• Journal of the Korean Statistical Society
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• v.32 no.1
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• pp.25-32
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• 2003

In this paper, we define the mean life process for the right censored data and show the asymptotic equivalence between two kinds of the mean life processes. We use the Kaplan-Meier and Susarla-Van Ryzin estimates as the estimates of survival function for the construction of the mean life processes. Also we show the asymptotic equivalence between two mean residual life processes as an application and finally discuss some difficulties caused by the censoring mechanism.

• Journal of the Korean Mathematical Society
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• v.43 no.2
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• pp.225-239
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• 2006

In [5], Csorgo and Zitikis exposed the strong $uniform-over-[0,\;{\infty}]$ consistency, and weak $uniform-over-[0,\;{\infty}]$ approximation of the empirical mean residual life process by employing weight functions. We carry on the uniform asymptotic behaviors of the empirical mean residual life process over the whole positive half line by representing the process as an integral form. We compare our results with those of Yang [15], Hall and Wellner [8], and Csorgo and Zitikis [5].

• 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.

• Journal of the Korean Statistical Society
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• v.22 no.2
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• pp.147-157
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• 1993

In the survivla analysis the problem of estimating mean residual life function (MRLF) under random censoring is very important. In this paper we propose and study a nonparametric estimator of MRLF, which is a functional form based on the estimator of the survival function due to Susarla and Van Ryzin (1980). The proposed estimator is shown to be better than some other estimators in terms of mean square errors for the exponential and Weibull cases via Monte Carlo simulation studies.

• Journal of the Korean Data and Information Science Society
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• v.4
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• pp.97-107
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• 1993

In this paper we propose a nonparametric estimator of the men residual life function (MRLF) on a coherent system under the condition that the component lifetimes are censored by system lifetime. It is shown that the proposed estimator, considered as a function of age t, converges weakly to a Gaussian process on a fixed interval. A consistent estimator of asymptotic variance of the proposed estimator is also given.

• Journal of the Korean Society for Precision Engineering
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• v.27 no.4
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• pp.79-86
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• 2010

Mechanical structures with power sources experience repeated force produced by motors. In result, the life of the pipes reduces and ultimately, the pipes collapse. Such pipes are formed into several shapes and particularly, the U-shape pipe is damaged frequently. In most cases, the U-shape pipe is made with a straight pipe by complicated bending work. During this work process, plastic deformation of the pipe produces residual stress in the pipe. This residual stress significantly affects the fracture behavior of the pipe and induces the change of the stress ratio (min. stress/Max. stress = R). For this reason, residual stress has to be evaluated. In this paper, the residual stress of a U-shaped pipe was evaluated by FEM analysis. In addition, fatigue tests of the U-shaped pipe were performed by using a uniaxial fatigue testing machine. The results of the fatigue test were modified with the results of FEM (Finite Element Method) analysis for residual stress. The modified fatigue test results of the U-shaped pipe were compared with those of a straight pipe.

• Journal of Mechanical Science and Technology
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• v.14 no.9
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• pp.935-946
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• 2000

Elastic-plastic stress analysis has been performed to evaluate the fatigue life of an autofrettaged pressure vessel containing cross-bores subjected to pulsating internal pressure of 200 MPa. Finite element analyses were used to calculate the residual and operating stress distributions of the pressure vessel due to the autofrettage process and pulsating internal pressure, respectively. Theoretical stress concentration factors of 3.06, 2.58, and 2.64 were obtained at the cross-bore of the pressure vessel due to internal pressure, 50%, and 100% autofrettage loadings, respectively. Local stresses and local strains determined from the elastic-plastic finite element analysis were employed to calculate the failure location and fatigue life of the pressure vessel with radial cross-bores, incorporating the low-cycle fatigue properties of the pressure vessel steel and fatigue damage parameters. Increase in the amount of overstrain by autofrettage process moved the crack initiation location from the inner radius toward a mid-wall, and extended the crack initiation life. Predicted fatigue life of the fully autofrettaged pressure vessel with cross-bores increased about 50%, compared to the unautofrettaged pressure vessel. At the autofrettage level higher than 50%, the failure location and fatigue life of the pressure vessel were not significantly influenced by the autofrettage level.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.34 no.2
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• pp.37-45
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• 2022

A simplified model using the lifetime distribution has been presented to estimate the Mean Residual Life (MRL) of rubble-mound breakwaters, which is not like a stochastic process model based on time-dependent history data to the cumulative damage progress of rubble-mound breakwaters. The parameters involved in the lifetime distribution can be easily estimated by using the upper and lower limits of lifetime and their likelihood that made a judgement by several experts taking account of the initial design lifetime, the past sequences of loads, and others. The simplified model presented in this paper has been applied to the rubble-mound breakwater with TTP armor layer. Wiener Process (WP)-based stochastic model also has been applied together with Monte-Carlo Simulation (MCS) technique to the breakwater of the same condition having time-dependent cumulative damage to TTP armor layer. From the comparison of lifetime distribution obtained from each models including Mean Time To Failure (MTTF), it has found that the lifetime distributions of rubble-mound breakwater can be very satisfactorily fitted by log-normal distribution for all types of cumulative damage progresses, such as exponential, linear, and logarithmic deterioration which are feasible in the real situations. Finally, the MRL of rubble-mound breakwaters estimated by the simplified model presented in this paper have been compared with those by WP stochastic process. It can be shown that results of the presented simplified model have been identical with those of WP stochastic process until any ages in the range of MTT F regardless of the deterioration types. However, a little of differences have been seen at the ages in the neighborhood of MTTF, specially, for the linear and logarithmic deterioration of cumulative damages. For the accurate estimation of MRL of harbor structures, it may be desirable that the stochastic processes should be used to consider properly time-dependent uncertainties of damage deterioration. Nevertheless, the simplified model presented in this paper can be useful in the building of the MRL-based preventive maintenance planning for several kinds of harbor structures, because of which is not needed time-dependent history data about the damage deterioration of structures as mentioned above.

• International Journal of Reliability and Applications
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• v.17 no.2
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• pp.149-158
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• 2016

We are enjoying a very comfortable life thanks to modern civilization, however, comfort is not guaranteed to us. Development of software system is a difficult and complex process. Therefore, the main focus of software development is on improving the reliability and stability of a software system. We have become aware of the importance of developing software reliability models and have begun to develop software reliability models. NHPP software reliability models have been developed through the fault intensity rate function and the mean value functions within a controlled testing environment to estimate reliability metrics such as the number of residual faults, failure rate, and reliability of the software. In this paper, we present a new NHPP software reliability model with Burr Type III fault detection rate, and present the goodness-of-fit of the fault detection rate software reliability model and other NHPP models based on two datasets of software testing data. The results show that the proposed model fits significantly better than other NHPP software reliability models.

• Journal of Animal Science and Technology
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• v.50 no.4
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• pp.561-572
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• 2008

Responses of real-time control parameters, such as ORP, DO and pH, to the conditions of biological animal wastewater treatment process were examined to evaluate the stability of real-time control using each parameter. Also an optimum index for supplemental carbon source addition based on NOx-N level was determined under a consideration of denitrification rate by endogenous respiration of microorganism and residual organic matter in liquor. Experiment was performed with lab-scale sequencing batch reactor(SBR) and working volume of the process was 45L. The distinctive nitrogen break point(NBP) on ORP-and DO-time profiles, which mean the termination of nitrification, started disappearing with the maintenance of low NH4-N loading rate. Also the NBP on ORP-and DO-time profiles was no longer observed when high NOx-N was loaded into the reactor, and the sensitivity of ORP became dull with the increase of NOx-N level. However, the distinctive NBP was constantly occurred on pH(mV)-time profile, maintaining unique profile patterns. This stable occurrence of NBP on pH(mV)-time profile was lasted even at very high NOx-N:NH4-N ratio(over 80:1) in reactor, and the specific point could be easily detected by tracking moving slope change(MSC) of the curve. Revelation of NBP on pH(mV)-time profile and recognition of the realtime control point using MSC were stable at a condition of over 300mg/L NOx-N level in reactor. The occurrence of distinctive NBP was persistent on pH(mV)-time profile even at a level of 10,000mg/L STOC(soluble total organic carbon) and the recognition of NBP was feasible by tracing MSC, but that point on ORP and DO-time profiles began to disappear with the increase of STOC level in reactor. The denitrfication rate by endogenous respiration and residual organic matter was about 0.4mg/L.hr., and it was found that 0.83 would be accepted as an index for supplemental carbon source addition when 0.1 of safety factor was applied.