• Journal of the Korean Ceramic Society
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• v.34 no.9
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• pp.927-934
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• 1997

Static and cyclic fatigue tests were carried out for alumina specimen to study the statistical analyses (normal, lognormal and Weibull distribution) of fatigue lifetime data and nominal initial crack length data. Fatigue lifetime data followed Weibull distribution better than normal or lognormal distribution, for the shape parameter of the notched specimen was larger than that of the unnotched specimen. The nominal initial crack length data obtained from fatigue lifetime followed the lognormal and Weibull distribution better than normal distribution, for the coefficient of variation of the unnotched specimen was larger than that of the notched specimen, and shape parameter of unnotched specimen was smaller than that of the notched specimen.

• Journal of Applied Reliability
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• v.13 no.3
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• pp.191-206
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• 2013

Application areas for Lifetime Performance Index(LPI), a kind of process capability index to be frequently used as a means of measuring process performance are illustrated with examples. Statistical properties for maximum likelihood and unbiased estimators of LPI are evaluated and discussed under Weibull distribution with known shape parameter. Furthermore, guidelines for selecting an estimator of LPI are also presented.

• Communications for Statistical Applications and Methods
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• v.23 no.5
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• pp.363-383
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• 2016

The Weibull family of lifetime distributions play a fundamental role in reliability engineering and life testing problems. This paper investigates the potential usefulness of transmuted new generalized Weibull (TNGW) distribution for modeling lifetime data. This distribution is an important competitive model that contains twenty-three lifetime distributions as special cases. We can obtain the TNGW distribution using the quadratic rank transmutation map (QRTM) technique. We derive the analytical shapes of the density and hazard functions for graphical illustrations. In addition, we explore some mathematical properties of the TNGW model including expressions for the quantile function, moments, entropies, mean deviation, Bonferroni and Lorenz curves and the moments of order statistics. The method of maximum likelihood is used to estimate the model parameters. Finally the applicability of the TNGW model is presented using nicotine in cigarettes data for illustration.

• International Journal of Reliability and Applications
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• v.16 no.1
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• pp.15-26
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• 2015

Present study investigates the fuzzy reliability of some systems using intuitionistic fuzzy Weibull lifetime distribution, in which the lifetime parameters are assumed to be fuzzy parameter due to uncertainty and inaccuracy of data. Expressions for fuzzy reliability, fuzzy mean time to failure, fuzzy hazard function and their ${\alpha}$-cut have been discussed when systems follow intuitionistic fuzzy Weibull lifetime distribution. A numerical example is also taken to illustrate the methodology to calculate the fuzzy reliability characteristics of systems.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2005.05a
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• pp.678-685
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• 2005

Estimating parameters of the lifetime distribution is investigated when field failure data are not completely reported. To take into account the reality and the accuracy of the estimates in such a case, the failure reporting probability is incorporated in estimating parameters. Firstly, method of maximum likelihood estimate(MLE) is used to estimate parameters of the lifetime distribution when failure reporting probability is known. Secondly, Expectation and Maximization(EM) algorithm is used to estimate the failure reporting probability and parameters of the lifetime distribution simultaneously when failure reporting probability is unknown. For both case, procedures of estimation are illustrated for single Weibull distribution and mixed Weibull distribution. Simulation results show that MLE obtained by the proposed method is more accurate than the conventional MLE.

• Journal of Applied Reliability
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• v.11 no.3
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• pp.225-234
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• 2011

In the fields of reliability application, the most commonly used test methods for reliability qualification are zero-failure acceptance tests since they require fewer test samples and less test time compared to other test methods that guarantee the same reliability with a given confidence level. Usually values of shape parameters are assumed to be known in designing reliability qualification tests for Weibull lifetime distribution. It is important to select correct values of shape parameters to guarantee the specified reliability with given confidence level exactly. The effect of using wrong values of shape parameters in designing reliability qualification test for products with Weibull lifetime distribution is examined and selecting proper values of shape parameters for conservative reliability qualification is discussed.

• Journal of Korean Institute of Industrial Engineers
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• v.33 no.1
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• pp.52-60
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• 2007

Estimating parameters of the lifetime distribution is investigated when field failure data are not completelyreported. To take into account the reality and the accuracy of the estimates in such a case, the failure reportingprobability is incorporated in estimating parameters, Firstly, method of maximum likelihood estimate (MLE) isused to estimate parameters of the lifetime distribution when failure reporting probability is known, Secondly,Expectation and Maximization (EM) algorithm is used to estimate the failure reporting probability and parame-ters of the lifetime distribution simultaneously when failure reporting probability is unknown. For both cases,procedures of estimation are illustrated for single Weibull distribution and mixed Weibull distribution. Simula-tion results show that MLE obtained by the proposed method is more accurate than the conventional MLE.

• Journal of Korean Society for Quality Management
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• v.28 no.3
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• pp.1-10
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• 2000

In this paper, we address the Bayesian hypotheses testing for the comparison of Weibull distributions. 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 for the comparison of Weibull lifetime model and we use these results to analyze real data sets.

• 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.

• Communications for Statistical Applications and Methods
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• v.24 no.4
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• pp.325-337
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• 2017

In this paper, we proposed a new long-term lifetime distribution with four parameters inserted in a risk competitive scenario with decreasing, increasing and unimodal hazard rate functions, namely the Weibull-Poisson long-term distribution. This new distribution arises from a scenario of competitive latent risk, in which the lifetime associated to the particular risk is not observable, and where only the minimum lifetime value among all risks is noticed in a long-term context. However, it can also be used in any other situation as long as it fits the data well. The Weibull-Poisson long-term distribution is presented as a particular case for the new exponential-Poisson long-term distribution and Weibull long-term distribution. The properties of the proposed distribution were discussed, including its probability density, survival and hazard functions and explicit algebraic formulas for its order statistics. Assuming censored data, we considered the maximum likelihood approach for parameter estimation. For different parameter settings, sample sizes, and censoring percentages various simulation studies were performed to study the mean square error of the maximum likelihood estimative, and compare the performance of the model proposed with the particular cases. The selection criteria Akaike information criterion, Bayesian information criterion, and likelihood ratio test were used for the model selection. The relevance of the approach was illustrated on two real datasets of where the new model was compared with its particular cases observing its potential and competitiveness.