• International Journal of Reliability and Applications
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• 제10권2호
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• pp.63-79
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• 2009

A new bivariate linear failure rate distribution is introduced through a shock model. It is proved that the marginal distributions of this new bivariate distribution are linear failure rate distributions. The joint moment generating function of the bivariate distribution is derived. Mixtures of bivariate linear failure rate distributions are also discussed. Application to a real data is given.

• Communications for Statistical Applications and Methods
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• 제18권4호
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• pp.467-475
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• 2011

This paper develops the noninformative priors for the stress-strength reliability from one parameter generalized exponential distributions. When this reliability is a parameter of interest, we develop the first, second order matching priors, reference priors in its order of importance in parameters and Jeffreys' prior. We reveal that these probability matching priors are not the alternative coverage probability matching prior or a highest posterior density matching prior, a cumulative distribution function matching prior. In addition, we reveal that the one-at-a-time reference prior and Jeffreys' prior are actually a second order matching prior. We show that the proposed reference prior matches the target coverage probabilities in a frequentist sense through a simulation study and a provided example.

• Communications for Statistical Applications and Methods
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• 제20권5호
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• pp.387-394
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• 2013

In this paper, we develop the noninformative priors for the ratio of the scale parameters in the inverted exponential distributions. The first and second order matching priors, the reference prior and Jeffreys prior are developed. It turns out that the second order matching prior matches the alternative coverage probabilities, is a cumulative distribution function matching prior and is a highest posterior density matching prior. In addition, the reference prior and Jeffreys' prior are the second order matching prior. We show that the proposed reference prior matches the target coverage probabilities in a frequentist sense through a simulation study as well as provide an example based on real data is given.

• Journal of the Korean Data and Information Science Society
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• 제24권4호
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• pp.949-957
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• 2013

In this paper, we consider the problem of testing the equality of the scale parameters in two parameter exponential distributions. We propose Bayesian testing procedures for the equality of the scale parameters under the noninformative priors. The noninformative prior is usually improper which yields a calibration problem that makes the Bayes factor to be defined up to a multiplicative constant. Thus, we propose the default Bayesian testing procedures based on the fractional Bayes factor and the intrinsic Bayes factors under the reference priors. Simulation study and an example are provided.

• 품질경영학회지
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• 제42권1호
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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.

• Journal of the Korean Statistical Society
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• 제20권1호
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• pp.57-66
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• 1991

This paper deals with the problem of estimating an arbitrary piecewise continuous function of the parameter under squared error loss in the one parameter exponential family. Using Blyth's(1951) method sufficient conditions are given for the admissibility of (possibly generalized Bayes) estimators. Also, some examples are provided for normal, binomial, and gamma distributions.

• KIEE International Transactions on Power Engineering
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• 제3A권3호
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• pp.155-160
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• 2003

Reliability assessment of power systems has been an important topic for the past several decades. It is becoming even more important nowadays as the power market moves toward a new competitive environment. This paper deals with two topics on reliability assessment. The first is how to select probability distributions and determine their parameters to model the probabilistic events in a power system. The second is how to consider restorative actions in the assessment, which directly influence reliability indices. This paper proposes simple but convincing alternative solutions on the two topics. In the case study, this paper shows the influences of the probability distributions that are used in power system modeling.

• 대한수학회논문집
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• 제26권4호
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• pp.709-720
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• 2011

We obtain special type of differential equations which their solution are random variable with known continuous density function. Stochastic differential equations (SDE) of continuous distributions are determined by the Fokker-Planck theorem. We approximate solution of differential equation with numerical methods such as: the Euler-Maruyama and ten stages explicit Runge-Kutta method, and analysis error prediction statistically. Numerical results, show the performance of the Rung-Kutta method with respect to the Euler-Maruyama. The exponential two parameters, exponential, normal, uniform, beta, gamma and Parreto distributions are considered in this paper.

• Management Science and Financial Engineering
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• 제18권2호
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• pp.5-11
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• 2012

In this paper, stochastic scheduling problems are considered when processing times and due dates follow arbitrary distributions and due dates are either common or exchangeable. For maximizing the expected number of early jobs, two policies, one, based on pairwise comparisons of the processing times, and the other, based on survivabilities, are introduced. In addition, it is shown that the former guarantees optimal solutions when the processing times and due dates are deterministic and that the latter guarantees optimal solutions when the due dates follow exponential distributions. Then a new approach, exploiting the two policies, is proposed and analyzed which turns out to give better job sequences in many situations. In fact, the new approach guarantees optimal solutions both when the processing times and due dates are deterministic and when the due dates follow exponential distributions.

• Journal of the Korean Data and Information Science Society
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• 제19권4호
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• pp.1059-1071
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• 2008

In a balanced factorial design with a nested factor where crossed factors as well as a nested factor exist simultaneously, powers of the rank transformed FR statistic for testing the main, nested and interaction effects are superior to those of the parametric F statistic. In heavy tailed distributions such as exponential and double exponential distributions, powers of the FR statistic show much higher level than those of the F statistic. Further powers of the F and FR statistic for testing the main effect show the highest level in an absolute size as compared with powers of the F and FR statistic for testing the nested and interaction effects. However powers of the FR statistic for testing the nested and interaction effects rather than the main effect are greater in a relative size than powers of F statistic for the all population distributions.