• 한국수자원학회논문집
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• 제42권4호
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• pp.331-341
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• 2009

본 연구에서는 generalized logistic(GL) 분포의 최우도 추정량(maximum likelihood estimate)에 대한 불확실성 추정을 위하여 사용되는 관측정보행렬(observed information matrix)과 Fisher 정보행렬(Fisher information matrix)의 정확도를 비교해 보고자 하였다. 타 분포형에 대한 기존의 연구결과에서 표본의 크기가 클 경우 매개변수 추정시 관측정보행렬이 동시에 추정되어 계산시간도 단축되고 Fisher 정보행렬의 정확도와도 차이도 거의 없어 관측정보행렬의 사용이 추천된 바 있으나, 최근 사용이 증가되고 있는 GL 분포에 대한 연구결과는 아직 전무한 실정이며 기존 연구문헌의 결과를 토대로 구체적인 연구 없이 관측정보행렬을 사용하고 있는 상황이다. 따라서 본 연구에서는 이를 위해 모의실험을 수행하였으며, 모의 결과 최우도법에 의한 매개변수의 분산 및 공분산은 기존의 연구 결과와 비슷한 결과를 보이나, quantile에 대한 불확실성 추정에는 관측정보행렬보다 Fisher 정보행렬의 사용이 더 적절할 것으로 판단되었다.

• 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.

• 품질경영학회지
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• 제32권4호
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• pp.208-219
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• 2004

This paper considers a nonparametric estimation of lifetime distribution for ramp stress tests with stress bound under intermittent inspection. The test items are inspected only at specified time points an⊂1 so the collected observations are grouped data. Under the cumulative exposure model, two nonparametric estimation methods of estimating the lifetime distribution at use condition stress are proposed for the situation which the time transformation function relating stress to lifetime is a type of the inverse power law. Each of items is initially put on test under ramp stress and then survivors are put on test under constant stress, where all failures in the Inspection interval are assumed to occur at the midi)oint or the endpoint of that interval. Two proposed estimators of quantile from grouped data consisting of the number of items failed in each inspection interval are numerically compared with the maximum likelihood estimator(MLE) based on Weibull distribution.

• 응용통계연구
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• 제18권2호
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• pp.411-420
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• 2005

본 논문에서는 불균형 일원랜덤효과모형에서 분산성분에 대한 MIVQUE 추정량들의 효율에 대하여 연구하였다. MIVQUE 추정량에 대한 초기 추정치로 3가지 추정치가 사용되었으며 이들을 이용하여 얻어지는 MIVQUE 추정량의 효율성을 척도화된 추정량의 경험적 분위수를 이용하는 EQDGs 플롯을 이용하여 비교하였다. 모의실험 결과 집단간 분산의 초기치를 0으로 하고 집단내 분산의 초기치를 1로 사용한 MIVQUE 추정량의 효율이 추정량의 안정성 관점에서 다른 초기치를 사용한 MIVQUE 추정량에 비하여 약간 효율적인 것으로 나타났다.

• Communications for Statistical Applications and Methods
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• 제10권3호
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• pp.859-871
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• 2003

In this paper we introduce some adaptive M-estimators using selector statistics to estimate the slope of regression model under the symmetric and continuous underlying error distributions. This selector statistics is based on the residuals after the preliminary fit L$_1$ (least absolute estimator) and the idea of Hogg(1983) and Hogg et. al. (1988) who used averages of some order statistics to discriminate underlying symmetric distributions in the location model. If we use L$_1$ as a preliminary fit to get residuals, we find the asymptotic distribution of sample quantiles of residual are slightly different from that of sample quantiles in the location model. If we use the functions of sample quantiles of residuals as selector statistics, we find the suitable quantile points of residual based on maximizing the asymptotic distance index to discriminate distributions under consideration. In Monte Carlo study, this adaptive M-estimation method using selector statistics works pretty good in wide range of underlying error distributions.

• 품질경영학회지
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• 제24권3호
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• pp.37-49
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• 1996

For highly reliable devices it is often defined to "fail" when its performance degrades below a specified value. In this paper we consider a method for optimally designing accelerated degradation tests(ADTs) in which the performance over exposure time and stress has Weibull distribution. For the product whose performance has Weibull distribution, the optimum plan - low stress level and sample proportions allocated to each test condition - is obtained, which minimize the asymptotic variance of maximum likelihood estimator of a stated quantile at design stress. We also present compromise ADTs plan that can be used for the practical purpose.

• 품질경영학회지
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• 제40권2호
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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.

• 응용통계연구
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• 제9권1호
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• pp.53-73
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• 1996

일정형 및 계단형 가속수명시험의 시험설계에 대한 일반적인 모형과 최적설계에 대한 최근의 연구결과를 소개하고, 수명분포가 와이블인 경우에 대하여 두가지 시험방법에 대한 최적설계를 점근분산의 행태, 설계변수의 효과, 최적시험조건에서 시험종결 시점까지의 기대고장개수 및 기대시험종결시간, 점근분산의 상대적효율과 설계변수의 사전추정치에 대한 둔감성의 측면에서 비교, 분석하였다.

• International Journal of Reliability and Applications
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• 제15권1호
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• pp.23-50
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• 2014

This paper deals with formulation of optimum multi-objective modified step-stress accelerated life test (ALT) plan for Burr type-XII distribution under type-I censoring. Since it is impractical to estimate only one objective parameter after conducting costly ALT tests; also, it is not desirable to assume instantaneous changes in stress levels because of limited capacity of test equipments and the presence of undesirable failure modes, therefore, an optimum multi-objective modified step-stress ALT plan has been designed. The optimal test plan consists in determining the optimum low stress level and optimal time at which stress starts linearly increasing from low stress by minimizing the weighted sum of the asymptotic variances of the maximum likelihood estimator of quantile lifetimes at design constant stress. The method developed has been illustrated using an example. Sensitivity analysis has been carried out. Comparative study has also been done to highlight the merits of the proposed model.

• 한국신뢰성학회지:신뢰성응용연구
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• 제13권2호
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• pp.87-98
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• 2013

Accelerated degradation tests (ADTs) measuring failure-related degradation characteristic at the accelerated condition are widely used to assess the reliability of highly reliable products. Often, however, little degradation could be observed even in single-stress ADTs due to the high reliability of test unit, and as a result poor estimate of the reliability may be obtained. ADTs with multiple stress variables can be employed to overcome such difficulties. In this paper, optimal ADT plans with two stress variables are developed assuming that the degradation characteristic follows Weibull distribution by determining the stress levels, the proportion of test units allocated to each stress level 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.