• Journal of Korean Society of Forest Science
• /
• v.101 no.4
• /
• pp.599-605
• /
• 2012

The purpose of this study is to estimate diameter distribution, volume per hectare, and carbon stock for Quercus variabilis stand. 354 Quercus variabilis stands were selected on the basis of age and structure, the data and samples for these stands are collected. For the prediction of diameter distribution, Weibull model was applied and for the estimation of the parameters, a simplified method-of-moments was applied. To verify the accuracy of estimates, models were developed using 80% of the total data and validation was done on the remaining 20%. For the verification of the model, the fitness index, the root mean square error, and Kolmogorov-Smirnov statistics were used. The fitness index of the site index, height, and volume equation estimated from verification procedure were 0.967, 0.727, and 0.988 respectively and the root mean square error were 2.763, 1.817, and 0.007 respectively. The Kolmogorov-Smirnov test applied to Weibull function resulted in 75%. From the models developed in this research, the estimated volume and above-ground carbon stock were derived as $188.69m^3/ha$, 90.30 tC/ha when site index and stem number of 50-years-old Quercus variabilis stand show 14 and 697 respectively. The results obtained from this study may provide useful information about the growth of broad-leaf species and prediction of carbon stock for Quercus variabilis stand.

• The Korean Journal of Applied Statistics
• /
• v.20 no.2
• /
• pp.357-371
• /
• 2007

For the time-to-failure data with competing risks, cumulative incidence functions (CIFs) are commonly estimated using nonparametric methods. If the cases of events due to the cause of primary interest are infrequent relative to other cause of failure, nonparametric methods may result in rather imprecise estimates for CIF. In such cases, Bryant et al. (2004) suggested to model the cause-specific hazard of primary interest parametrically, while accounting for the other modes of failure using nonparametric estimator. We represented the semiparametric cumulative incidence estimator and extended to the model of Weibull and log-normal distribution. We also conducted simulations to access the performance of the semiparametric cumulative incidence estimators and to investigate the impact of model misspecification in log-normal cause-specific hazard model.

• International Journal of Reliability and Applications
• /
• v.7 no.1
• /
• pp.27-39
• /
• 2006

Many real world cases in material failure analysis do not follow perfectly the normal distribution. Forcing of the normality assumption may lead to inaccurate predictions and poor product quality. We examine the failure process of the internal bond (IB or tensile strength) of medium density fiberboard (MDF). We propose a forced censoring technique that closer fits the lower tails of strength distributions and better estimates extremely smaller percentiles, which may be valuable to continuous quality improvement initiatives. Further analyses are performed to build an accelerated common-shaped Weibull model for different product types using the $JMP^{(R)}$ Survival and Reliability platform. In this paper, a forced censoring technique is implemented for the first time as a software module, using $JMP^{(R)}$ Scripting Language (JSL) to expedite data processing, which is crucial for real-time manufacturing settings. Also, we use JSL to automate the task of fitting an accelerated Weibull model and testing model homogeneity in the shape parameter. Finally, a package script is written to readily provide field engineers customized reporting for model visualization, parameter estimation, and percentile forecasting. Our approach may be more accurate for product conformance evaluation, plus help reduce the cost of destructive testing and data management due to reduced frequency of testing. It may also be valuable for preventing field failure and improved product safety even when destructive testing is not reduced by yielding higher precision intervals at the same confidence level.

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

• International Journal of Reliability and Applications
• /
• v.6 no.2
• /
• pp.79-85
• /
• 2005

We show how comparative mean residual life functions (MRL) can be used to give unique insights into strengths of materials data. Recall that Weibull's original reliability function was developed studying and fitting strengths for various materials. This creative comparing of MRL functions approach can be used for regular life data or any time to response data. We apply graphical MRL's to real data from tests of tensile strength of high quality engineered wood.

• Communications for Statistical Applications and Methods
• /
• v.12 no.3
• /
• pp.643-652
• /
• 2005

It has been known that the exponentiated exponential distribution can be used as a possible alternative to the gamma distribution or the Weibull distribution in many situations. But the maximum likelihood method does not admit explicit solutions when the sample is multiply censored. So we derive the approximate maximum likelihood estimators for the location and scale parameters in the exponentiated exponential distribution that are explicit function of order statistics. We also compare the proposed estimators in the sense of the mean squared error for various censored samples.

• Journal of Korean Society for Quality Management
• /
• v.29 no.2
• /
• pp.46-53
• /
• 2001

In this paper, a preventive maintenance(PM) policy for a repairable system is considered. The failure rate model proposed by Park et at.(2000) is generalized by assuming that after each PM not only the PM slows down the degradation process of the system but also reduces down the system failure rate by a certain fixed amount. Long-run expected cost rate of the PM policy is derived and the properties of joint solution of the optimal PM period and optimal number of PM which minimizes the expected cost rate are obtained. Numerical examples for the case of a Weibull-type failure rate are given.

• Journal of Applied Reliability
• /
• v.11 no.4
• /
• pp.319-330
• /
• 2011

We consider the stress-strength model in which a unit of strength $T_2$ is subjected to environmental stress $T_1$. An important measure considered in stress-strength model is the reliability parameter R=P($T_2$ > $T_1$). The greater the value of R is, the more reliable is the unit to perform its specified task. In this article, we consider the situations in which $T_1$ and $T_2$ are both independent and dependent, and have certain bivariate distributions as their joint distributions. To study the effect of dependency on R, we investigate several bivariate distributions of $T_1$ and $T_2$ and compare the values of R for these distributions. Numerical comparisons are presented depending on the parameter values as well.

• International Journal of Reliability and Applications
• /
• v.1 no.1
• /
• pp.15-26
• /
• 2000

This paper considers an aperiodic preventive maintenance (PM) model for repairable systems, in which the time intervals between two consecutive preventive maintenances are unequal. To propose such an aperiodic PM model, we assume that each PM reduces the current hazard rate by a certain amount which depends on the number of PMs performed previously. If the system fails between PMs, the minimal repair is performed and the hazard rate remains unchanged after the repair. We give the exact expressions for the hazard rate function for the aperiodic PM model. Based on the proposed aperiodic PM model, we suggest the maximum likelihood method to estimate the parameters characterizing the model and apply the method to the case of Weibull distribution. Numerical examples for estimating the parameters are presented for the purpose of illustration.

• The Korean Journal of Applied Statistics
• /
• v.7 no.2
• /
• pp.89-100
• /
• 1994

In this paper we consider a new estimator of mean residual life (MRL), based on the partial moment of the distribution. The parameters of a partial moment are estimated by its maximum likelihood estimators when the underlying distribution is known. Though the new estimator is not a consistent estimator of the MRL, it is shown to have smaller mean squared error than the well known empirical MRL estimator for certain parametric families. Numerical summaries of the mean squared errors of the new estimator are presented.