• Journal of Applied Reliability
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• v.2 no.2
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• pp.113-119
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• 2002

The estimation of mean lifetimes in presence of interval censoring with replacement procedure are examined when the distributions of lifetimes are exponential. It is assumed that, due to physical restrictions and/or economic constraints, the number of failures is investigated only at several inspection times during the lifetime test. The maximum likelihood estimator is found in an implicit form. The Cramer-Rao lower bounds of the estimates are found in places of variances and by simulations the properties of the estimates are examined.

• Journal of the Korean Statistical Society
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• v.35 no.3
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• pp.317-329
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• 2006

In the problem of estimating the error variance in the balanced fixed- effects one-way analysis of variance (ANOVA) model, Ghosh (1994) proposed hierarchical Bayes estimators and raised a conjecture for which all of his hierarchical Bayes estimators are admissible. In this paper we prove this conjecture is true by representing one-way ANOVA model to the distributional form of a multiparameter exponential family.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.60 no.9
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• pp.1754-1760
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• 2011

In this paper, a systematic design of a robust nonlinear multivariable variable structure controller based on state dependent nonlinear form is presented for the control of MIMO uncertain affine nonlinear systems with mismatched uncertainties and matched disturbance. After a MIMO uncertain affine nonlinear system is represented in the form of state dependent nonlinear system, a systematic design of a robust nonlinear variable structure controller is presented. To be linear in the closed loop resultant dynamics, the linear sliding surface is applied. A corresponding diagonalized control input is proposed to satisfy the closed loop global exponential stability and the existence condition of the sliding mode on the linear sliding surface, which will be investigated in Theorem 1. Through a design example and simulation study, the usefulness of the proposed controller is verified.

• KOREAN JOURNAL OF CROP SCIENCE
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• v.51 no.4
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• pp.362-368
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• 2006

A pot experiment was conducted to investigate the effects of soil burial depth on seedling emergences of rice (Oryza sativa) and Echinochloa spp. and to model such effects for mathematical prediction of seedling emergences. When the Gompertz curve was fitted at each soil depth, the parameter C decreased in a logistic form with increasing soil depth, while the parameter M increased in an exponential form and the parameter B appeared to be constant. The Gompertz curve was combined by incorporating the logistic model for the parameter C, the exponential model for the parameter M, and the constant for the parameter B. This combined model well described seedling emergence of rice and Echinochloa species as influenced by soil burial depth and predicted seedling emergence at a given time after sowing and a soil burial depth. Thus, the combined model can be used to simulate seedling emergence of crop sown in different soil depths and weeds present in various soil depths.

• International Journal of Reliability and Applications
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• v.2 no.3
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• pp.189-197
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• 2001

The estimation of mean lifetimes in presence of interval censoring with mixed replacement procedure is examined when the distributions of lifetimes are exponential. It is assumed that, due to physical restrictions and/or economic constraints, the number of failures is investigated only at several inspection times during the lifetime test; thus there is interval censoring. The maximum likelihood estimator is found in an implicit form. The Cramor-Rao lower bound, which is the asymptotic variance of the estimator, is derived. The estimation of mean lifetimes for competing failures model has been expanded.

• The Korean Journal of Applied Statistics
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• v.22 no.1
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• pp.221-235
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• 2009

This manuscript illustrates the comparative study between ARIMA and Exponential Smoothing modeling to develop forest fire forecasting system using different weather parameters. In this paper, authors have developed the most suitable and closest forecasting models like ARIMA and Exponential Smoothing techniques using different weather parameters. Authors have considered the extremes of the Wind speed, Radiation, Maximum Temperature and Deviation Temperature of the Summer Season form March to June month for the Ranchi Region in Jharkhand. The data is taken by own resource with the help of Automatic Weather Station. This paper consists a deep study of the effect of extreme values of the different parameters on the weather fluctuations which creates forest fires in the region. In this paper, the numerical illustration has been incorporated to support the present study. Comparative study of different suitable models also incorporated and best fitted model has been tested for these parameters.

• Journal of the Korean Mathematical Society
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• v.57 no.6
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• pp.1573-1590
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• 2020

In this paper, we classify all solutions bounded from below to uniformly elliptic equations of second order in the form of Lu(x) = a_ij(x)D_iju(x) + b_i(x)D_iu(x) + c(x)u(x) = f(x) or Lu(x) = D_i(a_ij(x)D_ju(x)) + b_i(x)D_iu(x) + c(x)u(x) = f(x) in unbounded cylinders. After establishing that the Aleksandrov maximum principle and boundary Harnack inequality hold for bounded solutions, we show that all solutions bounded from below are linear comb_inations of solutions, which are sums of two special solutions that exponential growth at one end and exponential decay at the another end, and a bounded solution that corresponds to the inhomogeneous term f of the equation.

• International Journal of Reliability and Applications
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• v.16 no.2
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• pp.55-79
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• 2015

It is well known that using any additional information in the estimation of unknown parameters with new sample of observations diminishes the sampling units needed and minimizes the risk of new estimators. There are many rational reasons to assure that the existence of additional information in practice and there exists many practical cases in which additional information is available in the form of target value (initial value) about the unknown parameters. This article is described the problem of how the prior initial value about the unknown parameters can be utilized and combined with classical Bayes estimator to get a new combination of Bayes estimator and prior value to improve the properties of the new combination. In this article, two classes of Bayes-shrinkage and preliminary test Bayes-shrinkage estimators are proposed for the scale parameter of exponential distribution. The bias, risk and risk ratio expressions are derived and studied. The performance of the proposed classes of estimators is studied for different choices of constants engaged in the estimators. The comparisons, conclusions and recommendations are demonstrated.

• Journal of ILASS-Korea
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• v.16 no.4
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• pp.176-185
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• 2011

The empirical correlations for the prediction of penetration height of liquid jet in crossflow are reviewed and classified in this study. Around thirty different correlations had been proposed by many investigators. It has generally known that the penetration height of a liquid jet in a cross-flow is a function of the liquid to air momentum flux ratio and the normalized downstream distance from the injector. However, several researchers incorporated the Weber number, liquid-to-water or air viscosity ratio, pressure ratio or Reynolds number, temperature ratio in the empirical correlations. The existing correlations can be grouped as correlations in a power-law, logarithmic, and exponential forms, respectively. Correlations in a power-law form can be further classified as three groups such as basic form, Weber number form and other parameters form. It should be pointed out that correlations in a logarithmic form in terms of Weber number or any other parameters could not be found. Universal correlation has still not been established due to the significant discrepancies between various correlations suggested to date. Several of the studies reported the significant discrepancies of predicted values by the existing correlations. The possible reasons for discrepancies will be summarized as measurement technique, assumptions made in defining terms in the liquid to air momentum flux ratio, difficulties in defining the boundaries of the liquid jets, and nozzle/injector geometry. Evaluation of validity for the correlations proposed recently by several investigators is essentially required. Those include eight power-law forms, two logarithmic forms, and one exponential form.

• Proceedings of the KSME Conference
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• 2001.06c
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• pp.386-391
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• 2001

This paper presents a new two-point approximation method based on the exponential intervening variable. To avoid the lack of definition of the conventional exponential intervening variables due to zero- or negative-valued design variables the shifting level into each exponential intervening variable is introduced. Then a new quadratic approximation, whose Hessian matrix has only diagonal elements of different values, is proposed in terms of these intervening variables. These diagonal elements are computed in a closed form, which correct the typical error in the approximate gradient of the TANA series due to the lack of definition of exponential type intervening variables and their incomplete second-order terms. Also, a correction coefficient is multiplied to the pre-determined quadratic term to match the value of approximate function with that of the original function at the previous point. Finally, the authors developed a sequential approximate optimizer, solved several typical design problems used in the literature and compared these optimization results with those of TANA-3. These comparisons show that the proposed method gives more efficient and reliable results than TANA-3.