Validation and Adjustment of Prior and Data for Bayesian Reliability Analysis in Engineering Design

Bayesian approaches have been demonstrated as effective methods for reliability analysis of complex systems with small-amount data, which integrate prior information and sample data using Bayes’ theorem. However, there is an assumption that precise prior probability distributions are available for unknown parameters, yet these prior distributions are sometimes unavailable in practical engineering. A possible way to avoiding this assumption is to generalize Bayesian reliability analysis approach by using imprecise probability theory. In this paper, we adopt a set of imprecise Dirichlet distributions as priors to quantify uncertainty of unknown parameters and extend traditional Bayesian reliability analysis approach by introducing an imprecise Dirichlet model (IDM). When the prior information is rare, the result of imprecise Bayesian analysis method is too rough to support engineering decision-making, so we proposed an optimization model to reduce the imprecision of the new method. Spindles are crucial for machine tools and reliability data related to spindles of new-developed machine tools are often rare. We can then use the imprecise Bayesian reliability analysis method to assess its reliability. In this paper, we mainly investigate the reliability assessment of a motorized spindle to illustrate the effectiveness of the proposed method.

In Memoriam: Dr. Clive L. Dym (1942–2016)

Prior information and elicitation are the prerequisite in Bayesian reliability inference. Multiple sources for priors such as probability fitting based on historical data and expert judgment are often available when estimating the reliability of complex systems. This paper investigates the integration of multiple priors in Bayesian reliability analysis. Specifically, methods for multiple priors' integration based on Bayesian Melding are investigated. The performance of the studied methods with different prior information integration algorithms such as the arithmetic and geometric averaging is investigated. The impacts of the prior misspecification and the pooling parameter selection for prior integration algorithms are also studied. In numerical examples, simulation methods are applied for posterior reliability inference under the proposed prior integration methods and the performance of the two methods are compared.

Failure Models. Qualitative System Analysis. Systems of Independent Components. Component Importance. Markov Models. Counting Processes. Dependent Failures. Life Data Analysis. Accelerated Life Testing. Bayesian Reliability Analysis. Reliability Data Sources. Appendices. References. Indexes.

Bayesian methods have become increasingly popular in recent years because of its central application in the new technologies related to artificial intelligence and machine learning. Here, a brief introduction to Bayesian thinking and Bayesian methods in reliability analysis is given with focus on the basic concepts and methods. These are illustrated by models including a single parameter. A number of practical examples are used to illustrate the concepts and methods. After having read this chapter, we hope the reader has got a sufficient background to probe further into specialized texts on Bayesian reliability analysis.

Describes how sampling distribution of the estimates of the reliability functions for various failure time distributions is either hard to obtain or is quite complicated and, as such, it becomes difficult to draw inferences about the reliability of a system. To overcome this situation, presents some distribution‐free inference techniques on system reliability and gives Bayesian reliability analysis using conjugate priors.

Updating the models and uncertainty of mechanical parameters for rock tunnels using Bayesian inference

Risk informed integrity management of sub-surface well production tubings subject to combined scale and corrosion degradations

This volume has been inspired by the aim of gathering a number of theoretical papers that, though from different schools of inference—frequentist andBayesian, share the same interest towards studying complex statistical models. Indeed, both frequentist and Bayesian inference can entail various drawbacks, due to the complexity or misspecification of the model, or to the presence of many nuisance parameters. These difficulties may be overcome from a theoretical point of view through approximate likelihoods and scoring rules, and from a computational point of view through higher-order asymptotic expansions or computational tools from Bayesian inference. Specifically, the volume focuses on the interplay between Bayesian and frequentist inference in addressing these problems. The goal is to highlight and to disseminate some of the topics emerged in the international Workshop Recent advances in Statistical Inference: Theory and case studies, held in Padova, Italy, March 21–23, 2013. The Workshop has been a forum for the exchange of new ideas and thoughts on recent and ongoing research in both Bayesian methodology and modern likelihood inference. Although the topics covered in this volume are diverse, similar themes recur, as research ismostly fueled by the need to deal with complex models, for which traditional methods do not provide viable solutions. Among the topics presented we have Bayesian/frequentist challenges for categorical data analysis, Bayesian-frequentist sample size determination, integrated likelihood inference in semi parametric regression models, approximate Bayesian computation with modified log-likelihood ratios, theory and applications of proper scoring rules, quasi likelihood approximation of posterior distributions for likelihood-intractable complex models, mitigating multicollinearity with spike-and-slab priors, empirical Bayes methods in classical and Bayesian inference. While not exhaustive, this list should give a feeling of the issues discussed at the Workshop.

Impact of the Scientific Registry of Transplant Recipients’ New Bayesian Method on Estimating Center Effects and Flagging of Centers as Worse Than Expected

Bayesian hypothesis testing with frequentist characteristics in clinical trials

A two-component parallel or series system is studied where the failure time of each component follows the Burr distribution. The testing environment of the system is assumed different from the operating one, causing the parameters (i=1, 2) to increase or decrease by a positive, random amount η. Two priors are considered for the behaviour of η, a gamma and a uniform. The Bayesian reliability is derived in closed form. Three hypothetical examples show how this approach could be used by reliability engineers.

Due to advances in technology, there is a presence of directional data in a wide variety of fields. Often distributions to model directional data are defined on manifold or constrained spaces. Regular statistical methods applied to data defined on special geometries can give misleading results, and this demands new statistical theory. This dissertation addresses two such problems and develops Bayesian methodologies to improve inference in these arenas. It consists of two projects: 1. A Bayesian Methodology for Estimation for Sparse Canonical Correlation, and 2. Bayesian Analysis of Finite Mixture Model for Spherical Data. In principle, it can be challenging to integrate data measured on the same individuals occurring from different experiments and model it together to gain a larger understanding of the problem. Canonical Correlation Analysis (CCA) provides a useful tool for establishing relationships between such data sets. When dealing with high dimensional data sets, Structured Sparse CCA (ScSCCA) is a rapidly developing methodological area which seeks to represent the interrelations using sparse direction vectors for CCA. There is less development in Bayesian methodology in this area. We propose a novel Bayesian ScSCCA method with the use of a Bayesian infinite factor model. Using a multiplicative half Cauchy prior process, we bring in sparsity at the level of the projection matrix. Additionally, we promote further sparsity in the covariance matrix by using graphical horseshoe prior or diagonal structure. We compare the results for our proposed model with competing frequentist and Bayesian methods and apply the developed method to omics data arising from a breast cancer study. In the second project, we perform Bayesian Analysis for the von Mises Fisher (vMF) distribution on the sphere which is a common and important distribution used for directional data. In the first part of this project, we propose a new conjugate prior for the mean vector and concentration parameter of the vMF distribution. Further we prove its properties like finiteness, unimodality, and provide interpretations of its hyperparameters. In the second part, we utilize a popular prior structure for a mixture of vMF distributions. In this case, the posterior of the concentration parameter consists of an intractable Bessel function of the first kind. We propose a novel Data Augmentation Strategy (DAS) using a Negative Binomial Distribution that removes this intractable Bessel function. Furthermore, we apply the developed methodology to Diffusion Tensor Imaging (DTI) data for clustering to explore voxel connectivity in human brain.

Considering the tedious and complex problem of solving joint probability with the bucket elimination algorithm, a parallel joint probability inference algorithm was proposed. The logical relation was analysed among each node variable and the inverse order method of the bucket elimination was used to introduce the mathematical expressions of joint probability and calculate the probabilities of one or more node failures when the network fails. The method is applied into the example of reliable analysis of electronic products and is demonstrated the simplicity and effectiveness of the method in the process of two-way Bayesian network inference. The results can be used to identify the weak links of electronic products and also provide a theoretical basis for reliability and maintenance strategies for electronic products.

A recent trend in engineering education related to the expected design competencies of graduating engineers is a shift from prescribing what the design requirements of a program should include toward examining the corresponding learning outcomes. One of the approaches used in implementing this trend is the adoption of outcome-based assessment criteria in the engineering design curriculum. Graduates should be able to apply knowledge of mathematics, science and engineering by designing systems, components and processes in learning environments that include both traditional and modern approaches, such as project-based learning, and should be able to apply their engineering design knowledge in open-ended real-life projects. The paper describes an approach to develop engineering design competencies using open-ended projects by providing detailed expected outcomes of the designed product and providing limited design specifications. Students are expected to go through all the steps of the engineering design process from defining the specifications of the designed product that addresses the expected outcomes to testing the final product. The purpose of the study is to find the engineering design competencies that are enhanced through international design collaboration.