• Journal of Korean Society for Quality Management
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• v.40 no.2
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• pp.117-125
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• 2012

For the highly reliable products, an accelerated degradation test (ADT) is a useful tool which has been employed in industry to obtain reliability-related information within an affordable amount of time and cost. In an ADT, as all other reliability tests, it is important to carefully design the ADT beforehand to obtain estimates of the quantities of interest as precisely as possible. In this paper, optimal ADTs are developed assuming that the constant-stress loading method is employed and the degradation characteristic follows a Wiener process. Under the constraint that the total cost does not exceed a pre-specified budget, the stress levels, the number of test units allocated to each stress level and the number of measurement (termination time) are determined such that the asymptotic variance of the maximum likelihood estimator of the q-th quantile of the lifetime distribution at the use condition is minimized.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.11 no.4
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• pp.245-249
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• 2011

In this paper, we propose an equivalent Wiener-Hopf equation. The proposed algorithm can obtain the weight vector of a TDL(tapped-delay-line) filter and the error simultaneously if the inputs are orthogonal to each other. The equivalent Wiener-Hopf equation was analyzed theoretically based on the MMSE(minimum mean square error) method. The results present that the proposed algorithm is equivalent to original Wiener-Hopf equation. In conclusion, our method can find the coefficient of the TDL (tapped-delay-line) filter where a lattice filter is used, and also when the process of Gram-Schmidt orthogonalization is used. Furthermore, a new cost function is suggested which may facilitate research in the adaptive signal processing area.

• The Pure and Applied Mathematics
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• v.16 no.1
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• pp.107-119
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• 2009

In this paper we define a Banach algebra on very general function space induced by a generalized Brownian motion process rather than on Wiener space, but the Banach algebra can be considered as a generalization of Fresnel class defined on Wiener space. We then show that several interesting functions in quantum mechanic are elements of the class.

• Proceedings of the Korean Information Science Society Conference
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• 1998.10b
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• pp.676-678
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• 1998

본 논문에서는 Information-Based Complexity분양의 문제들 중 그 complexity를 계산하기 매우 어렵거나 불가능한 문제들의 오차를 분석하기 위해서 k-fold Wiener process를 생성하는 algorithm에 대해 연구하고, 이 algorithm을 실제 프로그램 하였다. 또한 이 프로그램이 생성한 함수가 실제 k-fold Wiener process와 아주 근사하다는 것을 Kolmogorov-Smirnov test를 통하여 보여준다. 이 프로그램을 이용하면 여러 문제들의 average case error를 Monte-Carlo Simulation 과 같은 방법을 사용하여 실험적으로 계산할 수 있다.

• International Journal of Internet, Broadcasting and Communication
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• v.4 no.1
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• pp.18-22
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• 2012

In this paper, we propose an equivalent Wiener-Hopf equation. The proposed algorithm can obtain the weight vector of a TDL(tapped-delay-line) filter and the error simultaneously if the inputs are orthogonal to each other. The equivalent Wiener-Hopf equation was analyzed theoretically based on the MMSE(minimum mean square error) method. The results present that the proposed algorithm is equivalent to original Wiener-Hopf equation. In conclusion, our method can find the coefficient of the TDL (tapped-delay-line) filter where a lattice filter is used, and also when the process of Gram-Schmidt orthogonalization is used. Furthermore, a new cost function is suggested which may facilitate research in the adaptive signal processing area.

• Journal of the Korean Statistical Society
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• v.26 no.1
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• pp.57-74
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• 1997

Csorgo-Revesz type theorems for Wiener process are developed to those for Gaussian process. In particular, some results of superior and inferior limits for the increments of a Gaussian process are differently obtained under mild conditions, via estimating probability inequalities on the suprema of a Gaussian process.

• Journal of the Chungcheong Mathematical Society
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• v.5 no.1
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• pp.23-34
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• 1992

This is an extension of results of Wiener's nonlinear noise theory from noises generated by the Wiener process to noises generated by processes with stationary Gaussian increments. In particular, using Nisio's Approach, we show that every measurable ergodic noise can be approximated in law by Gaussian process-presentable noise.

• Journal of the Korean Institute of Telematics and Electronics
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• v.17 no.3
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• pp.1-11
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• 1980

For an ordinary engineer or researcher there are too diversified branches or even disciplines which have their own jargon to complicate an easy access, Nevertheless in many cases an isomorphism or even identity of notions exist to escape our grasp when expressed in different discipline or context, In this paper the masterwork of Box and Jenkins is introduced to accustom a few terms of statisticiens, to be followed by the technique of smoothing filtering of Wiener and Kalman - Bucy. The advantages of a transform (for example Hadamard) technique are explaned as well as authors personal philosophical views.

• Communications of the Korean Mathematical Society
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• v.15 no.4
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• pp.715-721
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• 2000

It is known that one can generate functions distributed according to ${\gamma}$-fold Wiener measure. So we could estimate the average case errors in a similar way as in Monte-Carlo method. Hence we study the basic properties of the generator of random functions. n addition, because the ${\gamma}$-fold Wiener process is truly infinitely dimensional and a computer can only handle finitely dimensional spaces, we study in this paper, the properties of generator for an m-dimensional approximation of the ${\gamma}$-fold Wiener process.

• Journal of information and communication convergence engineering
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• v.9 no.5
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• pp.500-504
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• 2011

In this paper, we propose an equivalent Wiener-Hopf equation. The proposed algorithm can obtain the weight vector of a TDL(tapped-delay-line) filter and the error simultaneously if the inputs are orthogonal to each other. The equivalent Wiener-Hopf equation was analyzed theoretically based on the MMSE(minimum mean square error) method. The results present that the proposed algorithm is equivalent to original Wiener-Hopf equation. The new algorithm was applied into the identification of an unknown system for evaluating the performance of the proposed method. We compared the Wiener-Hopf solution with the equivalent Wiener-Hopf solution. The simulation results were similar to those obtained in the theoretical analysis. In conclusion, our method can find the coefficient of the TDL (tapped-delay-line) filter where a lattice filter is used, and also when the process of Gram-Schmidt orthogonalization is used. Furthermore, a new cost function is suggested which may facilitate research in the adaptive signal processing area.