Multi-stage Bayesian evaluation method of reliability growth for large complex system

The reliability levels of SG-III component systems are directly relative to the global reliability and stability of SG-III laser facility. The systems consist of mass identical subsystems generally, whose integration process is complicated, and the evaluation of reliability growth is hard to perform directly. Therefore, accounting for subsystems characterized by small samples, hybrid fix modes and inadequate experts experience, a multi-stage Bayesian evaluation method of system reliability growth is proposed. This method integrates AMSAA with the Non-Homogeneous Poisson Process: The failure processes of subsystems in the first stage with enough samples are modeled by AMSAA, and the Non-Homogeneous Poisson Process is assumed to be in accordance with the failure processes at the latter stages where the samples dropped off gradually. And according to the inheritance information of homogeneous subsystems, equivalent conversion methods are used to obtain the growth factors between stages and to solve the problems of lacking experts experience; then the effective transfer of historical failure information and repair information are achieved by combining with the maximum entropy method. Finally, comparative analysis results of numerical case show that this method is suitable for the reliability growth evaluation of the systems of SG-III laser facility, and provides effective ideas of reliability growth evaluation for practical engineering.

PurposeThe purpose of this paper is to present a novel GREY‒ASMAA model for reliability growth evaluation in the large civil aircraft test flight phase.Design/methodology/approachAs limited data are collected during the large civil aircraft test flight phase, which are not enough to meet the requirements of the ASMAA model for reliability growth, four basic GM(1, 1) models, even grey model, original difference grey model, even difference grey model and discrete grey model, are presented. Then both forward and backward grey models GM(1,1) are built to forecast and obtain virtual test data on left and right sides. Then the ASMAA model for reliability growth evaluation can be built based on original and virtual test data.FindingsAiming at the background of poor information data during the large civil aircraft test flight phase, first, a novel GREY‒ASMAA model, which was combined by the grey model GM(1,1) with the ASMAA model, has been put forward in this paper.Practical implicationsThe GREY‒ASMAA model for reliability growth evaluation can be used to solve the problem of reliability growth evaluation with poor information data during the large civil aircraft test flight phase, and it has been used in reliability evaluation of C919 at the test flight stage.Originality/valueThis paper presents two new definitions of forward grey model GM(1,1) and backward grey model GM(1,1), as well as a novel GREY‒ASMAA model for reliability growth evaluation of large civil aircraft during test flight phase.

This paper proposed a Bayesian method-based structural equation model (SEM) of miners’ work injury for an underground coal mine in India. The environmental and behavioural variables for work injury were identified and causal relationships were developed. For Bayesian modelling, prior distributions of SEM parameters are necessary to develop the model. In this paper, two approaches were adopted to obtain prior distribution for factor loading parameters and structural parameters of SEM. In the first approach, the prior distributions were considered as a fixed distribution function with specific parameter values, whereas, in the second approach, prior distributions of the parameters were generated from experts’ opinions. The posterior distributions of these parameters were obtained by applying Bayesian rule. The Markov Chain Monte Carlo sampling in the form Gibbs sampling was applied for sampling from the posterior distribution. The results revealed that all coefficients of structural and measurement model parameters are statistically significant in experts’ opinion-based priors, whereas, two coefficients are not statistically significant when fixed prior-based distributions are applied. The error statistics reveals that Bayesian structural model provides reasonably good fit of work injury with high coefficient of determination (0.91) and less mean squared error as compared to traditional SEM.

Bayesian statistical methods have recently been combined with conventional methods for fisheries stock assessment (e.g. catch-age analysis) to provide a conceptually elegant approach for providing fishery management advice under uncertainty. Uncertainties in the advice provided can be conveyed using posterior probability distributions (or “posteriors”) for the potential outcomes of each policy option. Posteriors can be estimated using data (e.g. catch-age data and relative abundance indices) for the fish population of interest and prior probability distributions for population model parameters (e.g. stock-recruit function parameters) based on data from similar fish populations. Despite growing interest, Bayesian methods remain accessible to relatively few. To increase the accessibility of these methods, the conceptual basis for Bayesian statistical estimation is reviewed and set in the context of fisheries stock assessment. The use of Bayesian methods is illustrated by fitting a logistic model to relative abundance indices for Namibian hake (Merlucius capensis and M. paradoxus) and presenting a decision analysis of alternative harvest policy options. Some alternative approaches are outlined for constructing prior and posterior probability distributions and some recent applications in fisheries. Some of the problems that can be encountered while implementing Bayesian methods are also discussed.

Bayesian system reliability assessment method with maximum entropy as prior distribution is developed in the present analysis. The system reliability assessment model is established, and the method and process of system reliability assessment are put forward. The method is based on the theory of information entropy. The probability density function and distribution function of system reliability parameters are given by using maximum entropy method. Prior distribution of Bayesian analysis method is the distribution function. Likelihood function is given by a small amount of field test data. According to Bayesian methods, posterior distribution is determined by using prior distribution and likelihood function. The point estimation and interval estimation of system reliability parameters are calculated in order to evaluate the system reliability. The method solves better the problem of system reliability assessment for small sample cases, and is an optimum method for reliability assessment of large and complex systems.

In this paper, we propose a new software reliability growth model which is the mixture of two exponential reliability growth models, one of which has the reliability growth and the other one does not have the reliability growth after the software is released upon completion of testing phase. The mixture of two such models is characterized by a weighted factor p, which is the proportion of reliability growth part within the model. Firstly, this paper discusses an optimal software release problem with regard to the expected total software cost incurred during the warranty period under the proposed software reliability growth model, which generalizes Kimura, Toyota and Yamada's (1999) model with consideration of the weighted factor. The second main purpose of this paper is to apply the Bayesian approach to the optimal software release policy by assuming the prior distributions for the unknown parameters contained in the proposed software reliability growth model. Some numerical examples are presented for the purpose of comparing the optimal software release policies depending on the choice of parameters by the non-Bayesian and Bayesian methods.

Thermodynamic modeling and uncertainty quantification of CO2-loaded aqueous MEA solutions

This article discusses the Bayesian approach for count data using non-homogeneous Poisson processes, considering different prior distributions for the model parameters. A Bayesian approach using Markov Chain Monte Carlo (MCMC) simulation methods for this model was first introduced by [1], taking into account software reliability data and considering non-informative prior distributions for the parameters of the model. With the non-informative prior distributions presented by these authors, computational difficulties may occur when using MCMC methods. This article considers different prior distributions for the parameters of the proposed model, and studies the effect of such prior distributions on the convergence and accuracy of the results. In order to illustrate the proposed methodology, two examples are considered: the first one has simulated data, and the second has a set of data for pollution issues at a region in Mexico City.

The objective of this study is to examine the properties of Bayes estimators of the shape parameter of the Power Function Distribution (PFD-I), by using two different prior distributions for the parameter θ and different loss functions that were compared with the maximum likelihood estimators. In many practical applications, we may have two different prior information about the prior distribution for the shape parameter of the Power Function Distribution, which influences the parameter estimation. So, we used two different kinds of conjugate priors of shape parameter θ of the Power Function Distribution (PFD-I) to estimate it. The conjugate prior function of the shape parameter θ was considered as a combination of two different prior distributions such as gamma distribution with Erlang distribution and Erlang distribution with exponential distribution and Erlang distribution with non-informative distribution and exponential distribution with the non-informative distribution. We derived Bayes estimators for shape parameter θ of the Power Function Distribution (PFD-I) according to different loss functions such as the squared error loss function (SELF), the weighted error loss function (WSELF) and modified linear exponential (MLINEX) loss function (MLF), with two different double priors. In addition to the classical estimation (maximum likelihood estimation). We used simulation to get the results of this study, for different cases of the shape parameter of the Power Function Distribution used to generate data for different samples sizes.

Weibull distribution is one of the continous probability density function. This distribution is known as a flexible distribution. One of it’s flexibility is can be transformed into other distributions such as exponential distribution depends on parameter selected. Similar to other distribution, Weibull distribution also characterized by cumulative distribution function, mean, variance and moment generating function. One of the well-known application of this distribution is in the field of quality control utilizing reliability data and the well-known tool in quality control is control chart. Therefore, reliability data is not follow normal distribution then Shewhart control chart cannot be applied. To solve this problem, control chart can be formed with the control limit is obtained by Bayesian method. In applying Bayesian method, prior distribution of shape parameter is assumed to be uniform distribution and variables for reliability is assumed to be invers of Weibull distribution. The prior distribution is combine with likelihood function then posterior distribution is obtained which in then used as the control limits by find it’s mean.

The reliability of electronic circuits, systems and devices is one component of their quality. An electronic device has three phases of existence. First phase - the development is very important for reliability growth. In this phase constructor implements three basic components of reliability - reliability, longevity and maintainability in the electronic device. The reliability growth model (RGM) is a very specific tool used during the development phase of electronic devices and software products. New unconventional reliability growth models are based on the homogeneity testing of different Poisson process characteristics. This enables to find the time frame for finishing the technological constructing operations for further reliability growth in the next design of an electronic object. The goal is to find boundary time tb using statistical methods, from which the Poisson process is homogenous (stationary). We introduce experimental results those obtained by applying new unconventional reliability growth models. In the future it will be very interesting to develop algorithm testing the homogeneity of Poisson process of correlation function R (t1, t2), algorithm testing the homogeneity of Poisson process in his time-frequency representation. We review some new unconventional reliability growth models of electronic devices, compare and evaluate them in this paper.

Estimating phylogenies in which branch lengths are expressed in units of absolute time is crucial for testing hypotheses in evolutionary biology. However, bioinformatic tools to pre- and post-process data from Bayesian divergence time estimation analyses are often not easily interoperable, and documenting methodological choices is not a generalized practice. The R package tbea is a tool-set to integrate biological, geological, and paleontological information to optimize the specification of models, their parameters, and prior distributions in divergence time estimation analyses. tbea implements statistical models to (i) better translate time information in dating sources into the specified calibration densities, (ii) improve comparisons between prior and posterior distributions for parameters of interest, (iii) carry out inference on origination times for a set of distributions, (iv) summarize different distributions into a single one, and (v) improve the reproducibility of divergence time estimation analyses allowing users to document methodological choices. We illustrate the functionalities of tbea by carrying out two worked examples, one on the phylogenetic relationships and divergence time estimation of South American Cynodontidae, and the other on the separation time of drainages east and west of the Andes in South America. It is expected that the tools available in tbea will be key when estimating events in time from sets of point estimates, and the combination of different posterior densities from the same parameter will be useful in justifying the selection of secondary calibration points, or discussing the timing of biogeographical events when multiple sources are available.

We present a Bayesian approach of a Ricker stock-recruitment (S/R) analysis accounting for measurement errors on S/R data. We assess the sensitivity of posterior inferences to (i) the choice of Ricker model parameterizations, with special regards to management-related ones, and (ii) prior parameter distributions. Closed forms for Ricker parameter posterior distributions exist given S/R data known without error. We use this property to develop a procedure based on the Rao–Blackwell formula. This procedure achieves integration of measurement errors by averaging these closed forms over possible S/R data sets sampled from distributions derived from a stochastic model relating field data to the S and R variables. High-quality Bayesian estimates are obtained. The analysis of the influence of different parameterizations and of the priors is made easier. We illustrate our methodological approach by a case study of Atlantic salmon (Salmo salar). Posterior distributions for S and R are computed from a mark–recapture stochastic model. Ignoring measurement errors underestimates parameter uncertainty and overestimates both stock productivity and density dependence. We warn against using management-related parameterizations because it makes the strong prior assumption of long-term sustainability of stocks. Posterior inferences are sensitive to the choice of prior. The use of informative priors as a remedy is discussed.

ObjectiveTo show how a simple Bayesian analysis method can be used to improve the evidence base in patient populations where recruitment and retention are challenging.MethodsA Bayesian conjugate analysis method was...

Bayesian sensitivity analysis in elliptical linear regression models