• Journal of the Korean Statistical Society
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• 제28권1호
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• pp.73-92
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• 1999

In Bayesian model selection or testing problems, one cannot utilize standard or default noninformative priors, since these priors are typically improper and are defined only up to arbitrary constants. The resulting Bayes factors are not well defined. A recently proposed model selection criterion, the intrinsic Bayes factor overcomes such problems by using a part of the sample as a training sample to get a proper posterior and then use the posterior as the prior for the remaining observations to compute the Bayes factor. Surprisingly, such Bayes factor can also be computed directly from the full sample by some proper priors, namely intrinsic priors. The present paper explains how to derive intrinsic priors for simple tree ordered exponential means. Some numerical results are also provided to support theoretical results and compare with classical methods.

• International Journal of Reliability and Applications
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• 제13권1호
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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 the Korean Statistical Society
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• 제35권1호
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• pp.63-77
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• 2006

Maximum product of spacings estimator is proposed in this paper as a competent alternative of maximum likelihood estimator for the parameters of exponentiated-Weibull distribution, which does work even when the maximum likelihood estimator does not exist. In addition, a Bayes type estimator known as generalized maximum likelihood estimator is also obtained for both of the shape parameters of the aforesaid distribution. Though, the closed form solutions for these proposed estimators do not exist yet these can be obtained by simple appropriate numerical techniques. The relative performances of estimators are compared on the basis of their relative risk efficiencies obtained under symmetric and asymmetric losses. An example based on simulated data is considered for illustration.

• Communications for Statistical Applications and Methods
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• 제27권1호
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• pp.65-77
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• 2020

Geometric charts are effective in monitoring the fraction nonconforming in high-quality processes. The in-control fraction nonconforming is unknown in most actual processes; therefore, it should be estimated using the Phase I sample. However, if the Phase I sample size is small the practitioner may not achieve the desired in-control performance because estimation errors can occur when the parameters are estimated. Therefore, in this paper, we adjust the control limits of geometric charts with the bootstrap algorithm to improve the in-control performance of charts with smaller sample sizes. The simulation results show that the adjustment with the bootstrap algorithm improves the in-control performance of geometric charts by controlling the probability that the in-control average run length has a value greater than the desired one. The out-of-control performance of geometric charts with adjusted limits is also discussed.

• 품질경영학회지
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• 제26권4호
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• pp.265-276
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• 1998

A commercial nuclear power station contains at least two emergency diesel generators(EDG) to control the risk of severe core damage during station blackout accidnets. Therefore, thereliability of the EDG's to start and load-run on demand must be maintained at a sufficiently high level. Until now, a simple assessment of start and load-run success rates was used to calculate the EDG reliability. However, this method has been found to contain many defects. Recently, the work of Martz et al.(1996) proposed the use of the Bayes estimator to find EDG reliability. Shim(1996) proposed a confidence interval for the Bayes estimator, compare the above two methods. In this paper, we introduce the notion of "Composite Reliablility" to estimate the reliability of nuclear-power plant EDG, and using practical examples, illustrate which method is more a, pp.opriate in our situation.situation.

• Journal of the Korean Data and Information Science Society
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• 제4권
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• pp.87-95
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• 1993

We find a class of admissible Bayes estimator for the mean vector ${\theta}=({\theta}_{1},{\theta}_{2},...,{\theta}_{p}$ of Poisson distribution under a LINEX loss function. The Monte Carlo Simulation is performed to compare the emprical Bayes estimater under the LINEX loss function and weighted squared error loss respectively.

• Journal of the Korean Statistical Society
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• 제16권2호
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• pp.102-112
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• 1987

This paper treats the problem of estimating an arbitrary parametric function in the case when the parameter and sample spaces are countable and the decision space is arbitrary. Using the notions of a stepwise Bayesian procedure and finite admissibility, a theorem is proved. It shows that under some assumptions, every finitely admissible estimator is unique stepwise Bayes with respect to a finite or countable sequence of mutually orthogonal priors with finite supports. Under an additional assumption, it is shown that the converse is true as well. The first can be also extended to the case when the parameter and sample space are arbitrary, i.e., not necessarily countable, and the underlying probability distributions are discrete.

• Journal of the Korean Data and Information Science Society
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• 제8권1호
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• pp.31-39
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• 1997

we shall propose some Bayes estimators and some generalized maximum likelihood estimators for reliability of a two-unit hot standby system with perfect switch based upon a complete sample of failure times observed from the exponential model and compare the peformances of the proposed estimators in terms of mean squared error.

• 품질경영학회지
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• 제23권3호
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• pp.45-56
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• 1995

The method of lot by lot quality protection for sampling inspection by variables is widely used in quality control. In case of sampling inspection being done repeatedly, one can use the information from the previous sampling inspection to improve current estimates. This article shows that empirical Bayes estimator is superior to the usual sample mean in repeated sampling inspection by variables.

• Journal of applied mathematics & informatics
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• 제3권1호
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• pp.55-64
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• 1996

Let $X_1, ....$X_P be p($\geq$2) independent random variables, where each X1 has a gamma distribution with $k_i and ${\heta}_i$. The problem is to simultaneously estimate p gammar parameters ${\heta}_i$ under entropy loss where the parameters are believed priori. Hierarchical bayes(HB) and empirical bayes(EB) estimators are investigated. Next computer simulation is studied to compute the risk percentage improvement of the HB, EB and the estimator of Dey et al.(1987) compared to MVUE of ${\heta}$.