• Journal of Korean Society for Quality Management
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• v.24 no.4
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• pp.70-89
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• 1996

This paper discusses an optimal burn -in procedure to minimize total costs based on the assumption that some of the components are weak for stress and deteriorate faster than the main components. The procedure will define the costs of burn-in errors. An ideal burn-in consists of process in which all weak (substandard) components and no main (standard) components fail. In practice, the burn-in errors could occur for some reasons. For example, it is impossible to eliminate all weak components through burn-in, due to a nonzero proportion of defectives of the components. Probability model and cost function model are formulated to find the optimal burn-in time that minimizes the expected total cost. Several examples are included to show how to use the results.

• Communications for Statistical Applications and Methods
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• v.27 no.2
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• pp.163-175
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• 2020

We consider a wide class of general weakly-dependent processes, called ψ-weak dependence, which unify almost all weak dependence structures of interest found in statistics under natural conditions on process parameters, such as mixing, association, Bernoulli shifts, and Markovian sequences. For detecting the tail behavior of the weakly dependent processes, change point tests are developed by means of cumulative sum (CUSUM) statistics with the empirical distribution functions of sample extremes. The null limiting distribution is established as a Brownian bridge. Its proof is based on the ψ-weak dependence structure and the existence of the phantom distribution function of stationary weakly-dependent processes. A Monte-Carlo study is conducted to see the performance of sizes and powers of the CUSUM tests in GARCH(1, 1) models; in addition, real data applications are given with log-returns of financial data such as the Korean stock price index.

• Proceedings of the KIEE Conference
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• 1999.07c
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• pp.1067-1069
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• 1999

This paper presents a network reduction using weak coupling method. Weak coupling method of identifying coherent generator groups are proposed. The partitioning technique used in this paper is based on a property of sparse matrix factorization. When a matrix has been factorized, a system is divided into study area, boundary buses and external area. A reduction process for external system starts with the load bus elimination and coherent generator aggregation. An identification of coherent generator group, network partitioning and network reduction are presented.

• Journal of the Korean Statistical Society
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• v.33 no.4
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• pp.353-365
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• 2004

In this paper, we define the weighted U-empirical process for simple linear model and show the weak convergence to a Gaussian process under some conditions. Then we illustrate the usage of our result with examples. In the appendix, we derive the variance of the weighted U-empirical distribution function.

• Bulletin of the Korean Mathematical Society
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• v.46 no.1
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• pp.135-146
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• 2009

In the present note we study the properties of weak Armendariz rings, and the connections among weak Armendariz rings, Armendariz rings, reduced rings and IFP rings. We prove that a right Ore ring R is weak Armendariz if and only if so is Q, where Q is the classical right quotient ring of R. With the help of this result we can show that a semiprime right Goldie ring R is weak Armendariz if and only if R is Armendariz if and only if R is reduced if and only if R is IFP if and only if Q is a finite direct product of division rings, obtaining a simpler proof of Lee and Wong's result. In the process we construct a semiprime ring extension that is infinite dimensional, from given any semi prime ring. We next find more examples of weak Armendariz rings.

• Bulletin of the Korean Mathematical Society
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• v.40 no.2
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• pp.269-279
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• 2003

We prove an empirical LIL for the Kaplan-Meier integral process constructed from the random censorship model under bracketing entropy and mild assumptions due to censoring effects. The main method in deriving the empirical LIL is to use a weak convergence result of the sequential Kaplan-Meier integral process whose proofs appear in Bae and Kim [2]. Using the result of weak convergence, we translate the problem of the Kaplan Meier integral process into that of a Gaussian process. Finally we derive the result using an empirical LIL for the Gaussian process of Pisier [6] via a method adapted from Ossiander [5]. The result of this paper extends the empirical LIL for IID random variables to that of a random censorship model.

• Textile Coloration and Finishing
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• v.15 no.2
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• pp.86-92
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• 2003

It is already known that the color of wool fabric dyed with disazo acid dyes could be changed in dyeing process and this is accelerated under alkaline condition. Focus was given to figuring out the mechanism of this color change, through the LC-MS analysis. In this study, no color change was seen in wool fabrics dyed with C. I. Acid Blue 113 under weak acidic, neutral and weak alkaline conditions for 1hour. However, the wool fabrics dyed under weak alkaline condition for a long time over 3 hours fumed reddish orange. When the wool fabrics dyed under weak acidic, neutral and weak alkaline conditions were treated with $0.5g/L\;Na_2C0_3$ solution, all of them turned reddish orange. On the other hand, the color of silk fabrics dyed with C. I. Acid Blue 113 were not changed after the same alkaline treatment. Wool contains cystine and cysteine, whereas silk does not. Due to the reversible reduction/oxidation process of cystine and cysteine in wool dyeing, the C. I. Acid Blue 113 of the dis-azo type is decomposed by reduction and consequently turned them into the reddish orange mono-azo types dye.

• Journal of applied mathematics & informatics
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• v.30 no.1_2
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• pp.71-82
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• 2012

In this paper, we first show the weak convergence of the modified Ishikawa iteration process with errors of two total asymptotically nonexpansive mappings, which generalizes the result due to Khan and Fukhar-ud-din [1]. Next, we show the strong convergence of the modified Ishikawa iteration process with errors of two total asymptotically nonexpansive mappings satisfying Condition ($\mathbf{A}^{\prime}$), which generalizes the result due to Fukhar-ud-din and Khan [2].

• East Asian mathematical journal
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• v.29 no.1
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• pp.23-37
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• 2013

The purpose of this paper is to study an implicit iteration process with errors and establish weak and strong convergence theorems to converge to common fixed points for a finite family of generalized asymptotically quasi-nonexpansive mappings in the framework of uniformly convex Banach spaces. Our results extend, improve and generalize some known results from the existing literature.

• Korean Journal of Microbiology
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• v.7 no.3
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• pp.115-124
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• 1969

The mash of Takjoo, Korean flour wine, is fermented through two brewing processes ; the primary brewing process to saccharify and the main one to produce ethyl alcohol. The activities of acid proteinase (pH3), weak acid proteinase (pH 6), and alkaline proteinase (Ph 80 on the processes are determined with time by the Folin phenol method as a strength of casein digestion. Hydrogen ion concentration, the content of total organic acids, protein, free amino acids and oligopeptides, which effect the activities of proteinase, are also measured. The results are briefly summarized as follows : 1. In general, the activities of acid proteinase and weak acid proteinase in the mesh of primary brewing process are stronger than those in main brewing process. 2. The activities of acid proteinase are remarkably stronger than those of weak acid proteinase in both processes. It reveals that they decrease slowly through the fermentation. Activities of alkaline proteinase are weaker than others. 3. As the raw materials are mixtured, the total amount of organic acids is equivalent to 0.150 mg/ml acetic acid in the mesh of primary brewing process and 0.02 mg/ml acetic acid in the main one. They increase gradually with time. 4. Hydrogen ion concnetration shows 3.9 in the mesh of main brewing process and 3.28 in the primary one. They increase to the maximum in 60-72 hrs., and decrease since 108 hrs. 5. The content of crude protein shows 66.90mg/ml in the mesh of main brewing process, while shows 64.29mg/ml in the mesh of primary one. they decrease slowly with time. it seems that a small content of crude protein, as a substrate, converts into amino acids and soluble nitrogen compounds by proteinase. 6. The content of free amino acids and oligopeptides shows 0.36 mg/ml in the mesh of primary brewing process and 0.24mg/ml in the main brewing process. It is evident that the reason they increase continuously through the fermentation is the effect of proteinase. 7. According to the results, the strong activities of proteinase in primary brewing process has been derived from the decrease of hydrogen ion concentration due to the production of organic acids.