• 한국신뢰성학회:학술대회논문집
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• 한국신뢰성학회 2002년도 정기학술대회
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• pp.273-273
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• 2002

In this paper, we investigate a software release policy with software reliability growth factor during the warranty period by assuming that the software reliability growth is assumed to occur after the testing phase with probability p and the software reliability growth is not assumed to occur after the testing phase with probability 1-p. The optimal release policy to minimize the expected total software cost is discussed. Numerical examples are shown to illustrate the results of the optimal policy. And we consider a Bayesian decision theoretic approach to determine an optimal software release policy. This approach enables us to update our uncertainty when determining optimal software release time, When the failure time is Weibull distribution with uncertain parameters, a bayesian approach is established. Finally, numerical examples are presented for illustrative propose.

• 대한산업공학회지
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• 제26권3호
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• pp.193-199
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• 2000

In many studies, considerable attention has been focussed upon choosing a model which represents underlying process of time series and forecasting the future. In the real world, however, there may be some cases that one model can not reflect all the characteristics of original time series. Under such circumstances, we may get better performance by combining the forecasts from several models. The most popular methods for combining forecasts involve taking a weighted average of multiple forecasts. But the weights are usually unstable. In cases the assumptions of normality and unbiasedness for forecast errors are satisfied, a Bayesian method can be used for updating the weights. In the real world, however, there are many circumstances the Bayesian method is not appropriate. This paper proposes a PNN(Probabilistic Neural Net) approach as a method for combining forecasts that can be applied when the assumption of normality or unbiasedness for forecast errors is not satisfied. In this paper, PNN method, which is similar to Bayesian approach, is suggested as an updating method of the unstable weights in the combination of the forecasts. The PNN method has been usually used in the field of pattern recognition. Unlike the Bayesian approach, it requires no assumption of a specific prior distribution because it gets probabilities by using the distribution estimated from given data. Empirical results reveal that the PNN method offers superior predictive capabilities.

• Structural Engineering and Mechanics
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• 제69권4호
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• pp.361-369
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• 2019

The determination of Paris' law parameters based on crack growth experiments is an important procedure of fatigue life assessment. However, it is a challenging task because it involves various sources of uncertainty. This paper proposes a novel probabilistic method, termed the S-N Paris law (SNPL) method, to quantify the uncertainties underlying the Paris' law parameters, by finding the best estimates of their statistical parameters from the S-N curve data using a Bayesian approach. Through a series of steps, the SNPL method determines the statistical parameters (e.g., mean and standard deviation) of the Paris' law parameters that will maximize the likelihood of observing the given S-N data. Because the SNPL method is based on a Bayesian approach, the prior statistical parameters can be updated when additional S-N test data are available. Thus, information on the Paris' law parameters can be obtained with greater reliability. The proposed method is tested by applying it to S-N curves of 40H steel and 20G steel, and the corresponding analysis results are in good agreement with the experimental observations.

• 한국전산응용수학회:학술대회논문집
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• 한국전산응용수학회 2003년도 KSCAM 학술발표회 프로그램 및 초록집
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• pp.13.2-13
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• 2003

We propose some properties of Bayesian fuzzy hypotheses testing by revision for prior possibility distribution and posterior possibility distribution using weighted fuzzy hypotheses versus on with loss function.

• Journal of applied mathematics & informatics
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• 제6권2호
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• pp.589-598
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• 1999

Classification errors are included in sampling -with -re-placement model where items are sampled from a Bernoulli process. Bayesian imperfect inspection model is considered. In addition con-jugate prior and predctive densities for imperfect inspection model are obtained.

• Animal Bioscience
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• 제36권12호
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• pp.1806-1820
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• 2023

Objective: The present study was aimed primarily for estimating various genetic parameters (heritability, genetic correlations) of reproduction (age at first calving [AFC], first service period [FSP]); production (first lactation milk, solid-not fat, and fat yield) and lifetime traits (lifetime milk yield, productive life [PL], herd life [HL]) in Tharparkar cattle to check the association of reproduction traits with lifetime traits through two different methods (Frequentist and Bayesian) for comparative purpose. Methods: Animal breeding data of Tharparkar cattle (n = 964) collected from Livestock farm unit of ICAR-NDRI Karnal for the period 1990 through 2019 were analyzed using a Frequentist least squares maximum likelihood method (LSML; Harvey, 1990) and a multi-trait Bayesian-Gibbs sampler approach (MTGSAM) for genetic correlations estimation of all the traits. Estimated breeding values of sires was obtained by BLUP and Bayesian analysis for the production traits. Results: Heritability estimates of most of the traits were medium to high with the LSML (0.20±0.44 to 0.49±0.71) and Bayesian approach (0.24±0.009 to 0.61±0.017), respectively. However, more reliable estimates were obtained using the Bayesian technique. A higher heritability estimate was obtained for AFC (0.61±0.017) followed by first lactation fat yield, first lactation solid-not fat yield, FSP, first lactation milk yield (FLMY), PL (0.60±0.013, 0.60±0.006, 0.57±0.024, 0.57±0.020, 0.42±0.025); while a lower estimate for HL (0.38±0.034) by MTGSAM approach. Genetic and phenotypic correlations were negative for AFC-PL, AFC-HL, FSP-PL, and FSP-HL (-0.59±0.19, -0.59±0.24, -0.38±0.101 and -0.34±0.076) by the multi-trait Bayesian analysis. Conclusion: Breed and traits of economic importance are important for selection decisions to ensure genetic gain in cattle breeding programs. Favourable genetic and phenotypic correlations of AFC with production and lifetime traits compared to that of FSP indicated better scope of AFC for indirect selection of life-time traits at an early age. This also indicated that the present Tharparkar cattle herd had sufficient genetic diversity through the selection of AFC for the improvement of first lactation production and lifetime traits.

• Journal of the Korean Statistical Society
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• 제32권4호
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• pp.411-423
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• 2003

In this paper we develop a method for calculating a probability that a particular generalized variance is the smallest of all the K multivariate normal generalized variances. The method gives a way of comparing K multivariate populations in terms of their dispersion or spread, because the generalized variance is a scalar measure of the overall multivariate scatter. Fully parametric frequentist approach for the probability is intractable and thus a Bayesian method is pursued using a variant of weighted Monte Carlo (WMC) sampling based approach. Necessary theory involved in the method and computation is provided.

• 산업공학
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• 제13권2호
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• pp.211-216
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• 2000

A methodology that determines the optimal shutdown time of a nuclear power plant is suggested. The shutdown time is decided considering the trade off between the cost of accident and the loss of profit due to the early shutdown. We adopt the bayesian approach in manipulating the model parameter that predicts the accidents. We build decision tree models and apply dynamic programming approach to decide whether to shutdown immediately or operate one more period. The branch parameters in decision trees are updated by bayesian approach. We apply real data to this model and provide the cost of accidents that guarantees the immediate shutdown.

• Communications for Statistical Applications and Methods
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• 제13권1호
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• pp.191-204
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• 2006

This paper develops a Bayesian method to derive the optimal sequential preventive maintenance(PM) policy by determining the PM schedules which minimize the mean cost rate. Such PM schedules are derived based on a general sequential imperfect PM model proposed by Lin, Zuo and Yam(2000) and may have unequal length of PM intervals. To apply the Bayesian approach in this problem, we assume that the failure times follow a Weibull distribution and consider some appropriate prior distributions for the scale and shape parameters of the Weibull model. The solution is proved to be finite and unique under some mild conditions. Numerical examples for the proposed optimal sequential PM policy are presented for illustrative purposes.

• Communications for Statistical Applications and Methods
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• 제6권3호
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• pp.801-812
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• 1999

Change-point hazard rate models arise for example in applying "burn-in" techniques to screen defective items and in studing times until undesirable side effects occur in clinical trials. Sometimes in screening defectives it might be sensible to model two stages of burn-in. In a clinical trial there might be an initial hazard rate for a side effect which after a period of time changes to an intermediate hazard rate before settling into a long term hazard rate. In this paper we consider the multiple change points hazard rate model. The classical approach's asymptotics can be poor for the small to all moderate sample sizes often encountered in practice. We propose a Bayesian approach avoiding asymptotics to provide more reliable inference conditional only upon the data actually observed. The Bayesian models can be fitted using simulation methods. Model comparison is made using recently developed Bayesian model selection criteria. The above methodology is applied to a generated data and to a generated data and the Lawless(1982) failure times of electrical insulation.