Hazard Rate Modeling of Step-Stress Experiments


Book Description

Step-stress models form an essential part of accelerated life testing procedures. Under a step-stress model, the test units are exposed to stress levels that increase at intermediate time points of the experiment. The goal is to develop statistical inference for, e.g., the mean lifetime under each stress level, targeting to the extrapolation under normal operating conditions. This is achieved through an appropriate link function that connects the stress level to the associated mean lifetime. The assumptions made about the time points of stress level change, the termination point of the experiment, the underlying lifetime distributions, the type of censoring (if present), and the way of monitoring lead to alternative models. Step-stress models can be designed for single or multiple samples. We discuss recent developments in designing and analyzing step-stress models based on hazard rates. The inference approach adopted is mainly the maximum likelihood, but Bayesian approaches are briefly discussed.




Analysis of Step-Stress Models


Book Description

Analysis of Step-Stress Models: Existing Results and Some Recent Developments describes, in detail, the step-stress models and related topics that have received significant attention in the last few years. Although two books, Bagdonavicius and Nikulin (2001) and Nelson (1990), on general accelerated life testing models are available, no specific book is available on step-stress models. Due to the importance of this particular topic, Balakrishnan (2009) provided an excellent review for exponential step-stress models. The scope of this book is much more, providing the inferential issues for different probability models, both from the frequentist and Bayesian points-of-view. Explains the different distributions of the Cumulative Exposure Mode Covers many different models used for step-stress analysis Discusses Step-stress life testing under the competing or complementary risk model







Accelerated Life Models


Book Description

The authors of this monograph have developed a large and important class of survival analysis models that generalize most of the existing models. In a unified, systematic presentation, this monograph fully details those models and explores areas of accelerated life testing usually only touched upon in the literature. Accelerated Life Models:




The Cox Model and Its Applications


Book Description

This book will be of interest to readers active in the fields of survival analysis, genetics, ecology, biology, demography, reliability and quality control. Since Sir David Cox’s pioneering work in 1972, the proportional hazards model has become the most important model in survival analysis. The success of the Cox model stimulated further studies in semiparametric and nonparametric theories, counting process models, study designs in epidemiology, and the development of many other regression models that could offer more flexible or more suitable approaches in data analysis. Flexible semiparametric regression models are increasingly being used to relate lifetime distributions to time-dependent explanatory variables. Throughout the book, various recent statistical models are developed in close connection with specific data from experimental studies in clinical trials or from observational studies.







Advances in Degradation Modeling


Book Description

This volume is a collection of invited chapters covering recent advances in accelerated life testing and degradation models. The book covers a wide range of applications to areas such as reliability, quality control, the health sciences, economics and finance. It is an excellent reference for researchers and practitioners in applied probability and statistics, industrial statistics, the health sciences, quality control, economics, and finance.




Advances in Statistics - Theory and Applications


Book Description

This edited collection brings together internationally recognized experts in a range of areas of statistical science to honor the contributions of the distinguished statistician, Barry C. Arnold. A pioneering scholar and professor of statistics at the University of California, Riverside, Dr. Arnold has made exceptional advancements in different areas of probability, statistics, and biostatistics, especially in the areas of distribution theory, order statistics, and statistical inference. As a tribute to his work, this book presents novel developments in the field, as well as practical applications and potential future directions in research and industry. It will be of interest to graduate students and researchers in probability, statistics, and biostatistics, as well as practitioners and technicians in the social sciences, economics, engineering, and medical sciences.




Accelerated Life Testing of One-shot Devices


Book Description

Provides authoritative guidance on statistical analysis techniques and inferential methods for one-shot device life-testing Estimating the reliability of one-shot devices—electro-expolsive devices, fire extinguishers, automobile airbags, and other units that perform their function only once—poses unique analytical challenges to conventional approaches. Due to how one-shot devices are censored, their precise failure times cannot be obtained from testing. The condition of a one-shot device can only be recorded at a specific inspection time, resulting in a lack of lifetime data collected in life-tests. Accelerated Life Testing of One-shot Devices: Data Collection and Analysis addresses the fundamental issues of statistical modeling based on data collected from accelerated life-tests of one-shot devices. The authors provide inferential methods and procedures for planning accelerated life-tests, and describe advanced statistical techniques to help reliability practitioners overcome estimation problems in the real world. Topics covered include likelihood inference, competing-risks models, one-shot devices with dependent components, model selection, and more. Enabling readers to apply the techniques to their own lifetime data and arrive at the most accurate inference possible, this practical resource: Provides expert guidance on comprehensive data analysis of one-shot devices under accelerated life-tests Discusses how to design experiments for data collection from efficient accelerated life-tests while conforming to budget constraints Helps readers develops optimal designs for constant-stress and step-stress accelerated life-tests, mainstream life-tests commonly used in reliability practice Includes R code in each chapter for readers to use in their own analyses of one-shot device testing data Features numerous case studies and practical examples throughout Highlights important issues, problems, and future research directions in reliability theory and practice Accelerated Life Testing of One-shot Devices: Data Collection and Analysis is essential reading for graduate students, researchers, and engineers working on accelerated life testing data analysis.