1 Reliability: Past, Present, Future.- 2 Reliability Analysis as a Tool for Expressing and Communicating Uncertainty.- 3 Modeling a Process of Non-Ideal Repair.- 4 Some Models and Mathematical Results for Reliability of Systems of Components.- 5 Algorithms of Stochastic Activity and Problems of Reliability.- 6 Some Shifted Stochastic Orders.- 7 Characterization of Distributions in Reliability.- 8 Asymptotic Analysis of Reliability for Switching Systems in Light and Heavy Traffic Conditions.- 9 Nonlinearly Perturbed Markov Chains and Large Deviations for Lifetime Functionals.- 10 Evolutionary Systems in an Asymptotic Split Phase Space.- 11 An Asymptotic Approach to Multistate Systems Reliability Evaluation.- 12 Computer Intensive Methods Based on Resampling in Analysis of Reliability and Survival Data.- 13 Statistical Analysis of Damage Processes.- 14 Data Analysis Based on Warranty Database.- 15 Failure Models Indexed by Time and Usage.- 16 A New Multiple Proof Loads Approach For Estimating Correlations.- 17 Conditional and Partial Correlation For Graphical Uncertainty Models.- 18 Semiparametric Methods of Time Scale Selection.- 19 Censored and Truncated Lifetime Data.- 20 Tests for a Family of Survival Models Based on Extremes.- 21 Software Reliability Models - Past, Present and Future.- 22 Dynamic Analysis of Failures in Repairable Systems and Software.- 23 Precedence Test and Maximal Precedence Test.- 24 Hierarchical Bayesian Inference in Related Reliability Experiments.- 25 Tests for Equality of Intensities of Failures of a Repairable System Under Two Competing Risks.- 26 Semiparametric Estimation in Accelerated Life Testing.- 27 A Theoretical Framework for Accelerated Testing.- 28 Unbiased Estimation in Reliability and Similar Problems.- 29 Prediction Under Association.- 30 Uniform Limit Laws for Kernel Density Estimators on Possibly Unbounded Intervals.- 31 A Weak Convergence Result Relevant in Recurrent and Renewal Models.

At first there was the Markov property. The theory of stochastic processes, which can be considered as an exten­ sion of probability theory, allows the modeling of the evolution of systems through the time. It cannot be properly understood just as pure mathemat­ ics, separated from the body of experience and examples that have brought it to life. The theory of stochastic processes entered a period of intensive develop­ ment, which is not finished yet, when the idea of the Markov property was brought in. Not even a serious study of the renewal processes is possible without using the strong tool of Markov processes. The modern theory of Markov processes has its origins in the studies by A. A: Markov (1856-1922) of sequences of experiments "connected in a chain" and in the attempts to describe mathematically the physical phenomenon known as Brownian mo­ tion. Later, many generalizations (in fact all kinds of weakenings of the Markov property) of Markov type stochastic processes were proposed. Some of them have led to new classes of stochastic processes and useful applications. Let us mention some of them: systems with complete connections [90, 91, 45, 86]; K-dependent Markov processes [44]; semi-Markov processes, and so forth. The semi-Markov processes generalize the renewal processes as well as the Markov jump processes and have numerous applications, especially in relia­ bility.

At first there was the Markov property. The theory of stochastic processes, which can be considered as an exten­ sion of probability theory, allows the modeling of the evolution of systems through the time. It cannot be properly understood just as pure mathemat­ ics, separated from the body of experience and examples that have brought it to life. The theory of stochastic processes entered a period of intensive develop­ ment, which is not finished yet, when the idea of the Markov property was brought in. Not even a serious study of the renewal processes is possible without using the strong tool of Markov processes. The modern theory of Markov processes has its origins in the studies by A. A: Markov (1856-1922) of sequences of experiments "connected in a chain" and in the attempts to describe mathematically the physical phenomenon known as Brownian mo­ tion. Later, many generalizations (in fact all kinds of weakenings of the Markov property) of Markov type stochastic processes were proposed. Some of them have led to new classes of stochastic processes and useful applications. Let us mention some of them: systems with complete connections [90, 91, 45, 86]; K-dependent Markov processes [44]; semi-Markov processes, and so forth. The semi-Markov processes generalize the renewal processes as well as the Markov jump processes and have numerous applications, especially in relia­ bility.

Conceiving reliablesystems is a strategic issue for any industrial society. Hence, reliability has become a discipline at the beginning of the Second World War. In fact, reliability is a field of reseach common to mathematics, operational research, informatics, graph theory, physics, and so forth. We are concerned here with the mathematical side of reliability, of which probability, statistics, and more specially stochastic processes theory constitute the natural basis. US army during the war, and later in the US Problems encountered by the and Soviet space programs, have led to an awarenessofthe need for reliabilityor more generaly for dependability (a general term covering reliability, availability, security, maintainability, etc.) of the systems. The paper by W. Weibull of 1938 on the strength of materials, leading to the distribution that later took his name, and the paper by B. Epstein and M. Sobel of 1951, initiating the use of the exponential distribution as the basic (and now most used) model for reliability, are the founding papers of the field. At this time, the systems were merely seen as black boxes. During the 1960s, they began to be considered as the result of the interaction of their elements. Appropriate methods were then developed, from Shannon''s work to the beautiful theory of coherent systems initiated by Z.W. Birnbaum, J.D.

At first there was the Markov property. The theory of stochastic processes, which can be considered as an exten­ sion of probability theory, allows the modeling of the evolution of systems through the time. It cannot be properly understood just as pure mathemat­ ics, separated from the body of experience and examples that have brought it to life. The theory of stochastic processes entered a period of intensive develop­ ment, which is not finished yet, when the idea of the Markov property was brought in. Not even a serious study of the renewal processes is possible without using the strong tool of Markov processes. The modern theory of Markov processes has its origins in the studies by A. A: Markov (1856-1922) of sequences of experiments "connected in a chain" and in the attempts to describe mathematically the physical phenomenon known as Brownian mo­ tion. Later, many generalizations (in fact all kinds of weakenings of the Markov property) of Markov type stochastic processes were proposed. Some of them have led to new classes of stochastic processes and useful applications. Let us mention some of them: systems with complete connections [90, 91, 45, 86]; K-dependent Markov processes [44]; semi-Markov processes, and so forth. The semi-Markov processes generalize the renewal processes as well as the Markov jump processes and have numerous applications, especially in relia­ bility.

1 Reliability: Past, Present, Future.- 2 Reliability Analysis as a Tool for Expressing and Communicating Uncertainty.- 3 Modeling a Process of Non-Ideal Repair.- 4 Some Models and Mathematical Results for Reliability of Systems of Components.- 5 Algorithms of Stochastic Activity and Problems of Reliability.- 6 Some Shifted Stochastic Orders.- 7 Characterization of Distributions in Reliability.- 8 Asymptotic Analysis of Reliability for Switching Systems in Light and Heavy Traffic Conditions.- 9 Nonlinearly Perturbed Markov Chains and Large Deviations for Lifetime Functionals.- 10 Evolutionary Systems in an Asymptotic Split Phase Space.- 11 An Asymptotic Approach to Multistate Systems Reliability Evaluation.- 12 Computer Intensive Methods Based on Resampling in Analysis of Reliability and Survival Data.- 13 Statistical Analysis of Damage Processes.- 14 Data Analysis Based on Warranty Database.- 15 Failure Models Indexed by Time and Usage.- 16 A New Multiple Proof Loads Approach For Estimating Correlations.- 17 Conditional and Partial Correlation For Graphical Uncertainty Models.- 18 Semiparametric Methods of Time Scale Selection.- 19 Censored and Truncated Lifetime Data.- 20 Tests for a Family of Survival Models Based on Extremes.- 21 Software Reliability Models - Past, Present and Future.- 22 Dynamic Analysis of Failures in Repairable Systems and Software.- 23 Precedence Test and Maximal Precedence Test.- 24 Hierarchical Bayesian Inference in Related Reliability Experiments.- 25 Tests for Equality of Intensities of Failures of a Repairable System Under Two Competing Risks.- 26 Semiparametric Estimation in Accelerated Life Testing.- 27 A Theoretical Framework for Accelerated Testing.- 28 Unbiased Estimation in Reliability and Similar Problems.- 29 Prediction Under Association.- 30 Uniform Limit Laws for Kernel Density Estimators on Possibly Unbounded Intervals.- 31 A Weak Convergence Result Relevant in Recurrent and Renewal Models.

At first there was the Markov property. The theory of stochastic processes, which can be considered as an exten­ sion of probability theory, allows the modeling of the evolution of systems through the time. It cannot be properly understood just as pure mathemat­ ics, separated from the body of experience and examples that have brought it to life. The theory of stochastic processes entered a period of intensive develop­ ment, which is not finished yet, when the idea of the Markov property was brought in. Not even a serious study of the renewal processes is possible without using the strong tool of Markov processes. The modern theory of Markov processes has its origins in the studies by A. A: Markov (1856-1922) of sequences of experiments "connected in a chain" and in the attempts to describe mathematically the physical phenomenon known as Brownian mo­ tion. Later, many generalizations (in fact all kinds of weakenings of the Markov property) of Markov type stochastic processes were proposed. Some of them have led to new classes of stochastic processes and useful applications. Let us mention some of them: systems with complete connections [90, 91, 45, 86]; K-dependent Markov processes [44]; semi-Markov processes, and so forth. The semi-Markov processes generalize the renewal processes as well as the Markov jump processes and have numerous applications, especially in relia­ bility.

At first there was the Markov property. The theory of stochastic processes, which can be considered as an exten­ sion of probability theory, allows the modeling of the evolution of systems through the time. It cannot be properly understood just as pure mathemat­ ics, separated from the body of experience and examples that have brought it to life. The theory of stochastic processes entered a period of intensive develop­ ment, which is not finished yet, when the idea of the Markov property was brought in. Not even a serious study of the renewal processes is possible without using the strong tool of Markov processes. The modern theory of Markov processes has its origins in the studies by A. A: Markov (1856-1922) of sequences of experiments "connected in a chain" and in the attempts to describe mathematically the physical phenomenon known as Brownian mo­ tion. Later, many generalizations (in fact all kinds of weakenings of the Markov property) of Markov type stochastic processes were proposed. Some of them have led to new classes of stochastic processes and useful applications. Let us mention some of them: systems with complete connections [90, 91, 45, 86]; K-dependent Markov processes [44]; semi-Markov processes, and so forth. The semi-Markov processes generalize the renewal processes as well as the Markov jump processes and have numerous applications, especially in relia­ bility.

Conceiving reliablesystems is a strategic issue for any industrial society. Hence, reliability has become a discipline at the beginning of the Second World War. In fact, reliability is a field of reseach common to mathematics, operational research, informatics, graph theory, physics, and so forth. We are concerned here with the mathematical side of reliability, of which probability, statistics, and more specially stochastic processes theory constitute the natural basis. US army during the war, and later in the US Problems encountered by the and Soviet space programs, have led to an awarenessofthe need for reliabilityor more generaly for dependability (a general term covering reliability, availability, security, maintainability, etc.) of the systems. The paper by W. Weibull of 1938 on the strength of materials, leading to the distribution that later took his name, and the paper by B. Epstein and M. Sobel of 1951, initiating the use of the exponential distribution as the basic (and now most used) model for reliability, are the founding papers of the field. At this time, the systems were merely seen as black boxes. During the 1960s, they began to be considered as the result of the interaction of their elements. Appropriate methods were then developed, from Shannon''s work to the beautiful theory of coherent systems initiated by Z.W. Birnbaum, J.D.

At first there was the Markov property. The theory of stochastic processes, which can be considered as an exten­ sion of probability theory, allows the modeling of the evolution of systems through the time. It cannot be properly understood just as pure mathemat­ ics, separated from the body of experience and examples that have brought it to life. The theory of stochastic processes entered a period of intensive develop­ ment, which is not finished yet, when the idea of the Markov property was brought in. Not even a serious study of the renewal processes is possible without using the strong tool of Markov processes. The modern theory of Markov processes has its origins in the studies by A. A: Markov (1856-1922) of sequences of experiments "connected in a chain" and in the attempts to describe mathematically the physical phenomenon known as Brownian mo­ tion. Later, many generalizations (in fact all kinds of weakenings of the Markov property) of Markov type stochastic processes were proposed. Some of them have led to new classes of stochastic processes and useful applications. Let us mention some of them: systems with complete connections [90, 91, 45, 86]; K-dependent Markov processes [44]; semi-Markov processes, and so forth. The semi-Markov processes generalize the renewal processes as well as the Markov jump processes and have numerous applications, especially in relia­ bility.