A fraction defective based capability index

Two problems greatly affect the use of capability indices such as , and : the lack of affinity with the process fraction defective π and the difficulty of dealing with the sampling distributions of their natural estimators. In this paper, a capability index which is in one‐to‐one correspondence with π is introduced and simple inferential procedures under a Bayesian perspective are developed to facilitate its use in industrial applications. Copyright © 2001 John Wiley & Sons, Ltd.     

数据扩充下0-1膨胀几何分布的客观贝叶斯分析及应用

在交通安全、公共卫生、风险管理等实际应用领域,经常会遇到0观测值、1观测值出现较多的样本数据。为了更深入地研究这类数据集,本文提出了0-1膨胀几何分布模型,通过设计数据扩充策略和构造完全似然函数,得到了Jeffreys先验和reference先验。设置不同的样本容量和参数真值,对不同的客观先验进行数值仿真和比较分析。最后,利用0-1膨胀几何分布模型对底特律城市交通事故死亡数据集进行了分析。研究表明,采用客观贝叶斯方法比主观贝叶斯方法能够实现更佳的拟合效果。     

A Bayesian procedure for process capability assessment

The usual practice of judging process capability by evaluating point estimates of some process capability indices has a flaw that there is no assessment on the error distributions of these estimates. However, the distributions of these estimates are usually so complicated that it is very difficult to obtain good interval estimates. In this paper we adopt a Bayesian approach to obtain an interval estimation, particularly for the index C_pm. The posterior probability p that the process under investigation is capable is derived; then the credible interval, a Bayesian analogue of the classical confidence interval, can be obtained. We claim that the process is capable if all the points in the credible interval are greater than the pre‐specified capability level ω, say 1.33. To make this Bayesian procedure very easy for practitioners to implement on manufacturing floors, we tabulate the minimum values of Ĉ_pm/ω, for which the posterior probability p reaches the desirable level, say 95%. For the special cases where the process mean equals the target value for C_pm and equals the midpoint of the two specification limits for C_pk, the procedure is even simpler; only chi‐square tables are needed. Copyright © 1999 John Wiley & Sons, Ltd.     

Sensitivity estimations for Bayesian inference models solved by MCMC methods

The advent of Markov Chain Monte Carlo (MCMC) methods to simulate posterior distributions has virtually revolutionized the practice of Bayesian statistics. Unfortunately, sensitivity analysis in MCMC methods is a difficult task. In this paper, a computationally low-cost method to estimate local parametric sensitivities in Bayesian models is proposed. The sensitivity measure considered here is the gradient vector of a posterior quantity with respect to the parameter. The gradient vector components are estimated by using a result based on the integral/derivative interchange. The MCMC simulations used to estimate the posterior quantity can be re-used to estimate the sensitivity measures and their errors, avoiding the need for further sampling. The proposed method is easy to apply in practice as it is shown with an illustrative example.     

Bayesian inference for parameters estimation using experimental data

A finite element (FE) model is developed for a curved cable-stayed footbridge located in Terni (Umbria Region, Central Italy) which accounts for uncertainties in geometry, material properties, and boundary conditions as well as limited knowledge on the behavior of connections and other components. Ambient vibration tests (AVTs) are carried out to identify the main dynamic parameters which are used for model updating in the Bayesian framework. Sensitivity analysis is performed to identify the main mechanical parameters affecting natural frequencies and mode shapes to be used as updating parameters. Finally, the posterior probability distributions of the selected updating parameters is estimated and used to assess the accuracy of the FE-based model. The importance of using a proper informative reference data set in the updating framework is assessed using different observations together with the importance of reliable surrogate models able to reduce the computational costs related to the whole framework.     

贝叶斯网络推理在信息系统安全风险评估中的应用

提出了一种基于贝叶斯网络推理的安全风险评估方法。从实际出发建立信息系统的贝叶斯网络模型，根据专家给出的先验信息，结合获得的证据信息，运用Pearl方法完成对模型的评估，给出在特定条件下模型的计算——线性推理算法。最后，以实例分析信息系统安全评估的实现过程，结果表明，该方法可行、有效。     

Calibration of adhesion models based on Bayesian inference

The use of composite materials in a myriad of applications fostered the development of reliable procedures to connect components with adhesives. This led to a demand for reliable adhesion models to be used in engineering designs that are based on computer simulations. This paper presents a strategy to be used for calibration of adhesion models. The proposed methodology is built on the formalism of Statistical Inverse Problems. Uncertainties about the unknowns are inferred using Population-Based Markov Chain Monte Carlo and Adaptive Metropolis. It is proposed to perform model assessments based on the analysis of a validation metric. Realizations of the validation metric are computed with the posterior densities of model parameters that are provided by the calibration process. The analysis of the validation metric allows for model selection to be performed. Some numerical experiments are presented with noise-contaminated data. The calibration strategy proved effective when dealing with both the nonlinearity and nondifferentiability of the adhesion constitutive equation.     

A Bayesian Predictive Analysis of Step‐Stress Accelerated Tests in Gamma Degradation‐Based Processes

Degradation modeling might be an alternative to the conventional life test in reliability assessment for high quality products. This paper develops a Bayesian approach to the step‐stress accelerated degradation test. Reliability inference of the population is made based on the posterior distribution of the underlying parameters with the aid of Markov chain Monte Carlo method. Further sequential reliability inference on individual product under normal condition is also proposed. Simulation study and an illustrative example are presented to show the appropriateness of the proposed method. Copyright © 2017 John Wiley & Sons, Ltd.     

Process capability index for Poisson regression profile based on the Spmk index

In many process control applications, the quality of a process or a product can be characterized by a functional relationship between a response variable and one or more explanatory variables which is typically referred to as a profile. Such profiles can be expressed by a linear or a non-linear model. On the other hand, for an in-control process, capability indices are used for process quality improvement. In this article, we propose a method to measure the process capability when the quality of the process is characterized by a Poisson regression profile. The performance of the proposed index is evaluated through simulations studies. Two real data examples illustrate this method.     

Sensibility of Bayesian inference methods for reliability prediction of ageing systems,case of Diesel locomotives

This paper addresses the problem of reliability analysis of in-service identical systems when a limited number of lifetime data is available compared to censored ones. Lifetime (resp. censored) data characterise the life of failed (resp. non-failed) systems in the sample. Because, censored data induce biassed estimators of reliability model parameters, a methodology approach is proposed to overcome this inconvenience and improve the accuracy of the parameter estimation based on Bayesian inference methods. These methods combine, in an effective way, system’s life data and expert opinions learned from failure diagnosis of similar systems. Three Bayesian inference methods are considered: Classical Bayesian, Extended Bayesian and Bayesian Restoration Maximisation methods. Given a sample of lifetime data, simulated according to prior opinions of maintenance expert, a sensibility analysis of each Bayesian method is performed. Reliability analysis of critical subsystems of Diesel locomotives is established under the proposed methodology approach. The relevance of each Bayesian inference methods with respect to collected reliability data of critical subsystems and expert opinions is discussed.     

Bayesian inference in probabilistic risk assessment—The current state of the art

Markov chain Monte Carlo (MCMC) approaches to sampling directly from the joint posterior distribution of aleatory model parameters have led to tremendous advances in Bayesian inference capability in a wide variety of fields, including probabilistic risk analysis. The advent of freely available software coupled with inexpensive computing power has catalyzed this advance. This paper examines where the risk assessment community is with respect to implementing modern computational-based Bayesian approaches to inference. Through a series of examples in different topical areas, it introduces salient concepts and illustrates the practical application of Bayesian inference via MCMC sampling to a variety of important problems.     

An analytic model for situation assessment of nuclear power plant operators based on Bayesian inference

Simulation-based human reliability analysis (HRA) methods such as IDAC seem to provide a new direction for the development of advanced HRA methods. In such simulation-based HRA methods, the simulation model for the situation assessment of nuclear power plant (NPP) operators is essential, especially for addressing the issue of errors-of-commission (EOCs). Therefore, we propose an analytic model for the situation assessment of NPP operators based on Bayesian inference. The proposed model is found to be able to address several important features of the situation assessment of NPP operators, and is expected to provide good approximations to some parts of the situation assessment. A comparison with an existing model and identification of several other features of the situation assessment of NPP operators that should be further addressed are also provided.     

A Bayesian Semiparametric Analysis of the Reliability and Maintenance of Machine Tools

A Bayesian semiparametric proportional hazards model is presented to describe the failure behavior of machine tools. The semiparametric setup is introduced using a mixture of Dirichlet processes prior. A Bayesian analysis is performed on real machine tool failure data using the semiparametric setup, and development of optimal replacement strategies are discussed. The results of the semiparametric analysis and the replacement policies are compared with those under a parametric model.     

Process selection for higher production yield based on capability index Spk

Process selection is the problem of comparing two processes and selecting the one that has a higher capability value. In this paper, we consider the process selection problem by using the yield index S_pk to compare two production processes and select one that has higher production yield. An analytical exact approach is proposed to solve this problem. Testing hypotheses with two phases for comparing two processes are developed. Critical values of the test are obtained to determine the selection decisions. Sample sizes required for designated selection power and confidence level are also investigated. The results provide useful information to practitioners. An application example on comparing two thin‐film transistor (TFT) type liquid‐crystal display (LCD) production processes is presented to illustrate the practicality of the proposed approach to a real problem in the factory. Copyright © 2009 John Wiley & Sons, Ltd.     

PriorVAE: encoding spatial priors with variational autoencoders for small-area estimation

Gaussian processes (GPs), implemented through multivariate Gaussian distributions for a finite collection of data, are the most popular approach in small-area spatial statistical modelling. In this context, they are used to encode correlation structures over space and can generalize well in interpolation tasks. Despite their flexibility, off-the-shelf GPs present serious computational challenges which limit their scalability and practical usefulness in applied settings. Here, we propose a novel, deep generative modelling approach to tackle this challenge, termed PriorVAE: for a particular spatial setting, we approximate a class of GP priors through prior sampling and subsequent fitting of a variational autoencoder (VAE). Given a trained VAE, the resultant decoder allows spatial inference to become incredibly efficient due to the low dimensional, independently distributed latent Gaussian space representation of the VAE. Once trained, inference using the VAE decoder replaces the GP within a Bayesian sampling framework. This approach provides tractable and easy-to-implement means of approximately encoding spatial priors and facilitates efficient statistical inference. We demonstrate the utility of our VAE two-stage approach on Bayesian, small-area estimation tasks.     

Bayesian conjugate analysis of the Galton-Watson process

In this article we consider the Bayesian statistical analysis of a simple Galton-Watson process. Problems of interest include estimation of the offspring distribution, classification of the process, and prediction. We propose two simple analytic approximations to the posterior marginal distribution of the reproduction mean. This posterior distribution suffices to classify the process. In order to assess the accuracy of these approximations, a comparison is provided with a computationally more expensive approximation obtained via standard Monte Carlo techniques. Similarly, a fully analytic approximation to the predictive distribution of the future size of the population is discussed. Sampling-based and hybrid approximations to this distribution are also considered. Finally, we present some illustrative examples. The first author is supported by the Alberto Baillères Chair on Insurance and International Finance of ITAM. This work was partially supported by Sistema Nacional de Investigadores, Mexico.     

关于过程能力指数和不合格品率之间的关系研究

研究过程能力指数和过程产品不合格品率的关系,指出这是两个有密切联系又有重要区别的概念;它们分别从不同的角度描述了过程的质量能力水平:好的不合格品率是好的过程能力的必要条件;要改进过程产品质量水平就不能只满足于保持基本的合格品率,还应该进一步查找问题,分析波动产生的原因,采取措施消除影响,纳入标准.     

A new methodology for Bayesian history matching using parallel interacting Markov chain Monte Carlo

This paper presents an innovative application of a new class of parallel interacting Markov chains Monte Carlo to solve the Bayesian history matching (BHM) problem. BHM consists of sampling a posterior distribution given by the Bayesian theorem. Markov chain Monte Carlo (MCMC) is well suited for sampling, in principle, any type of distribution; however the number of iteration required by the traditional single-chain MCMC can be prohibitive in BHM applications. Furthermore, history matching is typically a highly nonlinear inverse problem, which leads in very complex posterior distributions, characterized by many separated modes. Therefore, single chain can be trapped into a local mode. Parallel interacting chains is an interesting way to overcome this problem, as shown in this paper. In addition, we presented new approaches to define starting points for the parallel chains. For validation purposes, the proposed methodology is firstly applied in a simple but challenging cross section reservoir model with many modes in the posterior distribution. Afterwards, the application to a realistic case integrated to geostatistical modelling is also presented. The results showed that the combination of parallel interacting chain with the capabilities of distributed computing commonly available nowadays is very promising to solve the BHM problem.