• Journal of the Korean Data and Information Science Society
• /
• v.1
• /
• pp.35-45
• /
• 1990

The problem of estimating the reliability using the Bayesian approach and the prior information about tile reliability of a lognormal distribution is considered. Some Bayes estimators are proposed and studied under the squared error loss and tile Harris loss. Also Monte Carlo simulations are carried out to examine the performances of the proposed estimators and results are provided in the tables.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.33 no.10
• /
• pp.1163-1170
• /
• 2009

Reliability analysis is of great importance in the advanced product design, which is to evaluate reliability due to the associated uncertainties. There are three types of uncertainties: the first is the aleatory uncertainty which is related with inherent physical randomness that is completely described by a suitable probability model. The second is the epistemic uncertainty, which results from the lack of knowledge due to the insufficient data. These two uncertainties are encountered in the input variables such as dimensional tolerances, material properties and loading conditions. The third is the metamodel uncertainty which arises from the approximation of the response function. In this study, an integrated method for the reliability analysis is proposed that can address all these uncertainties in a single Bayesian framework. Markov Chain Monte Carlo (MCMC) method is employed to facilitate the simulation of the posterior distribution. Mathematical and engineering examples are used to demonstrate the proposed method.

• Journal of the Korean Society for Aeronautical & Space Sciences
• /
• v.47 no.10
• /
• pp.747-752
• /
• 2019

By using the failure information and the cumulative test execution time obtained by performing the reliability growth test, it is possible to estimate the parameter of the reliability growth model, and the Mean Time Between Failure (MTBF) of the product can be predicted through the parameter estimation. However the failure information could be acquired periodically or the number of sample data of the obtained failure information could be small. Because there are various constraints such as the cost and time of test or the characteristics of the product. This may cause the error of the parameter estimation of the reliability growth model to increase. In this study, the Bayesian method is applied to estimating the parameters of the reliability growth model when the number of sample data for the fault information is small. Simulation results show that the estimation accuracy of Bayesian method is more accurate than that of Maximum Likelihood Estimation (MLE) respectively in estimation the parameters of the reliability growth model.

• Journal of the Korean Data and Information Science Society
• /
• v.22 no.5
• /
• pp.977-989
• /
• 2011

The half logistic distribution has been used intensively in reliability and survival analysis especially when the data is censored. In this paper, we provide Bayesian estimation of the shape parameter and reliability function in the generalized half logistic distribution based on progressively Type-II censored data under various loss functions. We here consider conjugate prior and noninformative prior and corresponding posterior distributions are obtained. As an illustration, we examine the validity of our estimation using real data and simulated data.

• Journal of the Korean Data and Information Science Society
• /
• v.22 no.3
• /
• pp.565-574
• /
• 2011

The exponenetiated distribution has been used in reliability and survival analysis especially when the data is censored. In this paper, we derive Bayesian estimation of shape parameter and reliability function in the exponenetiated half triangle distribution based on Type-I hybrid censored data. Here we consider conjugate prior and noninformative prior and obtained corresponding posterior distributions. As an illustration, the mean square errors of the estimates are computed. Comparisons are made between these estimators using Monte Carlo simulation study.

• Journal of Korean Society of Industrial and Systems Engineering
• /
• v.35 no.2
• /
• pp.98-105
• /
• 2012

This paper describes the Bayesian approach for reliability demonstration test based on the samples from a finite population. The Bayesian approach involves the technical method about how to combine the prior distribution and the likelihood function to produce the posterior distribution. In this paper, the hypergeometric distribution is adopted as a likelihood function for a finite population. The conjugacy of the beta-binomial distribution and the hypergeometric distribution is shown and is used to make a decision about whether to accept or reject the finite population judging from a viewpoint of faulty goods. A numerical example is also given.

• Communications for Statistical Applications and Methods
• /
• v.18 no.5
• /
• pp.603-613
• /
• 2011

Exponentiated distribution has been used in reliability and survival analysis especially when the data is censored. In this paper, we derive Bayesian estimation of the shape parameter, reliability function and failure rate function in the exponentiated distribution family based on Type-II right censored data. We here consider conjugate prior and noninformative prior and corresponding posterior distributions are obtained. As an illustration, the mean square errors of the estimates are computed. Comparisons are made between these estimators using Monte Carlo simulation study.

• International Journal of Reliability and Applications
• /
• v.14 no.2
• /
• pp.55-70
• /
• 2013

This paper deals with the Bayesian analysis of the failure data of a repairable mechanical system subject to minimal repairs and periodic overhauls. The effect of overhauls on the reliability of the system is modeled by a proportional age reduction model and the failure process between two successive overhauls is assumed to be 2-parameter Engelhardt-Bain process (2-EBP). Power Law Process (PLP) model has a disadvantage which 2-EBP can overcome. On the basis of the observed data and of a number of suitable prior densities, point and interval estimation of model parameters, as well as quantities of relevant interest are found. Also hypothesis tests on the effectiveness of performed overhauls have been developed using Bayes factor. Sensitivity analysis of improvement parameter is carried out. Finally, a numerical application is used to illustrate the proposed method.

• Journal of Korea Game Society
• /
• v.11 no.6
• /
• pp.53-60
• /
• 2011

Since the importance of software reliability for game service increases continuously, the reliability evaluation becomes very important. This research performed an experiment which was intended to analyze the effect of software verification and validation, a representative activity of the software development process, on the software reliability. The results from the experiments provided the reliability evaluation based on the development process (e.g., Bayesian Belief Network based reliability estimation) with very useful bases.

• Nuclear Engineering and Technology
• /
• v.46 no.1
• /
• pp.55-62
• /
• 2014

A method for estimating software reliability for nuclear safety software is proposed in this paper. This method is based on the software reliability growth model (SRGM), where the behavior of software failure is assumed to follow a non-homogeneous Poisson process. Two types of modeling schemes based on a particular underlying method are proposed in order to more precisely estimate and predict the number of software defects based on very rare software failure data. The Bayesian statistical inference is employed to estimate the model parameters by incorporating software test cases as a covariate into the model. It was identified that these models are capable of reasonably estimating the remaining number of software defects which directly affects the reactor trip functions. The software reliability might be estimated from these modeling equations, and one approach of obtaining software reliability value is proposed in this paper.