Bayesian estimation of reliability function and hazard rate

The Bayes estimates of reliability function and hazard rate function of the finite range failure model have been developed based on life tests that are terminated at a preassigned time point or after a certain number of failures have occurred, taking the order of observations into consideration. For the prior distribution of the parameter involved, the uniform, exponential and inverted gamma densities have been considered. As an example, failure data for a V600 indicator tube used in aircraft radar sets, which fit well the finite range failure model, have been considered as the current distribution for obtaining the Bayes estimates of the reliability function.     

Estimation of a composite hazard rate model

The increasing hazard rate model is widely used in estimating reliability of mechanical items. The common life distributions such as Weibul, normal, and log-normal allow for strictly increasing hazard rates. In this paper we propose a composite hazard rate model which is constant over a period of unknown duration, and then strictly increases after the threshold value. In reliability engineering graphical regression methods are used to estimate unknown parameters. We investigate the performance of two such estimators. Comparisons are made using Monte Carlo simulation. Applications of some real world problems are given.     

Bayesian reliability analysis of a series system

Bayesian analysis combines subjective judgement with experimental data. Using failure information in accumulated time, the present paper deals with the posterior analysis of a series system in respect of its reliability characteristics.     

A Bayesian estimation of reliability model using the linex loss function

In this paper the problem of Bayes estimation of the reliability and the shape parameter p of a finite range failure time model is considered (assuming scale parameter θ is known). Following Zellner [A. Zellner, J. Am. Statist. Assoc. 81, 446–451 (1986)] the asymmetric loss function is used to obtain the Bayes estimators. Efficiencies of the proposed Bayes estimators are obtained with respect to the ordinary Bayes estimators and it was found that the proposed Bayes estimators are better than the ordinary Bayes estimators for quite a wide range of parameters.     

Effects of Weibull hazard rate on common cause failure analysis of reliability networks

This paper presents formulae for system mean life, variance of time to failure, hazard rate and reliability of parallel, k-out-of-n, parallel-series and bridge networks with common cause failures. The components in every configuration are assumed to be identical and characterized by a Weibull time to failure density function. The graphical plots of the system reliability and mean life gain are shown.     

Software reliability analysis based on a nonhomogeneous error detection rate model

A software reliability growth model discussed here assumes a nonhomogeneous error detection rate per error which characterizes a software reliability growth process during the testing phase. The methods for software reliability assessment are reviewed, and the model fitting and software reliability analysis for some software error data sets are presented. The optimum software release times are also given for the data analysis results.     

A hazard function approximation used in reliability theory

The cumulative hazard function H(n) should accumulate to infinity over the distribution support, because the survivor function is Sf(n)=exp(-H(n)). The widely used approximation for the cumulative hazard function, H(n)≈Σ_k=1ⁿh(k), for a small value of the hazard function, h(k), can be useful and reasonably accurate for computing the survivor function. For the continuous case, assuming that pdf exists, the H(n) diverges as it should. For the discrete case, two examples show the use of the hazard function approximation. In example A for the uniform probability mass function, the approximation diverges. In example B for the geometric probability mass function, the approximation converges to the finite value, 1.606695, when it should be diverging. The result is surprising in light of the difference between the continuous case, pdf, and the discrete case, pmf. Thus in practice, the approximation must be used with caution     

Comment on: a hazard function approximation used in reliability theory

In a recent paper, Keren & Mehrez have shown that in the case of a geometric probability mass function, the approximation to the cumulative hazard function converges to a finite value (1.606695), when the actual value of the cumulative hazard function should be diverging. In this commentary, we show that gives incorrect results, and that the corresponding results for the approximation are actually diverging.     

Bayesian analysis of the mixture of exponential failure distributions

In this paper, a Bayesian reliability analysis is carried out for the mixture of two exponential failure distributions on the basis of failure time data x₁ < x₂ <…< x_r, for a preassigned r, and (n − r) survivors from this mixed failure model. Under the assumptions of the squared error loss function (SELF) and suitable prior densities on the underlying parameter space, exact results for the Bayes estimators of the mean life and the reliability function are obtained.     

A continuous-time Bayesian network reliability modeling, and analysis framework

We present a continuous-time Bayesian network (CTBN) framework for dynamic systems reliability modeling and analysis. Dynamic systems exhibit complex behaviors and interactions between their components; where not only the combination of failure events matters, but so does the sequence ordering of the failures. Similar to dynamic fault trees, the CTBN framework defines a set of 'basic' BN constructs that capture well-defined system components' behaviors and interactions. Combining, in a structured way, the various 'basic' Bayesian network constructs enables the user to construct, in a modular and hierarchical fashion, the system model. Within the CTBN framework, one can perform various analyses, including reliability, sensitivity, and uncertainty analyses. All the analyses allow the user to obtain closed-form solutions.     

System reliability with common-cause hazard to obey an exponential power model

A model is proposed for the analysis of systems subject to common-cause failures that are not considered constant and assume that they obey an exponential power model. To represent common-cause failures, we use the Marshall, Olkin formulation of the multivariate exponential distribution. That is, the components are subject to failure by Poisson failure processes that govern simultaneous failure of a specific subset of the components. The method for calculating system reliability requires that a procedure exists for determining system reliability from component reliabilities under the statistically-independent component assumption. The paper includes examples to illustrate the method.     

Hierarchical Bayesian reliability analysis using Erlang families of priors and hyperpriors

An hierarchical Bayes approach to reliability estimation for the exponential model with an unknown scale parameter, based on life tests that are terminated after a preassigned number of failures, is considered under the assumptions of squared error loss and Erlang distributions as the prior and hyperprior. The Bayesian estimation of reliability for the case of ‘attribute testing’ is also discussed.     

A reliability analysis technique for object-oriented model using a reliability petri net

We propose a reliability analysis technique for the design specifications which are made by CRC methodology. We use a reliability Petri net as an analysis technique for CRC specification. The procedure of analyzing the system reliability is as follows: first, the collaboration graphs and message flow diagrams of CRC specification are transformed into an equivalent reliability Petri net which consists of places, transitions, input functions, output functions, failure rate of the input and output functions, and tokens. Secondly, we construct a reachability tree from a reliability Petri net, and establish the paths of all transitions for the reachability tree. These paths can be test cases. Finally, we calculate the values of reliability effect for all transitions in a reliability Petri net, select the transitions that have most effect on the system reliability, and search the messages and classes that are places of input and output fucntion in these transitions. Therefore, we can design these messages and classes very well for increasing the system reliability.     

Online nonparametric Bayesian analysis of parsimonious Gaussian mixture models and scenes clustering

The mixture model is a very powerful and flexible tool in clustering analysis. Based on the Dirichlet process and parsimonious Gaussian distribution, we propose a new nonparametric mixture framework for solving challenging clustering problems. Meanwhile, the inference of the model depends on the efficient online variational Bayesian approach, which enhances the information exchange between the whole and the part to a certain extent and applies to scalable datasets. The experiments on the scene database indicate that the novel clustering framework, when combined with a convolutional neural network for feature extraction, has meaningful advantages over other models.     

The generalized Gamma distribution: its hazard rate andstress-strength model

The 3-parameter generalized Gamma distribution (GG3) is very versatile for life distributions. Basic properties of GG3 are reviewed here, together with the major available inferential work on its parameters. Original results are presented on the hazard rate of GG3 and on its stress-strength model     

基于贝叶斯网络的装备供应链可靠性评估模型

为对装备供应链可靠性进行评估,构建了一种基于贝叶斯网络的评估模型.首先,阐述了装备供应链可靠性的基本概念,然后,介绍了装备供应链的主要环节,最后,根据贝叶斯网络的基本原理,将装备供应链的故障树模型转化为贝叶斯网络模型.     

一种采用混合高斯模型与贝叶斯判别的彩色图像人脸检测方法

介绍了一种采用混合高斯模型与贝叶斯判别的彩色人脸检测方法。该方法首先利用图像的彩色信息以及人脸的基本特征信息来进行人脸粗检测,得到图像中的多个候选人脸区域;然后对训练图像集中的全部候选人脸区域进行判别特征分析和混合高斯建模;最后采用贝叶斯判别方法对候选人脸区域进行判决,得到人脸检测结果。实验结果显示该方法具有较好的推广效率和工程应用前景。     

Bayesian estimation and prediction for Burr‐Rayleigh mixture model using censored data

In this study, Burr‐XII and Rayleigh distributions are combined to form a new mixture model that is considered to model heterogeneous data. Our objective is to estimate parameters of the proposed mixture model using Bayesian technique under type‐I censoring. Bayesian parameter estimation for the said mixture model is conducted by using informative priors, ie, gamma and squared root inverted gamma (SRIG) as well as noninformative prior, ie, Jeffrey's prior. Squared error loss function (SELF) and quadratic loss function (QLF) are employed to obtain and Bayes estimators. Properties of the proposed Bayes estimators are highlighted through a simulation study. When prior distributions and loss functions utilized in the study are compared in terms of posterior risks, informative prior found to be more suitable and decision turns out to be in favor of QLF. Prediction limits for the single sample case and two sample case are obtained to provide an insight into future sample data. Application of the proposed model is also elaborated using a real‐life example.     

On Bayesian estimation of system reliability

For a system with n s-independent components, the uncertainty regarding the reliability of components for a fixed point of time is expressed by a Bayesian probability distribution. Using the moments of these distributions, the exact moments of the system reliability distribution are derived, from which a discrete probability density function is obtained on the basis of the principle of maximum entropy. Taking this distribution as a prior distribution for system reliability, a posterior density function for the system reliability is constructed either using the data obtained from life tests conducted at a system level or from field data. For tracking the evolution of the reliability distribution over time, a modified Kalman filter technique, along with use of a Bayesian procedure, is proposed. This method is simple, elegant and easy to compute.     

Imaging radiotracer model parameters in PET: a mixture analysis approach

Two methodologies for fitting radiotracer models on a pixel-wise basis to PET data are considered. The first method does parameter optimization for each pixel considered as a separate region of interest. The second method also does pixel-wise analysis but incorporates an additive mixture representation to account for heterogeneity effects induced by instrumental and biological blurring. Several numerical and statistical techniques including cluster analysis, constrained nonlinear optimization, subsampling, and spatial filtering are used to implement the methods. A computer simulation experiment, modeling a standard F-18 deoxyglucose (FDG) imaging protocol using the UW-PET scanner, is conducted to evaluate the statistical performance of the parametric images obtained by the two methods. The results obtained by mixture analysis are found to have substantially improved mean square error performance characteristics. The total computation time for mixture analysis is on the order of 0.7 s/pixel on a 16 MIPS workstation. This results in a total computation time of about 1 h per slice for a typical FDG brain study.