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The paper develops Bayesian estimators and HPD intervals for the stress strength reliability of generalised inverted exponential distribution using upper record values. For prior distribution, informative prior as well as non-informative prior both are considered. The Bayes estimators are obtained under both symmetric and asymmetric loss functions. A simulation study is conducted to obtain the Bayes estimates of stress strength reliability. Simulated data sets are also considered here for illustration purpose.

In this paper, the problem of estimating unknown parameters of a generalized halfnormal distribution is considered under Type II progressive hybrid censoring which is a combination of Type II progressive and hybrid censoring schemes. We obtain maximum likelihood estimators of parameters and also construct asymptotic intervals using the observed Fisher information matrix. Further Bayes estimates are computed under the squared error loss function by applying different approximation methods. We also obtain prediction estimates and prediction intervals of censored observations. The performance of different methods is compared using Monte Carlo simulations and a real data set is analyzed for illustrative purposes. [ABSTRACT FROM AUTHOR]

We present a diagnostic for monitoring convergence of a Markov chain Monte Carlo (MCMC) sampler to its target distribution. In contrast to popular existing methods, we monitor convergence to the joint target distribution directly rather than a select scalar projection. The method uses a simple nonparametric posterior approximation based on a state-space partition obtained by clustering the pooled draws from multiple chains, and convergence is determined when the estimated posterior probabilities of partition elements under each chain are sufficiently similar. This framework applies to a wide variety of problems, and generalizes directly to non-Euclidean state spaces. Our method also provides approximate high-posterior-density regions, and a characterization of differences between nonconverged chains, all with little additional computational burden. We demonstrate this approach on applications to sampling posterior distributions over, graphs, and partitions. Supplementary materials for this article are available online. [ABSTRACT FROM PUBLISHER]

The objective of the present article is to study about the prediction bound lengths of a considered repairable model under Bayesian approach. The prediction length of bounds and HPD intervals has been obtained under the assumption that the repair failure rate increases monotonically as time parameter increases in the underlying model for censored data. [ABSTRACT FROM AUTHOR]

A committee of neural networks is the aggregation of two or more neural networks for making overall predictions that are supposedly more accurate than those obtained by the individual networks. The objective of this paper was to assign some uncertainty over the predictions of neural networks, using a network committee to estimate the nitrogen-corrected metabolizable energy (AMEn) values of the energetic and protein concentrate feedstuffs for broilers. The dataset used to implement each expert network contains 568 experimental results. Another dataset with 48 bioassay results was used as test data. From several implemented multilayer perceptrons, the networks that presented the best generalization performance were selected to constitute the committee. The percentage of correct predictions was used as the criterion to compare committees that contained different numbers of networks. The highest probability density intervals were obtained for each feedstuff in the test data in this comparison. The estimator that ensured more accurate predictions was selected. The highest accuracy for predicting the AMEn values of concentrate feedstuffs for broilers was achieved by a committee with 1,000 networks with the use of the mode of the empirical distribution obtained from 1,000 estimated values of the AMEn. The accuracy of the models was evaluated based on their values of error measures between the observed and predicted values, in which the mode of the empirical distribution presented lower values of mean squared error (MSE = 45,285.43), mean absolute deviation (MAD = 177.66) and mean absolute percentage error (MAPE = 5.97 %) compared to the mean and the median. [ABSTRACT FROM AUTHOR]

In response-surface methodology, when the data are fitted using a quadratic model, it is important to make inference about the eigenvalues of the matrix of pure and mixed second-order coefficients, since they contain information on the nature of the stationary point and the shape of the surface. In this article, we propose a Bayesian simulation-based approach to explore the behavior of the posterior distributions of these eigenvalues. Highest posterior density (HPD) intervals for the ordered eigenvalues are then computed and their empirical coverage probabilities are evaluated. A user-friendly software tool has been developed to get the kernel density plots of these simulated posterior distributions and to obtain the corresponding HPD intervals. It is provided online as supplementary materials to this article. [ABSTRACT FROM AUTHOR]

System performance measures of a repairable system are studied from a Bayesian viewpoint with different types of priors assumed for unknown parameters, in which the system consists of two active components and one warm standby. There is a failure probability q that switches from standby state to active state. Time-to-failure of components is assumed to be an exponential distribution. The reboot time and repair time are also exponential distributions. When time-to-failure, time-to-repair and reboot time are with uncertain parameters, a Bayesian assessing is adopted to evaluate system performance measures. Monte Carlo simulation is used to derive the posterior distribution for the steady-state availability and the mean time-to-system failure. Some numerical experiments are performed to illustrate the results derived in this article. [ABSTRACT FROM AUTHOR]

System characteristics of a redundant repairable system are studied from a Bayesian viewpoint with different types of priors assumed for the unknown parameters. The system consists of two primary units, one standby unit, and one repair facility which is activated when switching to standby fails. Times to failure and times to repair of the operating units are assumed to follow exponential distributions. When time to failure and time to repair have uncertain parameters, a Bayesian approach is adopted to evaluate system characteristics. Monte Carlo simulation is used to derive the posterior distribution for the mean time to system failure and steady-state availability. Some numerical experiments are performed to illustrate the results derived in this paper. [ABSTRACT FROM AUTHOR]

This article considers the estimation of R = P(Y < X) when X and Y are distributed as two independent three-parameter generalized exponential (GE) random variables with different shape parameters but having the same location and scale parameters. A modified maximum likelihood method and a Bayesian technique are used to estimate R on the basis of independent complete samples. The Bayes estimator cannot be obtained in explicit form, and therefore it has been determined using an importance sampling procedure. An analysis of a real life data set is presented for illustrative purposes. [ABSTRACT FROM AUTHOR]

Abstract: System characteristics of a two-unit repairable system are studied from a Bayesian viewpoint with different types of priors assumed for unknown parameters, in which the service station is unreliable. Times to failure and times to repair of the operating units are assumed to follow exponential distributions. In addition, failure times and repair times of the service station also follow exponential distributions. When times to failure and times to repair of operating units, failure times and repair times of the service station are with uncertain parameters, a Bayesian approach is adopted to evaluate system characteristics. Monte Carlo simulation is used to derive the posterior distribution for the mean time to system failure and the steady-state availability. Some numerical experiments are performed to illustrate the results derived in this paper. [Copyright &y& Elsevier]

System characteristics of a redundant repairable system with two primary units and one standby are studied from a Bayesian viewpoint with different types of priors assumed for unknown parameters, in which the coverage factor is the same for an operating unit failure as that for a standby unit failure. Times to failure and times to repair of the operating and standby units are assumed to follow exponential distributions. When times to failure and times to repair with uncertain parameters, a Bayesian approach is adopted to evaluate system characteristics. Monte Carlo simulation is used to derive the posterior distribution for the mean time to system failure and the steady-state availability. Some numerical experiments are performed to illustrate the results derived in this paper. [ABSTRACT FROM AUTHOR]

Abstract: System characteristics of a repairable system are studied from a Bayesian viewpoint with different types of priors assumed for unknown parameters, in which the system consists of one active component and one standby component. The detection of standby, the coverage factor and reboot delay of failed components are possibly considered. Time to failure of the components is assumed to follow exponential distribution. Time to repair and time to reboot of the failed components also follow exponential distributions. When time to failure, time to repair and time to reboot have uncertain parameters, a Bayesian approach is adopted to evaluate system characteristics. Monte Carlo simulation is used to derive the posterior distribution for the mean time to system failure and the steady-state availability. Some numerical experiments are performed to illustrate the results derived in this paper. [Copyright &y& Elsevier]

We formulate Bayesian approaches to the problems of determining the required sample size for Bayesian interval estimators of a predetermined length for a single Poisson rate, for the difference between two Poisson rates, and for the ratio of two Poisson rates. We demonstrate the efficacy of our Bayesian-based sample-size determination method with two real-data quality-control examples and compare the results to frequentist sample-size determination methods. [ABSTRACT FROM AUTHOR]