Analysis and Optimization written by Gregory Levitin and published by Springer Science & Business Media. This book was released on 2006-02-04 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many real systems are composed of multi-state components with different performance levels and several failure modes. These affect the whole system's performance. Most books on reliability theory cover binary models that allow a system only to function perfectly or fail completely. "The Universal Generating Function in Reliability Analysis and Optimization" is the first book that gives a comprehensive description of the universal generating function technique and its applications in binary and multi-state system reliability analysis. Features: - an introduction to basic tools of multi-state system reliability and optimization; - applications of the universal generating function in widely used multi-state systems; - examples of the adaptation of the universal generating function to different systems in mechanical, industrial and software engineering. This monograph will be of value to anyone interested in system reliability, performance analysis and optimization in industrial, electrical and nuclear engineering.