• Communications for Statistical Applications and Methods
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• v.30 no.4
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• pp.411-421
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• 2023

This paper provides a new estimation equation based on the concept of a minimum distance between the empirical and theoretical distribution functions under the most widely used progressive Type-II censoring scheme. For illustrative purposes, simulated and real datasets from a three-parameter Weibull distribution are analyzed. For comparison, the most popular estimation methods, the maximum likelihood and maximum product of spacings estimation methods, are developed together. In the analysis of simulated datasets, the excellence of the provided estimation method is demonstrated through the degree of the estimation failure of the likelihood-based method, and its validity is demonstrated through the mean squared errors and biases of the estimators obtained from the provided estimation equation. In the analysis of the real dataset, two types of goodness-of-fit tests are performed on whether the observed dataset has the three-parameter Weibull distribution under the progressive Type-II censoring scheme, through which the performance of the new estimation equation provided is examined.

• Journal of Ocean Engineering and Technology
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• v.10 no.2
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• pp.61-68
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• 1996

Weibull distribution function is applied very successfully to the strength of brittle materials such as ceramics and the weakest link model is applied to explain the ovents. This paper deals with the effect of specimen size on the strength of ceramics. The values of tensile strength were calculated by the Monte-Calro simuation. The tensile strength obtained was plotted on Weibull probabillity papers and represented by the 3-parameter Weibull distribution. The strength distribution function was compared with the theoretical weibull distribution. As a result, it was found that the Weibull shape parameter was changed due to the size and there was a possibility of a false indication as if the weakest link model holds good. We should be very careful when we apply the Weibull statistics to estimate the strength of products.

• Journal of Korean Society for Quality Management
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• v.43 no.4
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• pp.471-488
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• 2015

Purpose: Double sampling $T^2$ chart is a useful tool for detecting a relatively small shift in process mean when the process is controlled by multiple variables. This paper finds the optimal design of the double sampling $T^2$ chart in both economical and statistical sense under Weibull failure model. Methods: The expected cost function is mathematically derived using recursive equation approach. The optimal designs are found using a genetic algorithm for numerical examples and compared to those of single sampling $T^2$ chart. Sensitivity analysis is performed to see the parameter effects. Results: The proposed design outperforms the optimal design of the single sampling $T^2$ chart in terms of the expected cost per unit time and Type-I error rate for all the numerical examples considered. Conclusion: Double sampling $T^2$ chart can be designed to satisfy both economic and statistical requirements under Weibull failure model and the resulting design is better than the single sampling counterpart.

• The Korean Journal of Applied Statistics
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• v.29 no.5
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• pp.823-833
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• 2016

The lifetime is a key characteristic of product quality. It is best to obtain the lifetime data of all samples, but they are often censored due to time or expense limitations. In this paper, we propose a binomial cumulative sum (CUSUM) chart to monitor the mean of type I right-censored Weibull lifetime data, for a xed value of the Weibull shape parameter. We compare the performance of the proposed binomial CUSUM chart with CUSUM charts studied previously using the steady-state average run length (ARL). The results show that the performance of the binomial CUSUM chart is better when the censoring rate is high and/or the sample size is small.

• Journal of applied mathematics & informatics
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• v.39 no.5_6
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• pp.785-804
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• 2021

The proposal of new families has been worked out by many authors over recent years. Many ways to generate new families have been developed as the methods of addition, linear combination, composition and, one of the newer, the T-X family of distributions. Using this latter method, Korkmaz et al. (2018) proposed a new class called Weibull Marshall-Olkin-G (WMO-G) family. In the present work, we propose a new distribution, based on the WMO-G family, using the Lomax distribution as baseline, called Weibull Marshall-Olkin Lomax (WMOL) distribution. The hazard rate function of this distribution can be increasing, decreasing, bathtub-shaped, decreasing-increasing-decreasing and unimodal. Some properties of the proposed model are developed. Besides that, we consider method of maximum likelihood for estimating the unknown parameters of the WMOL distribution. We provide a simulation study in order to verify the asymptotic properties of the maximum likelihood estimates. The applicability of the new distribution to modeling real life data is proved by two real data sets.

• Communications for Statistical Applications and Methods
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• v.16 no.2
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• pp.349-361
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• 2009

In this paper, we derive the approximate maximum likelihood estimators of the shape parameter and the scale parameter in a Weibull distribution under multiply Type-II censoring by the approximate maximum likelihood estimation method. We develop three modified empirical distribution function type tests for the Weibull distribution based on multiply Type-II censored samples. We also propose modified normalized sample Lorenz curve plot and new test statistic.

• The Korean Journal of Applied Statistics
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• v.30 no.5
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• pp.647-663
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• 2017

Weibull distribution is a popular distribution for modeling lifetimes because it reflects the characteristics of failure adequately and it models either increasing or decreasing failure rates simply. It is a standard method of the lifetimes test to wait until all samples failed; however, censoring can occur due to some realistic limitations. In this paper, we propose a generalized likelihood ratio (GLR) chart to monitor changes in the scale parameter for type I right-censored Weibull lifetime data. We also compare the performance of the proposed GLR chart with two CUSUM charts proposed earlier using average run length (ARL). Simulation results show that the Weibull GLR chart is effective to detect a wide range of shift sizes when the shape parameter and sample size are large and the censoring rate is not too high.

• Journal of the Korean Data and Information Science Society
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• v.14 no.2
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• pp.279-287
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• 2003

In this paper we propose a local smoothing of the Nelson type estimator for the survival function based on an approximation by the Weibull distribution function. It appears that Mean Square Error and Bias of the smoothed estimator of the Nelson type survival function estimators are significantly smaller than that of the smoothed estimator of the Kaplan-Meier survival function estimator.

• Journal of Korean Society for Quality Management
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• v.27 no.4
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• pp.153-166
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• 1999

In this paper, we address the Bayesian hypotheses testing for the shape parameter of weibull model. In Bayesian testing problem, conventional Bayes factors can not typically accommodate the use of noninformative priors which are improper and are defined only up to arbitrary constants. To overcome such problem, we use the recently proposed hypotheses testing criterion called the intrinsic Bayes factor. We derive the arithmetic and median intrinsic Bayes factors and use these results to analyze real data sets.

• Journal of the Korean Data and Information Science Society
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• v.7 no.2
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• pp.179-188
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• 1996

Accelerated life testing(ALT) of products quickly yields information on life. In this paper, we investigate asymptotic normalities of maximum likelihood(ML) estimators of parameters for ALT model under Type II censored data using results of Bhattacharyya(1985). Further illustrations include the treatment of asymptotic of the exponential and Weibull regression models.