• Communications for Statistical Applications and Methods
• /
• 제28권2호
• /
• pp.151-159
• /
• 2021

In this article, our interest is to estimate the association between consecutive gap times which are subject to interval censoring. Such data are referred as doubly interval censored data (Sun, 2006). In a context of serial event, an induced dependent censoring frequently occurs, resulting in biased estimates. In this study, our goal is to propose a Kendall's 𝜏 based association measure for doubly interval censored data. For adjusting the impact of induced dependent censoring, the inverse probability censoring weighting (IPCW) technique is implemented. Furthermore, a multiple imputation technique is applied to recover unknown failure times owing to interval censoring. Simulation studies demonstrate that the suggested association estimator performs well with moderate sample sizes. The proposed method is applied to a dataset of children's dental records.

• Communications for Statistical Applications and Methods
• /
• 제27권1호
• /
• pp.47-64
• /
• 2020

In this paper, we derive some estimators of the scale parameter of the exponentiated half-logistic distribution based on the multiply Type-I hybrid censoring scheme. We assume that the shape parameter λ is known. We obtain the maximum likelihood estimator of the scale parameter σ. The scale parameter is estimated by approximating the given likelihood function using two different Taylor series expansions since the likelihood equation is not explicitly solved. We also obtain Bayes estimators using prior distribution. To obtain the Bayes estimators, we use the squared error loss function and general entropy loss function (shape parameter q = -0.5, 1.0). We also derive interval estimation such as the asymptotic confidence interval, the credible interval, and the highest posterior density interval. Finally, we compare the proposed estimators in the sense of the mean squared error through Monte Carlo simulation. The average length of 95% intervals and the corresponding coverage probability are also obtained.

• Journal of the Korean Data and Information Science Society
• /
• 제21권5호
• /
• pp.927-934
• /
• 2010

본 논문은 점진 제1종 구간 중도절단표본과 점진 제2종 중도절단표본에서 모수를 추정하는 방법을 소개하고, 점진 제2종 중도절단표본에서 모수를 추정하는 방법을 활용하고자 점진 제1종 구간 중도절단표본에서 얻은 자료를 변환하여 모수를 추정하는 새로운 방법을 제안하였다. 척도모수가 미지인 지수 분포를 따르는 점진 제1종 구간 중도절단표본을 이용하여 점진 제2종 중도절단표본의 최대우도추정량을 사용하여 모수를 추정하였고, 모의실험을 통하여 두 방법에서 구한 추정량을 비교한 결과 본 논문에서 새로 제시한 방법을 이용하여 구한 모수의 추정량이 평균제곱오차 측면에서 더 우수한 추정량임이 나타났다.

• Communications for Statistical Applications and Methods
• /
• 제8권1호
• /
• pp.127-135
• /
• 2001

In this paper, we consider a simple method for testing the assumption of independent censoring on the basis of a Cox proportional hazards regression model with a time-dependent covariate. This method involves a two-stage sampling in which a random subset of censored observations is selected and followed-up until their true survival times are observed. Lee and Wolfe(1998) proposed an adjusted estimate of the survivor function for the dependent censoring under a proportional hazards alternative. This paper extends their result to obtain a bootstrap confidence interval for the adjusted survivor function under the dependent censoring. The proposed procedure is illustrated with an example of a clinical trial for lung cancer analysed in Lee and Wolfe(1998).

• Journal of the Korean Data and Information Science Society
• /
• 제25권3호
• /
• pp.643-653
• /
• 2014

In this paper, we propose some estimators for the extreme value distribution based on the interval method and mid-point approximation method from the progressive Type-I interval censored sample. Because log-likelihood function is a non-linear function, we use a Taylor series expansion to derive approximate likelihood equations. We compare the proposed estimators in terms of the mean squared error by using the Monte Carlo simulation.

• Journal of the Korean Data and Information Science Society
• /
• 제24권6호
• /
• pp.1309-1317
• /
• 2013

일반화 지수분포 (generalized exponential distribution)를 따르는 점진 제 1종 구간 중도절단 (progressive type-I interval censoring) 표본에서 모수 추정은 Chen과 Lio (2010)가 최대우도 추정법 (maximum likelihood estimation), 중간점 근사법 (mid-point approximation method), EM 알고리즘 (expectation maximization algorithm), 적률 추정법 (method of moments estimation; MME)으로 하였으며, 그 방법들 중 평균제곱오차 (mean square error; MSE)가 가장 작은 추정법은 중간점 근사법이다. 하지만 중간점 근사법을 바탕으로 최대우도 추정법을 이용하여 모수를 추정하려고 한다면 모수에 대한 해를 전개할 수 없기 때문에 수치 해석적인 방법을 이용하여 추정하여야 한다. 본 논문에서는 이러한 문제를 해결하기 위해서 근사 최대우도 추정법 (approximate maximum likelihood estimation)을 이용하여 두 종류의 모수를 추정하고, 모의실험을 통하여 수치해석학적인 방법을 이용한 중간점 근사법의 해 (estimate of mid-point approximation method; MP)와 제시한 두 가지 추정량을 평균제곱오차 측면에서 비교한다.

• International Journal of Reliability and Applications
• /
• 제2권3호
• /
• pp.189-197
• /
• 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.

• Communications for Statistical Applications and Methods
• /
• 제6권2호
• /
• pp.443-456
• /
• 1999

The estimation of mean lifetimes in presence of interval censoring with mixed replacement procedure are examined when the distribution s 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. Comparisons of mixed replacement designs are made with those with and without replacement The maximum likelihood estimator is found in an implicit form. The Cramer-Rao lower bound which is the asymptotic variance of the estimator is derived. The test conditions for minimizing the Cramer-Rao lower bound and minimizing the test costs within a desired width of the Cramer-Rao bound have been studied.

• 마이크로전자및패키징학회지
• /
• 제22권2호
• /
• pp.1-4
• /
• 2015

Qualification includes all activities to demonstrate that a product meets and exceeds the reliability goals. Manufacturers need to spend time and resources for the qualification processes under the pressure of reducing time to market, as well as offering a competitive price. Failure to qualify a product could result in economic loss such as warranty and recall claims and the manufacturer could lose the reputation in the market. In order to provide valid and reliable qualification results, manufacturers are required to make extra effort based on the operational and environmental characteristics of the product. This paper discusses optimal interval censoring design for reliability prediction of electronic packages under limited time and resources. This design should provide more accurate assessment of package capability and thus deliver better reliability prediction.

• 한국신뢰성학회지:신뢰성응용연구
• /
• 제2권2호
• /
• pp.113-119
• /
• 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.