By Michael S. Hamada, Alyson Wilson, C. Shane Reese, Harry Martz
Bayesian Reliability provides sleek tools and methods for reading reliability information from a Bayesian standpoint. The adoption and alertness of Bayesian tools in nearly all branches of technological know-how and engineering have considerably elevated during the last few many years. This raise is essentially as a result of advances in simulation-based computational instruments for enforcing Bayesian tools.
The authors broadly use such instruments all through this publication, targeting assessing the reliability of elements and structures with specific recognition to hierarchical types and versions incorporating explanatory variables. Such types comprise failure time regression types, speeded up trying out types, and degradation types. The authors pay certain consciousness to Bayesian goodness-of-fit trying out, version validation, reliability try layout, and insurance try out making plans. through the ebook, the authors use Markov chain Monte Carlo (MCMC) algorithms for enforcing Bayesian analyses--algorithms that make the Bayesian method of reliability computationally possible and conceptually straightforward.
This publication is essentially a reference selection of smooth Bayesian tools in reliability to be used through reliability practitioners. There are greater than 70 illustrative examples, so much of which make the most of real-world facts. This publication is usually used as a textbook for a direction in reliability and comprises greater than one hundred sixty exercises.
Noteworthy highlights of the e-book comprise Bayesian methods for the following:
- Goodness-of-fit and version choice methods
- Hierarchical versions for reliability estimation
- Fault tree research technique that helps info acquisition in any respect degrees within the tree
- Bayesian networks in reliability analysis
- Analysis of failure count number and failure time info gathered from repairable structures, and the overview of assorted comparable functionality criteria <
- Analysis of nondestructive and damaging degradation data
- Optimal layout of reliability experiments
- Hierarchical reliability coverage testing
Dr. Michael S. Hamada is a Technical employees Member within the Statistical Sciences workforce at Los Alamos nationwide Laboratory and is a Fellow of the yankee Statistical organization. Dr. Alyson G. Wilson is a Technical employees Member within the Statistical Sciences workforce at Los Alamos nationwide Laboratory. Dr. C. Shane Reese is an affiliate Professor within the division of data at Brigham younger collage. Dr. Harry F. Martz is retired from the Statistical Sciences crew at Los Alamos nationwide Laboratory and is a Fellow of the yank Statistical Association.
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Additional resources for Bayesian Reliability
Dπ 2 π (1 − π)2 Substituting the MLE π into this expression and taking the reciprocal and square root, we estimate the standard deviation of the MLE as π(1 − π) . n For binomial data, the MLE π is asymptotically normally distributed with mean π and standard deviation π(1 − π)/n. The standard deviation of an estimator is usually called its standard error (se), although this distinction is often not made when conducting a Bayesian analysis. 2 Classical Point and Interval Estimation for a Proportion In the last section, we described the large sample properties of the MLE.
9 extends directly to more general settings. If θ denotes a generic parameter, p(θ | y) its posterior distribution based on the data vector y, and f (z | θ) the sampling distribution of z given θ, then the predictive distribution for z may be expressed as f (z | θ) p(θ | y)dθ. p(z | y) = Θ In most cases, the areas under predictive densities must be evaluated numerically, but, as we demonstrate in Chap. 3, this typically presents little diﬃculty when using modern Markov chain Monte Carlo (MCMC) algorithms.
Bayesians summarize knowledge of the parameter after seeing the results of an experiment using a probability density function. The use of a probability density function to summarize uncertainty about the value of a parameter does not mean that we believe that values of unknown parameters are random; it only means that our knowledge of a parameter’s value is uncertain, and that our uncertainty about this value can be represented using an appropriate probability density function. The mechanism for updating probability density functions that represent uncertainty about the value of a parameter is Bayes’ Theorem.
Bayesian Reliability by Michael S. Hamada, Alyson Wilson, C. Shane Reese, Harry Martz