• Communications for Statistical Applications and Methods
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• v.8 no.1
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• pp.209-217
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• 2001

We obtain the approximate maximum likelihood estimators (AMLEs) for the scale and location parameters $\theta$ and $\mu$ in the three-parameter Weibull distribution based on Type-II censored samples. We also compare the AMLEs with the modified maximum likelihood estimators (MMLEs) in the sense of the mean squared error (MSE) based on complete sample.

• Journal of Korean Society for Quality Management
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• v.9 no.1
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• pp.51-60
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• 1981

This paper deals with the estimation of the Weibull parameters, which have a close relation with product reliability characteristics. Among the many kinds of estimation methods, Ishikawa's Weibull Probability Paper (WPP) is commonly used. The WPP is very convenient, but it has a great disadvantage in estimation accuracy by plotting method. It is very difficult to get the same results even if one use the same data several times. A computer program for the regression method is used for the parameter estimation to reduce these errors.

• Communications for Statistical Applications and Methods
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• v.20 no.6
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• pp.427-438
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• 2013

Based on progressive Type II censored sampling which is an important method to obtain failure data in a lifetime study, we suggest a very general form of Bayesian prediction bounds from two parameters exponentiated Weibull distribution using the proper general prior density. For this, Markov chain Monte Carlo approach is considered and we also provide a simulation study.

• Journal of Applied Reliability
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• v.1 no.1
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• pp.17-33
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• 2001

The characteristics of Weibull distribution are investigated as a function of shape parameter. The statistical estimation methods of the shape parameter and statistical comparison methods of two or more shape parameters are studied. Assuming Weibull distribution, statistical analysis of bending-strength data of alumina titanium carbide ceramic matrix composites machined two different methods are performed.

• International Journal of Reliability and Applications
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• v.14 no.2
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• pp.107-114
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• 2013

Modelling of failures is an important element of reliability modelling. Empirical modelling approach suitable for complex item is explored in this paper. First step of the empirical modelling approach is to plot hazard function, density function, Weibull probability plot as well as cumulative intensity function to see which model fits best for the given data. Next step of the empirical modelling approach is select appropriate model for the data and fit the parametric model accordingly and estimate the parameters.

• Communications for Statistical Applications and Methods
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• v.19 no.3
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• pp.479-493
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• 2012

The inverse Weibull distribution(IWD) is a complementary Weibull distribution and plays an important role in many application areas. In this paper, we develop a Bayesian estimator in the context of record statistics values from the exponentiated inverse Weibull distribution(EIWD). We obtained Bayesian estimators through the squared error loss function (quadratic loss) and LINEX loss function. This is done with respect to the conjugate priors for shape and scale parameters. The results may be of interest especially when only record values are stored.

• Journal of the Korean Data and Information Science Society
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• v.25 no.3
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• pp.611-622
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• 2014

The inverse Weibull distribution (IWD) is the complementary Weibull distribution and plays an important role in many application areas. In Bayesian analysis, Soland's method can be considered to avoid computational complexities. One limitation of this approach is that parameters of interest are restricted to a finite number of values. This paper introduce nonparametric Bayesian estimator in the context of record statistics values from the exponentiated inverse Weibull distribution (EIWD). In stead of Soland's conjugate piror, stick-breaking prior is considered and the corresponding Bayesian estimators under the squared error loss function (quadratic loss) and LINEX loss function are obtained and compared with other estimators. The results may be of interest especially when only record values are stored.

• Journal of the Korea Concrete Institute
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• v.16 no.5 s.83
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• pp.581-589
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• 2004

This paper compares the fatigue behaviors of concretes subjected to flexural and split-tensional loadings, and proposes the fatigue reliability models based on experimental results and reliability analysis. The fatigue tests were performed for the specimens of $150 mm{\times}75 mm$ split tensional cylinders and $150 mm{\times}150 mm{\times}550 mm$ flexural beams under constant loadings at three levels (70, 80 and $90\%$) with 0.1 stress ratio, 20 Hz loading speed and sine wave. The reliability analysis on fatigue data was based on Weibull distribution of two-parameters. From fatigue test results, two criteria were proposed to reject the experimental fatigue data because of statistical variation of concrete fatigue data. Two parameters ($\alpha$and u) of Weibull distribution were obtained using graphical method, moment method and maximum likelihood method. The probability density function(P.D.F) and cumulative distribution function(C.D.F) of the Weibull distribution for fatigue life of pavement concrete were derived for various stress levels using parameters, $\alpha$ and u. The goodness-of-fit test by Kolmogorov-Smirnov test was acceptable at $5\%$ level of significance. Based on reliability analysis, a fatigue model for pavement concrete was proposed and compared from existing models.

• Journal of the Korean Data and Information Science Society
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• v.7 no.2
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• pp.263-272
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• 1996

In this parer, under random censorship model, an estimation of scale and shape parameters in Weibull lifetime model is considered. Based on nonparametric estimator of survival function, the least square method is proposed. The proposed estimation method is simple and the performance of the proposed estimator is as efficient as maximum likelihood estimators. An example is presented, using field winding data. Simulation studies are performed to compare the performaces of the proposed estimator and maximum likelihood estimator.

• IE interfaces
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• v.19 no.4
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• pp.316-323
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• 2006

In this study, based on Weibull proportional age reduction model and age replacement policy, we analyze economic life of cutting tool which allows re-grinding. Re-grinding task, usually for high-priced machining tools(e.g., broaching tool), is a kind of preventive maintenance activities to extend tool life at the completion of a lot production. The numerical results are also presented. Among the parameters of Weibull proportional age reduction model, the re-grinding effect parameter and Weibull shape parameter have a strong effect on economic tool life, and in the cost parameters, shortage cost is most sensitive. With further study on the parameter estimation of tool life process and cost function, this study can be expected to give more practical contribution to management of general machining tools.