EXACT BAYESIAN ESTIMATION OF SYSTEM RELIABILITY WITH POTENTIAL MISCLASSIFICATIONS IN SAMPLING

2004 ◽  
Vol 11 (03) ◽  
pp. 223-241
Author(s):  
N. TURKKAN ◽  
T. PHAM-GIA
Keyword(s):  
Bayesian Estimation ◽  
Bayesian Approach ◽  
Posterior Distribution ◽  
System Reliability ◽  
Exact Expression ◽  
System Level ◽  
Posterior Density ◽  
Approximate Methods ◽  
Credible Intervals ◽  
Highest Posterior Density

We provide the exact expression of the reliability of a system under a Bayesian approach, using beta distributions as both native and induced priors at the system level, and allowing uncertainties in sampling, expressed under the form of misclassifications, or noises, that can affect the final posterior distribution. Exact 100(1-α)% highest posterior density credible intervals, for system reliability, are computed, and comparisons are made with results from approximate methods proposed in the literature.

scholarly journals Computation of posterior distribution in Bayesian analysis – application in an intermittently used reliability system

2002 ◽  
Vol 21 (3) ◽  
pp. 78-82
Author(s):  
V. S.S. Yadavalli ◽  
P. J. Mostert ◽  
A. Bekker ◽  
M. Botha
Keyword(s):  
Posterior Distribution ◽  
Jeffreys Prior ◽  
Posterior Density ◽  
Unknown Parameters ◽  
Stationary Rate ◽  
Analysis Application ◽  
Definition Of ◽  
Hpd Intervals ◽  
Highest Posterior Density ◽  
Bayes Procedure

Bayesian estimation is presented for the stationary rate of disappointments, D∞, for two models (with different specifications) of intermittently used systems. The random variables in the system are considered to be independently exponentially distributed. Jeffreys’ prior is assumed for the unknown parameters in the system. Inference about D∞ is being restrained in both models by the complex and non-linear definition of D∞. Monte Carlo simulation is used to derive the posterior distribution of D∞ and subsequently the highest posterior density (HPD) intervals. A numerical example where Bayes estimates and the HPD intervals are determined illustrates these results. This illustration is extended to determine the frequentistical properties of this Bayes procedure, by calculating covering proportions for each of these HPD intervals, assuming fixed values for the parameters.

Revisit to progressively Type-II censored competing risks data from Lomax distributions

2021 ◽  
pp. 1748006X2098397
Author(s):  
Rui Hua ◽  
Wenhao Gui
Keyword(s):  
Confidence Intervals ◽  
Competing Risks ◽  
Maximum Likelihood Estimates ◽  
Type Ii ◽  
Posterior Density ◽  
Unknown Parameters ◽  
Linex Loss ◽  
Credible Intervals ◽  
Competing Risks Data ◽  
Highest Posterior Density

In survival analysis, more than one factor typically contributes to individual failure. In addition, censoring is inevitable in lifespan tests or reliability studies due to external causes or experimental purposes. In this article, the competing risks model is considered and investigated under progressively Type-II censoring where data is from Lomax distributions. Assumptions are further made that these competitive factors are independently distributed, and the latent lifetimes of these factors follow Lomax distributions where both scale parameters and shape parameters are different. For all unknown parameters, maximum likelihood estimates have been attained by Newton-Raphson (NR) method as well as expectation maximization (EM) method, and then the approximate confidence intervals are acquired, in addition to bootstrap confidence intervals. Furthermore, under square error and LINEX loss functions, Bayes estimates and corresponding highest posterior density credible intervals are successively constructed. Finally, simulation experiments are implemented to access performance of several proposed methods in this article, and laboratory dataset is presented and analyzed for illustrative purposes.

scholarly journals Statistical Inferences of Type-II Progressively Hybrid Censored Fuzzy Data with Rayleigh Distribution

2018 ◽  
Vol 47 (3) ◽  
pp. 40-62 ◽  
Author(s):  
Ankita Chaturvedi ◽  
Sanjay Kumar Singh ◽  
Umesh Singh
Keyword(s):  
Real Data ◽  
Rayleigh Distribution ◽  
Model Parameters ◽  
Type Ii ◽  
Posterior Density ◽  
Numerical Illustration ◽  
Data Set ◽  
Bayesian Procedures ◽  
Credible Intervals ◽  
Highest Posterior Density

This article presents the procedures for the estimation of the parameter of Rayleighdistribution based on Type-II progressive hybrid censored fuzzy lifetime data. Classicalas well as the Bayesian procedures for the estimation of unknown model parameters has been developed. The estimators obtained here are Maximum likelihood (ML) estimator, Method of moments (MM) estimator, Computational approach (CA) estimator and Bayes estimator. Highest posterior density (HPD) credible intervals of the unknown parameter are obtained by using Markov Chain Monte Carlo (MCMC) technique. For numerical illustration, a real data set has been considered.

Liquid Propulsion System Reliability Estimation using Computational Bayesian Approach with Multi-level Data

2019 ◽  
Vol 11 (4) ◽  
Author(s):  
S. Muthukumar ◽  
P. Subhash Chandra Bose ◽  
R.A. Srivardhan
Keyword(s):  
Test Data ◽  
Bayesian Approach ◽  
System Reliability ◽  
Propulsion System ◽  
Reliability Estimation ◽  
System Level ◽  
Space Applications ◽  
Unique Challenge ◽  
Cost Constraints ◽  
Level Data

Liquid propulsion system (LPS) is a highly reliable and complex system that is used for the military and space applications. It consists of many flight critical components arranged in series configuration. Reliability is the most critical parameter for this system, even one subsystem failure leads to total failure of flight vehicle. Determining the achieved reliability of a LPS is a unique challenge for designer of these systems. The system reliability needs to be estimated with limited number of tests due to the destructive nature of tests, time and cost constraints. In this paper, reliability of LPS was estimated with subsystem test data using computational Bayesian approach. Component level, subsystem level and system level data are considered and a framework is created by combing all information. The reliability of the LPS was calculated using Markov Chain Monte Carlo (MCMC) simulation which has avoided numerical integration. Results are compared with Lindstorm Madden method and Bayesian hybrid method. Computational Bayesian approach can give reasonably better reliability estimate with limited test data.

scholarly journals A Bayesian approach to construct confidence intervals for comparing the rainfall dispersion in Thailand

PeerJ ◽  
2020 ◽  
Vol 8 ◽  
pp. e8502 ◽  
Author(s):  
Patcharee Maneerat ◽  
Sa-aat Niwitpong ◽  
Suparat Niwitpong
Keyword(s):  
Drainage Basin ◽  
Average Length ◽  
Small Sample ◽  
Posterior Density ◽  
Natural Rainfall ◽  
Credible Intervals ◽  
Small Sample Sizes ◽  
Variance Estimates ◽  
Highest Posterior Density ◽  
Normal Gamma Prior

Natural disasters such as drought and flooding are the consequence of severe rainfall fluctuation, and rainfall amount data often contain both zero and positive observations, thus making them fit a delta-lognormal distribution. By way of comparison, rainfall dispersion may not be similar in enclosed regions if the topography and the drainage basin are different, so it can be evaluated by the ratio of variances. To estimate this, credible intervals using the highest posterior density based on the normal-gamma prior (HPD-NG) and the method of variance estimates recovery (MOVER) for the ratio of delta-lognormal variances are proposed. Monte Carlo simulation was used to assess the performance of the proposed methods in terms of coverage probability and relative average length. The results of the study reveal that HPD-NG performed very well and was able to meet the requirements in various situations, even with a large difference between the proportions of zeros. However, MOVER is the recommended method for equal small sample sizes. Natural rainfall datasets for the northern and northeastern regions of Thailand are used to illustrate the practical use of the proposed credible intervals.

scholarly journals Sample Size Requirements for Calibrated Approximate Credible Intervals for Proportions in Clinical Trials

2021 ◽  
Vol 18 (2) ◽  
pp. 595
Author(s):  
Fulvio De Santis ◽  
Stefania Gubbiotti
Keyword(s):  
Clinical Trials ◽  
Posterior Probability ◽  
Interval Estimation ◽  
Small Sample ◽  
Sample Sizes ◽  
Posterior Density ◽  
Unknown Parameters ◽  
Credible Intervals ◽  
Small Sample Sizes ◽  
Highest Posterior Density

In Bayesian analysis of clinical trials data, credible intervals are widely used for inference on unknown parameters of interest, such as treatment effects or differences in treatments effects. Highest Posterior Density (HPD) sets are often used because they guarantee the shortest length. In most of standard problems, closed-form expressions for exact HPD intervals do not exist, but they are available for intervals based on the normal approximation of the posterior distribution. For small sample sizes, approximate intervals may be not calibrated in terms of posterior probability, but for increasing sample sizes their posterior probability tends to the correct credible level and they become closer and closer to exact sets. The article proposes a predictive analysis to select appropriate sample sizes needed to have approximate intervals calibrated at a pre-specified level. Examples are given for interval estimation of proportions and log-odds.

scholarly journals The Confidence Density for Correlation

Sankhya A ◽  
2021 ◽  
Author(s):  
Gunnar Taraldsen
Keyword(s):  
Explicit Formula ◽  
Posterior Distribution ◽  
Hypergeometric Functions ◽  
Real Data ◽  
Numerical Calculations ◽  
Posterior Density ◽  
Fiducial Inference ◽  
Objective Prior ◽  
Confidence Distribution ◽  
New Formula

AbstractInference for correlation is central in statistics. From a Bayesian viewpoint, the final most complete outcome of inference for the correlation is the posterior distribution. An explicit formula for the posterior density for the correlation for the binormal is derived. This posterior is an optimal confidence distribution and corresponds to a standard objective prior. It coincides with the fiducial introduced by R.A. Fisher in 1930 in his first paper on fiducial inference. C.R. Rao derived an explicit elegant formula for this fiducial density, but the new formula using hypergeometric functions is better suited for numerical calculations. Several examples on real data are presented for illustration. A brief review of the connections between confidence distributions and Bayesian and fiducial inference is given in an Appendix.

scholarly journals Efeito materno e paterno sobre as taxas de fertilização e eclosão em curimba (Prochilodus lineatus)

2012 ◽  
Vol 64 (6) ◽  
pp. 1584-1590 ◽  
Author(s):  
I.B. Allaman ◽  
R.T.F. Freitas ◽  
A.T.M. Viveiros ◽  
A.F. Nascimento ◽  
G.R. Oliveira ◽  
...  
Keyword(s):  
Posterior Density ◽  
Prochilodus Lineatus ◽  
Highest Posterior Density

Avaliou-se o quanto fêmeas e machos contribuem para a variação total das taxas de fertilização e de eclosão em curimba (Prochilodus lineatus). Utilizou-se sêmen criopreservado proveniente de cinco machos para fertilizar ovócitos de seis fêmeas em um esquema fatorial cruzado 5x6, totalizando 30 famílias. Além das características reprodutivas dos machos e fêmeas, foram avaliadas as taxas de fertilização e eclosão para cômputo dos efeitos materno e paterno. Os componentes da variância foram estimados por meio da máxima verossimilhança restrita, sendo construídos intervalos Highest Posterior Density (HPD) para cada componente. Verificou-se que as fêmeas contribuíram muito mais para a variação total em relação aos machos para as taxas de fertilização e eclosão. Para a taxa de fertilização, as fêmeas contribuíram com 26,3% da variação total e os machos com 8,9%. Em relação à taxa de eclosão, as fêmeas contribuíram com 11,9% e os machos com 1,6%. Concluiu-se que houve efeito materno sobre as taxas de fertilização e eclosão e que o efeito paterno avaliado individualmente foi pouco expressivo ou até mesmo insignificante.

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