• Communications for Statistical Applications and Methods
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• v.24 no.5
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• pp.519-531
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• 2017

We consider goodness-of-fit test statistics for Weibull distributions when data are randomly censored and the parameters are unknown. Koziol and Green (Biometrika, 63, 465-474, 1976) proposed the $Cram\acute{e}r$-von Mises statistic's randomly censored version for a simple hypothesis based on the Kaplan-Meier product limit of the distribution function. We apply their idea to the other statistics based on the empirical distribution function such as the Kolmogorov-Smirnov and Liao and Shimokawa (Journal of Statistical Computation and Simulation, 64, 23-48, 1999) statistics. The latter is a hybrid of the Kolmogorov-Smirnov, $Cram\acute{e}r$-von Mises, and Anderson-Darling statistics. These statistics as well as the Koziol-Green statistic are considered as test statistics for randomly censored Weibull distributions with estimated parameters. The null distributions depend on the estimation method since the test statistics are not distribution free when the parameters are estimated. Maximum likelihood estimation and the graphical plotting method with the least squares are considered for parameter estimation. A simulation study enables the Liao-Shimokawa statistic to show a relatively high power in many alternatives; however, the null distribution heavily depends on the parameter estimation. Meanwhile, the Koziol-Green statistic provides moderate power and the null distribution does not significantly change upon the parameter estimation.

• International Journal of Quality Innovation
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• v.6 no.2
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• pp.31-45
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• 2005

The target costing technique, mathematically discussed by Sauers, only uses the $C_p$ index along with Taguchi loss function and ${\bar{X}}-R$ control charts to set up goal control limits. The new specification limits derived from Taguchi loss function is linked through the $C_p$ value to ${\bar{X}}-R$ control charts to obtain goal control limits. This study further considers the reflected normal loss function as well as the $C_{pk}$ index along with its lower confidence interval in forming goal control limits. With the use of lower confidence interval to replace the point estimator of the $C_{pk}$ index and reflected normal loss function proposed by Spiring to measure the loss to society, this modified and improved target costing technique would become more robust and applicable in practice. Finally, an example is provided to illustrate how this modified and improved target costing technique works.

• Journal of the Korean Data and Information Science Society
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• v.28 no.4
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• pp.947-955
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• 2017

A competing risk analysis has been applied when subjects experience more than one type of end points. Geskus (2011) showed three types of estimators of CIF are equivalent under left truncated and right censored data. We extend his approach to an interval censored competing risk data by using a modified risk set and evaluate their performance under several sample sizes. These estimators show very similar results. We also suggest a test statistic combining Sun's test for interval censored data and Gray's test for right censored data. The test sizes and powers are compared under several cases. As a real data application, the suggested method is applied a data where the feasibility of the vaccine to HIV was assessed in the injecting drug uses.

• International Journal of Reliability and Applications
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• v.4 no.4
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• pp.171-181
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• 2003

This paper proposes a U-test statistic for the problem of testing that a life distribution is exponential against the alternative that it is harmonic new better (worse) than used in expectation upper tail HNBUET (HNWUET), but not exponential on complete data. Selected critical values are tabulated for sample sizes n =5(1)60. The asymptotic normality of the statistic is proved and a comparison is made of the asymptotic efficiency between the statistic and other statistics. The power of the test is studied by simulation. A test for HNBUET in the case of randomly right-censored data is also considered. An application of the proposed test statistic in medical sciences is given.

• Journal of Oral Medicine and Pain
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• v.20 no.2
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• pp.317-325
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• 1995

This study was performed to investigate the mean life expectancy of dental prosthetic restorations. The author has examined 352 dental prosthesis clinically and radiologically, and decided the success(survival) and failure(mortality) of the dental prosthesis. The dental prosthesis which had been treated in the Seoul National University Dental Hospital, two private clinics in Seoul, one university dental hospital, and two private clinics in local province were included in this study. The survival analysis using product limit estimator was used and the mean life expectancy of each type of dental prosthesis was calculated. The results were as follows : 1. The life expectancies were 10.5 years in gold crown and bridge, 8.5 years in porcelain fused to metal crown and bridge, 8.3 years in nonprecious metal crown and bridge, 8.1 years in removal partial denture, and 7.7 years in full denture. 2. The causes of mortality were in the order of dental caries(24.6%), fracture of dental prosthesis(19.2%), periodontal problems(18.6%), chronic chewing difficulty and dysfunction due to dental prosthesis(15.0%), excessive exposure of abutments due to the marginal defect of dental prosthesis(14.4%), abnormal occlusion due to severe attrition of artificial teeth in dentures(3.0%), periapical problems(2.4%), perforation of dental prosthesis(1.8%), and loose contacts with neighboring tooth(1.2%). 3. Among survival cases, 66.5% showed normal chewing ability and 31.9% showed partial chewing ability. However, 1.6% of them complained loss of chewing ability. 4. Among failure cases, 6.6% showed normal chewing ability and 38.9% showed partial chewing ability. However, 54.5% of them complained loss of chewing ability.