• Journal of the Korean Data and Information Science Society
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• v.17 no.2
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• pp.521-527
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• 2006

In this paper, we consider the Bayesian hypotheses testing for independence in bivariate exponential model. In Bayesian testing problem, we use the noninformative priors for parameters which are improper and are defined only up to arbitrary constants. And we use the recently proposed hypotheses testing criterion called the fractional Bayes factor. Also we give some numerical results to illustrate our results.

• Journal of the Korean Data and Information Science Society
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• v.25 no.4
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• pp.921-929
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• 2014

A bivariate exponential distribution with a location parameter is proposed as a model for a two-component shared load system with a guarantee time. Some statistical properties of the proposed model are investigated. The maximum likelihood estimators and uniformly minimum variance unbiased estimators of the parameters, mean time to failure, and the reliability function of system are obtained with unknown guarantee time. Simulation studies are given to illustrate the results.

• 한국데이터정보과학회:학술대회논문집
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• 2006.04a
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• pp.327-333
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• 2006

In this paper, we consider the Bayesian hypotheses testing for independence in bivariate exponential model. In Bayesian testing problem, we use the noninformative priors for parameters which are improper and are defined only up to arbitrary constants. And we use the recently proposed hypotheses testing criterion called the fractional Bayes factor. Also we give some numerical results to illustrate our results.

• Journal of the Korean Data and Information Science Society
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• v.19 no.4
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• pp.1391-1396
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• 2008

In this paper, we consider two components system which the lifetimes have Marshall and Olkin's bivariate exponential model with bivariate type I censored data. We propose a Bayesian independent test procedure for above model using fractional Bayes factor method by O'Hagan based on improper prior distributions. And we compute the fractional Bayes factor and the posterior probabilities for the hypotheses, respectively. Also we select a hypothesis which has the largest posterior probability. Finally a numerical example is given to illustrate our Bayesian testing procedure.

• Journal of the Korean Data and Information Science Society
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• v.18 no.2
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• pp.553-560
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• 2007

In this paper, we consider two components system which lifetimes have Freund's bivariate exponential model with equal failure rates. We propose Bayesian multiple comparisons procedure for the failure rates of I Freund's bivariate exponential populations based on Dirichlet process priors(DPP). The family of DPP is applied in the form of baseline prior and likelihood combination to provide the comparisons. Computation of the posterior probabilities of all possible hypotheses are carried out through Markov Chain Monte Carlo(MCMC) method, namely, Gibbs sampling, due to the intractability of analytic evaluation. The whole process of multiple comparisons problem for the failure rates of bivariate exponential populations is illustrated through a numerical example.

• Journal of the Korean Data and Information Science Society
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• v.10 no.1
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• pp.37-45
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• 1999

In this paper, we consider two components system having Marshall-Olkin's bivariate exponential model. For the bivariate random censorship, we obtain maximum likelihood estimators of parameters and system reliability. And we propose the methods of homogeniety and independence tests using asymptotic normality. Also we compute the estimators and p-values of the testings through Monte Carlo simulation.

• Journal of Korean Society for Quality Management
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• v.25 no.4
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• pp.79-87
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• 1997

In this paper, we obtain maximum likelihood estimator(MLE) of a parallel system reliability for the Marshall and Olkin's bivariate exponential model with birariate type 1 consored data. The asymptotic normal distribution of the estimator is obtained. Also we construct an a, pp.oximate confidence interval for the reliability based on MLE. We present a numerical study for obtaining MLE and a, pp.oximate confidence interval of the reliability.

• International Journal of Reliability and Applications
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• v.13 no.1
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• pp.37-47
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• 2012

In this article we attempted reliability analysis of a component under the stress-strength pattern with both classical as well as Bayesian techniques. The main focus is made to develop the theory for dealing the reliability problems in various circumstances for bivariate environmental set up in context of Bayesian paradigm. A stress-strength based model describes the life of a component which has strength (Y) and is subjected to stress(X). We develop the Bayes and moment estimators of reliability of a component for each of the three possible conditions, under the assumption that the two stresses (i.e. $X_1$ and $X_2$) on a component are dependent and follow a Bivariate exponential (BVE) of Marshall-Olkin distribution, the strength of a component (Y) following exponential distribution is independent of the stresses. The simulation study is performed with Markov Chain Monte Carlo technique via Gibbs sampler to obtain the estimates of Bayes estimators of reliability, are compared with moment estimators of reliabilities on the basis of absolute biases.

• Journal of Korean Society for Quality Management
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• v.18 no.2
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• pp.101-116
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• 1990

The objectives of this thesis are : first, to estimate the parameters and Pr[X < Y] in the Marshall and Olkin's Bivariate Exponential Distribution ; and secondly, to compare the Bayes estimators of Pr[X < Y] with maximum likelihood estimator of Pr[X < Y] in the Marshall and Olkin's Bivariate Exponential Distribution. Through the Monte Carlo Simulation, we observed that the Bayes estimators of Pr[X < Y] perform better than the maximum likelihood estimator of Pr[X < Y] and the Bayes estimator of Pr[X < Y] with gamma prior distribution performs better than with vague prior distribution with respect to bias and mean squared error in the Marshall and Olkin's Bivariate Exponential Distribution.

• Journal of Korean Society for Quality Management
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• v.42 no.1
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• pp.1-14
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• 2014

Purpose: In this paper, the minimal repair-replacement warranty policy is used to carry out a warranty cost analysis with warranty servicing times and failure times that are statistically correlated to bivariate distributions. Methods: Based on the developed approach by Park and Pham (2012a), we investigate the property of the Freund's bivariate exponential distribution and obtain the number of warranty services using the field data to conduct the warranty cost analysis. Results: Maximum likelihood estimates are presented to estimate the parameters and the warranty model is investigated using a Freund's bivariate exponential distribution. A numerical example is discussed to deal with the applicability of the developed approach in the paper. Conclusion: A novel approach of analyzing the warranty cost is proposed for a product in which failure times and warranty servicing times are used simultaneously to investigate the eligibility of a warranty claim.