• Communications for Statistical Applications and Methods
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• 제12권3호
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• pp.783-795
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• 2005

We consider to obtain an estimate of bivariate survival function for the right censored data with the assumption that the two components of censoring vector are independent. The estimate is derived from an ad hoc approach based on the representation of survival function. Then the resulting estimate can be considered as an extension of the Susarla- Van Ryzin estimate to the bivariate data. Also we show the consistency and weak convergence for the proposed estimate. Finally we compare our estimate with Dabrowska's estimate with an example and discuss some properties of our estimate with brief comment on the extension to the multivariate case.

• 응용통계연구
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• 제11권1호
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• pp.113-127
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• 1998

생존자료의 분석에 있어 두 집단간의 생존분포의 비교는 자주 관심의 대상이 되고 있다. 중도절단(censoring)이 존재하는 생존자료에 있어 두 생존분포의 동일성을 검정하는 방법으로 log-rank 통계량과 Gehan의 일반화된 Wilcoxon 통계량에 근거한 검정법이 주로 사용되어 왔다. 그러나 이 두 가지 검정통계량이 어떤 상황에서나 적절한 것은 아니고, 두 생존분포의 여러가지 형태와 중도절단의 정도에 따라 통계량의 검정력은 크게 달라진다. 따라서 본 논문에서는 두 생존분포의 비교를 위해 제안된 몇 가지 검정통계량들을 여러가지 상황에서 모의실험을 통하여 비교하고, 그 결과를 토대호 주어진 상황에서 적절한 통계량을 선택하는데 대한 유용한 정보를 제공하였다.

• Journal of the Korean Statistical Society
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• 제28권4호
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• pp.415-433
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• 1999

This paper considers the design of step-stress accelerated life tests for the Weibull distribution with a nonconstant shape parameter under Type I censoring. It is assumed that scale and shape parameters are log-linear functions of (possibly transformed) stress and that a cumulative exposure model holds for the effect of changing stress. The asymptotic variance of the maximum likelihood estimator of a stated quantile at design stress is used as an optimality criterion. The optimum three step-stress plans are presented for selected values of design parameters and the effects of errors in pre- estimates of the design parameters are investigated.

• Journal of the Korean Statistical Society
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• 제32권2호
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• pp.163-174
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• 2003

We propose a test for independence of bivariate censored data under univariate censorship. To do this, we first introduce a process defined by the difference between bivariate survival function estimator proposed by Lin and Ying (1993) and the product of the product-limit estimators (Kaplan and Meier, 1958) for the marginal survival functions, and derive its asymptotic properties under the null hypothesis of independence. We propose a Cramer-von Mises-type test procedure based on the process . We conduct simulation studies to investigate the finite-sample performance of the proposed test and illustrate the proposed test with a real example.

• 대한산업공학회지
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• 제17권1호
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• pp.95-108
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• 1991

For the case where the lifetime at a constant stress level has exponential distribution, optimal accelerated life test plans are developed under the assumptions of intermittent inspection and Type I censoring. In a optimal plan, the low and high stress levels, the proportion of test units allocated and the inspection times at each stress are determined such that the asymptotic variance of the maximum likelihood estimator of logarithmic transformed mean at the use condition is minimized. In addition to the optimal plan in which numerical technique to solve the set of nonlinear equations must be employed to determine inspection times at each stress level, we also propose another plans which employ equally-spaced or equal probability inspection schemes at two overstress levels of corresponding optimal one. For both optimal and proposed plans, computational results indicate that the asymptotic variance of the estimated mean at the use stress is insensitive to number of inspections at overstress levels for the range of parameter values considered.

• 품질경영학회지
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• 제24권1호
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• pp.32-43
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• 1996

In this paper we develop nonparametric methods for regression analysis when the response variable is subject to censoring that arises naturally in quality engineering. This development is based on a general missing information principle that enables us to apply, via an iterative scheme, nonparametric regression techniques for complete data to iteratively reconstructed data from a given sample with censored observations. In particular, additive regression models are extended to right-censored data. This nonparametric regression method is applied to a simulated data set and the estimated smooth functions provide insights into the relationship between failure time and explanatory variables in the data.

• Journal of the Korean Statistical Society
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• 제24권1호
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• pp.197-218
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• 1995

We first consider the random censorship model of survival analysis. Efron (1981) introduced two equivalent bootstrap methods for censored data. We propose a new bootstrap scheme, called Method 3, that acts conditionally on the censoring pattern when making inference about aspects of the unknown life-time distribution F. This article contains (a) a motivation for this refined bootstrap scheme ; (b) a proof that the bootstrapped Kaplan-Meier estimatro fo F formed by Method 3 has the same limiting distribution as the one by Efron's approach ; (c) description of and report on simulation studies assessing the small-sample performance of the Method 3 ; (d) an illustration on some Danish data. We also consider the model in which the survival times are censered by death times due to other caused and also by known fixed constants, and propose an appropriate bootstrap method for that model. This bootstrap method is a readily modified version of the Method 3.

• 한국경영과학회:학술대회논문집
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• 대한산업공학회/한국경영과학회 1995년도 춘계공동학술대회논문집; 전남대학교; 28-29 Apr. 1995
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• pp.678-681
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• 1995

가속수명시험은 매우 신뢰성이 높은 제품의 수명분포에 대한 정보를 빨리 얻기 위해 사용된다. 이때, 빠른 시간안에 정보를 얻기 위해 제품의 사용조건보다 높은 스트레스 즉 온도, 압력, 전압, 진동등을 사용하여 시험을 하게 되는데 최대 시험 스트레스는 미리 실험자에 의해 선택되게 된다. 그러나 주어진 최대 시험 스트레스가 스트레스의 한계범위를 벗어나는 경우에는 사용조건과 다른 고장구조가 발생할 수 있고, 이로 인하여 편의가 큰 신뢰수명의 추정치를 얻을 수 있다. 기존의 논문에서는 실험자의 경험 또는 사전시험을 통해 미리 설정된 최대 시험 스트레스하에서 제품수명의 표준편차를 최소화하기 위한 최적가속수명시험 설계방법을 제시하였다. 그러나 본 논문에서는 와이불 분포에서 1) 사용조건에서의 수명추정치의 분산 .leq. k, 2) 스트레스의 범위를 벗어나지 않는 최대 시험 스트레스의 최소값을 구하는 설계방법을 제시하고, 또한 구한 스트레스에서의 수명 및 최소 시험 스트레스에서 시험되어야 할 제품의 수를 추정한다. 이때, 사용전압에서의 수명을 계산하기 위하여 inverse power law 모형을 도입하였으며, type I censoring 방법을 사용하여 수명 데이타들은 모든 제품이 고장나기 전에 분석될 수 있도록 하였다.

• 대한수학회보
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• 제40권2호
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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.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2006년도 추계학술대회 논문집 전력기술부문
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• pp.372-374
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• 2006

This paper presents a methodology to predict a failure probability related to the aging generating units in Korea power system. Each generator is represented by a combined reliability model of its individual components, which is determined by failure data. The Weibull distribution is used to calculate failure probability and its parameters are obtained from Type II Censoring. Consequently, the proposed methods would likely to permit utilities to reduce overall costs in the new deregulated environment.