• Journal of the Korean Mathematical Society
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• v.58 no.1
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• pp.237-264
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• 2021

In this work the stationary bootstrap of Politis and Romano [27] is applied to the empirical distribution function of stationary and associated random variables. A weak convergence theorem for the stationary bootstrap empirical processes of associated sequences is established with its limiting to a Gaussian process almost surely, conditionally on the stationary observations. The weak convergence result is proved by means of a random central limit theorem on geometrically distributed random block size of the stationary bootstrap procedure. As its statistical applications, stationary bootstrap quantiles and stationary bootstrap mean residual life process are discussed. Our results extend the existing ones of Peligrad [25] who dealt with the weak convergence of non-random blockwise empirical processes of associated sequences as well as of Shao and Yu [35] who obtained the weak convergence of the mean residual life process in reliability theory as an application of the association.

• International Journal of Reliability and Applications
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• v.8 no.1
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• pp.83-94
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• 2007

In this paper, we consider a standby redundant structure with a function of switchover processing which may not be not perfect. The switchover processing is governed by a control module whose failure may cause the failure of the whole system. The parameters measuring such an effect of failure of the control module is included in our reliability model. We compute several reliability measures such as reliability function, failure rate, MTBF, mean residual life function, and the steady state availability. We also compare a single unit structure and the redundant structure with regard to those reliability measures. An example is given to illustrate our results.

• Journal of the Korean Data and Information Science Society
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• v.22 no.1
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• pp.89-97
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• 2011

The aims of this study were to propose a method of estimation for mean residual life function (MRLF) from conditional survival function using the Buckley and James's (1979) pseudo random variables, and then to assess the performance of the proposed method through the simulation studies. The mean squared error (MSE) of proposed method were less than those of the Cox's proportional hazard model (PHM) and Beran's nonparametric method for non-PHM case. Futhermore in the case of PHM, the MSE's of proposed method were similar to those of Cox's PHM. Finally, to evaluate the appropriateness of practical use, we applied the proposed method to the gastric cancer data. The data set consist of the 1, 192 patients with gastric cancer underwent surgery at the Department of Surgery, K-University Hospital.

• Journal of Applied Reliability
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• v.18 no.3
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• pp.220-228
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• 2018

Purpose: The purpose of this study is to investigate the tail behavior of the life distribution which exhibits an increasing failure rate or other positive aging effects after a certain time point. Methods: We characterize the tail behavior of the life distribution with regard to certain reliability measures such as failure rate, mean residual life and reliability function and derive several stochastic properties regarding such life distributions. Also, utilizing an L-statistic and its asymptotic normality, we propose new nonparametric testing procedures which verify if the life distribution has an increasing tail failure rate. Results: We propose the IFR-Tail (Increasing Failure Rate in Tail), DMRL-Tail (Decreasing Mean Residual Life in Tail) and NBU-Tail (New Better than Used in Tail) classes, all of which represent the tail behavior of the life distribution. And we discuss some stochastic properties of these proposed classes. Also, we develop a new nonparametric test procedure for detecting the IFR-Tail class and discuss its relative efficiency to explore the power of the test. Conclusion: The results of our research could be utilized in the study of wide range of applications including the maintenance and warranty policy of the second-hand system.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.11 no.6
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• pp.1997-2003
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• 2010

Mean Residual Life (MRL) function plays a very important role in the area of engineering, medical science, survival studies, social sciences, and many other fields. Specially, in the reliability study of technical systems, the MRL estimation of a component is very important because the sudden stop of a system brings a serious problem. So, many simulation studies of MRL estimation have been done considering various situation variables. In this paper, four estimators of MRL are proposed under random censoring and their performances re compared through bias and Mean Square Error (MSE) by Monte Carlo simulation.

• Journal of applied mathematics & informatics
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• v.41 no.6
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• pp.1275-1301
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• 2023

This paper introduced the Weibull Marshall-Olkin Power Lomax (WMOPL) distribution. The statistical aspects of the proposed model are presented, such as the quantiles function, moments, mean residual life and mean deviations, variance, skewness, kurtosis, and reliability measures like the residual life function, and stress-strength reliability. The parameters of the new model are estimated using six different methods, and simulation research is illustrated to compare the six estimation methods. In the end, two real data sets show that the Weibull Marshall-Olkin Power Lomax distribution is flexible and suitable for modeling data.

• Women's Health Nursing
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• v.17 no.3
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• pp.294-303
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• 2011

Purpose: This study aimed to describe bladder dysfunction in elderly women such as frequency, nocturia, and residual urine. Methods: One hundred elderly women aged 60 and over. The Bristol Female Lower Urinary Symptoms (BFLUT) was used to evaluate the bladder function and to measure the residual urine amount by using a bladder scanner. Data was analyzed with the differences between voiding dysfunction by age group and life habits by t-test, ANOVA and correlation by Pearson correlation coefficient. Results: the mean daytime frequency was 6.8 times and night-time frequency 2.7 times. Sixty three percent of subjects had urgency and 41% had urgent incontinence. Over half of subjects had problem in voiding function. There were significant differences in frequency by age groups and constipation, but not in daytime frequency and residual urine. Lastly, there were significant positive relations between daytime frequency and night-time frequency. Also results indicate that more frequency in daytime equaled to a less residual urine amount. Conclusion: We know many elderly women have lower urinary tract symptoms. Specially women over 75 years have more daytime frequency and night-time frequency. This suggests further research needed in order to understand the relation of voiding patterns and life habits and its influence on quality of life.

• Journal of Korean Society for Quality Management
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• v.25 no.3
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• pp.11-21
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• 1997

The mean residual life(MRL) function gives the expected remaining life of a item at age t. In particular F is said to be an increasing intially then decreasing MRL(IDMRL) distribution if there exists a turing point $t^*\ge0$ such that m(s)$\le$ m(t) for 0$$\le s$\le$ t $t^*$, m(s)$\ge$ m(t) for $t^*\le$ s$\le$ t. If the preceding inequality is reversed, F is said to be a decreasing initially then increasing MRL(DIMRL) distribution. Hawkins, et al.(1992) proposed test of H0 : F is exponential versus$H_1$: F is IDMRL, and $H_0$ versus $H_1$' : F is DIMRL when turning point is unknown. Their test is based on a complete random sample $X_1$, …, $X_n$ from F. In this paper, we generalized Hawkins-Kochar-Loader test to random censored data.

• Communications for Statistical Applications and Methods
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• v.3 no.2
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• pp.275-282
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• 1996

A life distribution F with survival function $\overline{F}$=1-F, finite mean $\mu$ and mean residual life m(t) is said to be NBUE(NWUE) if m(t)$\leq$($\geq$) .$\mu$ for t$\geq$0. This NBUE property can equivalently be characterized by the fact that $\varphi$(u)$\geq$($\leq$)u for 0$\leq$u$\leq$1, where $\varphi$(u) is the scaled total-time-on test transform of F. A generalization of the NBUE properties is that there is a value of p such that $\varphi$(u)\geq.u$ for 0$\leq$u$\leq$p and $\varphi$(u)\leq$$\leq$u$\leq$1, or vice versa. This means that we have a trend change in the NBUE property. In this paper we point out an error of Klefsjo's paper (1988). He erroneously takes advantage of trend change point of failure rate to calculate the empirical test size and power in lognormal distribution. We solves the trend change point of mean residual lifetime and recalculate the empirical test size and power of Klefsjo (1988) in mocensoring case.

• International Journal of Reliability and Applications
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• v.3 no.1
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• pp.1-16
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• 2002

In reliability engineering, the bathtub-shaped hazard rates play an important role in survival analysis and many other applications as well. For the bathtub-shaped, initially the hazard rate decreases from a relatively high value due to manufacturing defects or infant mortality to a relatively stable middle useful life value and then slowly increases with the onset of old age or wear out. In this paper, we present a new two-parameter lifetime distribution function, called the Loglog distribution, with Vtub-shaped hazard rate function. We illustrate the usefulness of the new Vtub-shaped hazard rate function by evaluating the reliability of several helicopter parts based on the data obtained in the maintenance malfunction information reporting system database collected from October 1995 to September 1999. We develop the S-Plus add-in software tool, called Reliability and Safety Assessment (RSA), to calculate reliability measures include mean time to failure, mean residual function, and confidence Intervals of the two helicopter critical parts. We use the mean squared error to compare relative goodness of fit test of the distribution models include normal, lognormal, and Weibull within the two data sets. This research indicates that the result of the new Vtub-shaped hazard rate function is worth the extra function-complexity for a better relative fit. More application in broader validation of this conclusion is needed using other data sets for reliability modeling in a general industrial setting.