Topic
Failure rate
About: Failure rate is a research topic. Over the lifetime, 4901 publications have been published within this topic receiving 70471 citations.
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Book•
01 Jun 1981
TL;DR: A number of new classes of life distributions arising naturally in reliability models are treated systematically and each provides a realistic probabilistic description of a physical property occurring in the reliability context, thus permitting more realistic modeling of commonly occurring reliability situations.
Abstract: : This is the first of two books on the statistical theory of reliability and life testing. The present book concentrates on probabilistic aspects of reliability theory, while the forthcoming book will focus on inferential aspects of reliability and life testing, applying the probabilistic tools developed in this volume. This book emphasizes the newer, research aspects of reliability theory. The concept of a coherent system serves as a unifying theme for much of the book. A number of new classes of life distributions arising naturally in reliability models are treated systematically: the increasing failure rate average, new better than used, decreasing mean residual life, and other classes of distributions. As the names would seem to indicate, each such class of life distributions provides a realistic probabilistic description of a physical property occurring in the reliability context. Also various types of positive dependence among random variables are considered, thus permitting more realistic modeling of commonly occurring reliability situations.
3,876 citations
Book•
01 Jan 1996
TL;DR: In this paper, the authors present a basic reliability model for failure distribution and a constant failure rate model for time-dependent failure models, as well as a design for maintainability.
Abstract: 1 IntroductionI Basic Reliability Models2 The Failure Distribution3 Constant Failure Rate Model4 Time-Dependent Failure Models5 Reliability of Systems6 State Dependent Systems7 Physical Reliability Models8 Design for Reliability9 Maintainability10 Design for Maintainability11 AvailabilityII The Analysis of Failure Data12 Data Collection and Empirical Methods13 Reliability Testing14 Reliability Growth Testing15 Identifying Failure and Repair Distributions16 Goodness-of-Fit TestsIII Application17 Reliability Estimation and Application18 Implementation
1,469 citations
TL;DR: In this article, a simple generalization of the Weibull distribution is presented, which is well suited for modeling bathtub failure rate lifetime data and for testing goodness-of-fit of the weibull and negative exponential models as subhypotheses.
Abstract: A simple generalization of the Weibull distribution is presented. The distribution is well suited for modeling bathtub failure rate lifetime data and for testing goodness-of-fit of the Weibull and negative exponential models as subhypotheses. >
1,028 citations
TL;DR: In this paper, the authors proposed to model failure time data by F*(f) = [F(t)]θ where F(t) is the baseline distribution function and θ is a positive real number.
Abstract: The proportional hazards model has been extensively used in the literature to model failure time data. In this paper we propose to model failure time data by F*(f) = [F(t)]θ where F(t) is the baseline distribution function and θ is a positive real number. This model gives rise to monotonic as well as non-monotonic failure rates even though the baseline failure rate is monotonic. The monotonicity of the failure rates are studied, in general, and some order relations are examined. Some examples including exponentiated Weibull, exponential, gamma and Pareto distributions are investigated in detail.
670 citations
TL;DR: In this article, the authors used the theorem that a mixture of distributions each having a non-increasing failure rate (e.g., a mix of exponential distributions) itself has a non increasing failure rate, and the apparent decreasing failure rate of the pooled air-conditioning life distribution was satisfactorily explained.
Abstract: Pooled data on the times of successive failures of the air conditioning system of a fleet of jet airplanes seemed to indicate that the life distribution had a decreasing failure rate. More refined analysis showed that the failure distribution for each airplane separately was exponential, but with a different failure rate. Using the theorem that a mixture of distributions each having a non-increasing failure rate (e.g., a mixture of exponential distributions) itself has a non-increasing failure rate, the apparent decreasing failure rate of the pooled air-conditioning life distribution was satisfactorily explained. The present study has implications in other areas where an observed decreasing failure rate may well be the result of mixing exponential distributions having different parameters.
611 citations