• Communications for Statistical Applications and Methods
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• v.31 no.4
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• pp.365-375
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• 2024

Diverse methods to evaluate the prediction model of a time to event have been proposed in the context of right censored data where all subjects are subject to be susceptible. A time-dependent AUC (area under curve) measures the predictive ability of a marker based on case group and control one which are varying over time. When a substantial portion of subjects are event-free, a population consists of a susceptible group and a cured one. An uncertain curability of censored subjects makes it difficult to define both case group and control one. In this paper, our goal is to propose a time-dependent AUC for a cure rate model when a censoring distribution is related with covariates. A class of inverse probability of censoring weighted (IPCW) AUC estimators is proposed to adjust the possible sampling bias. We evaluate the finite sample performance of the suggested methods with diverse simulation schemes and the application to the melanoma dataset is presented to compare with other methods.

• Journal of the Korean Data and Information Science Society
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• v.11 no.2
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• pp.225-233
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• 2000

In life-testing experiments, in which the longest time an experimental unit is on test is not a failure time, but rather a censored observation. For the situation the Kaplan-Meier estimator is known to be a baised estimator of the survival function. Several modifications of the Kaplan-Meier estimator are examined and compared with bias and mean squared error.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.35 no.2
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• pp.71-79
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• 2012

In this paper, an evaluation of a product replacement ratio of irreparable items to the normally working ones is performed with a view to a warranty analysis. It is demonstrated that the replacement ratio during the warranty period can be estimated from the field data collected during the period of operation, and one can provide the management with a useful information regarding the appropriateness for the warranty period, which is vital to the product marketing strategy. Although warranty data usually take the form of multiply right censored interval data, the conventional reliability analysis method seems to be good enough as in this case. More sophisticated method such as warranty cost analysis and 2-dimensional warranty analysis is yet desired.

• International Journal of Reliability and Applications
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• v.4 no.3
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• pp.113-129
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• 2003

Based on moments inequalities new testing procedures are derived for testing exponentiality against new renewal better than used (NRBU) and renewal new better than used (RNBU). These classes play an important role in formulating repair or replacement policies. The asymptotic Pitman efficiency of (NRBU) and (RNBU) testes are studied. Selected critical values are tabulated for sample sizes n=5(1) 50. The power estimates for some commonly used life distributions in reliability are also calculated. Some set of real data is used as an example to elucidate the use of the proposed test statistic for practical reliability analysis. The problem in case of right-censored data is also handled.

• International Journal of Reliability and Applications
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• v.13 no.2
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• pp.57-69
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• 2012

Our goal in this paper is to establish inequalities for the moments of new better than used in the moment generating function class ($NBU_{mgf}$). Using these inequalities we propose a new test for exponentiality versus $NBU_{mgf}$ class. Pitman's asymptotic relative efficiency, power and critical values of this test are calculated to assess the performance of the test. We proposed also a new test for exponentiality versus $NBU_{mgf}$ in the right censored data. Sets of real data are used as an example to elucidate the use of the proposed test for practical problems.

• Journal of the Korean Data and Information Science Society
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• v.22 no.4
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• pp.755-764
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• 2011

In many companies field failure data is used to predict the future number of failures, especially when an unexpected failure mode happens to be a problem. It is because they want to predict the number of spare parts needed and the future quality warranty cost associated with the part based on the predictions of the future number of failures. In this paper field summary data is used to predict the future number of failures based on an appropriate distribution. Other types of data are also investigated to identify the appropriate distribution.

• Nuclear Engineering and Technology
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• v.55 no.5
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• pp.1924-1934
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• 2023

In this study, the probabilistic fatigue life model for Ni-base alloys was developed based on the Weibull distribution using statistical analysis of fatigue data reported in NUREG/CR-6909 and the new fatigue data of Alloy 52M/152 and 82/182. The developed Weibull model can consider right-censored data (i.e., non-failed data) and quantify the improved safety (or reliability) based on the level of failure probability. The overall margin in the current fatigue design limit model (ASME design curve + NUREG/CR-6909 F_en model) is similar to that of the Weibull model with a cumulative failure probability of approximately 2.5%. The margin in the current fatigue design limit model demonstrated inconsistencies for the Ni-base alloy weld data, whereas the Weibull model showed a consistent margin. Therefore, the Weibull model can systematically mitigate the excessive safety margin.

• Communications for Statistical Applications and Methods
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• v.26 no.5
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• pp.445-461
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• 2019

It is possible that data are not always fitted with sufficient precision by the existing distributions; therefore this article presents a methodology that enables the use of families of asymmetric distributions as alternative probabilistic models for survival analysis, with censorship on the right, different from those usually studied (the Exponential, Gamma, Weibull, and Lognormal distributions). We use a more flexible parametric model in terms of density behavior, assuming that data can be fit by a distribution of stable distribution families considered unconventional in the analyses of survival data that are appropriate when extreme values occur, with small probabilities that should not be ignored. In the methodology, the determination of the analytical expression of the risk function h(t) of the $L{\acute{e}}vy$ distribution is included, as it is not usually reported in the literature. A simulation was conducted to evaluate the performance of the candidate distribution when modeling survival times, including the estimation of parameters via the maximum likelihood method, survival function ${\hat{S}}$(t) and Kaplan-Meier estimator. The obtained estimates did not exhibit significant changes for different sample sizes and censorship fractions in the sample. To illustrate the usefulness of the proposed methodology, an application with real data, regarding the survival times of patients with colon cancer, was considered.

• Journal of Korean Society for Quality Management
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• v.18 no.1
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• pp.40-47
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• 1990

The two-sample problem where an experimental treatment is compared with a control is considered. Without making any parametric-model assumptions for the distributions(or survival distributions), a measure for summarizing the differences between the treatment and the control is introduced. A method for constructing a confidence interval for the proposed measure is given in cases of complete and right random censored data. This method is illustrated with two numerical examples.

• International Journal of Reliability and Applications
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• v.4 no.2
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• pp.57-69
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• 2003

A non-parametric test based on U-statistic for testing exponentiality against the new better than used renewal failure rate (NBURFR) alternatives is introduced and the percentiles of this test statistic are tabulated for sample size 5(1)50. Its properties are also discussed including the Pitman asymptotic efficiency relative to the tests of the new better than used and new better than used failure rate (Ahmed (1994) and Hendi (2000)). The powers of this test are also calculated for some used life distributions. An example from blood cancer patients demonstrates a practical application of our test in the medical sciences is presented. Finally the problem when right-censored data is available is handled.