• Journal of Korean Society for Quality Management
• /
• v.7 no.2
• /
• pp.7-10
• /
• 1979

In this paper the Rao-Blackwell and Lehmann-$Scheff{\acute{e}}$ Theorem are used to drive the minimum variance unbiased estimators of system reliability for a number of distributions when a system consists of n Components whose random life times are assumed to be independent and identically distributed. For the case of a negative exponential life time, we obtain the maximum likelihood estimator of the system reliability and compair it with minimum variance unbiased estimator of the system reliability.

• Journal of the Korean Statistical Society
• /
• v.25 no.2
• /
• pp.235-241
• /
• 1996

The ordinary least squares estimator of the disturbance variance in the linear regression model with stationary errors is shown to be asymptotically unbiased when the error process has a spectral density bounded from the above and away from zero. Such error processes cover a broad class of stationary processes, including ARMA processes.

• Journal of the Korean Statistical Society
• /
• v.23 no.1
• /
• pp.187-198
• /
• 1994

We derive a new Cramer-Rao type lower bound for the reciprocal of the density height of the median-unbiased estimators which improves most of the previous lower bounds and is attainable under much weaker conditions. We also identify useful necessary and sufficient condition for the attainability of the lower bound which is considerably weaker than those for the mean-unbiased estimators. It is shown that these lower bounds are attained not only for the family of continuous distributions with monotone likelihood ratio (MLR) property but also for the location and scale families with strong unimodal property.

• Journal of the Korean Statistical Society
• /
• v.22 no.1
• /
• pp.1-12
• /
• 1993

An approach to make the information bound sharper in median-unbiased estimation, based on an analogue of the Cramer-Rao inequality developed by Sung et al. (1990), is introduced for continuous densities with a nuisance parameter by considering information quantities contained both in the parametric function of interest and in the nuisance parameter in a linear fashion. This approach is comparable to that of improving the information bound in mean-unbiased estimation for the case of two unknown parameters. Computation of an optimal weight corresponding to the nuisance parameter is also considered.

• ETRI Journal
• /
• v.25 no.5
• /
• pp.418-421
• /
• 2003

We propose an unbiased signal-to-interference ratio (SIR) estimator for the high speed downlink packet access (HSDPA) system. The proposed SIR estimator solves the problem of underestimation present in conventional SIR estimators and is suitable for channel quality measurement in the adaptive modulation and coding scheme of HSDPA, which requires accurate SIR estimation for optimum adaptive modulation and coding selection. Our analysis and simulation results demonstrate the improved estimation performance of the proposed SIR estimator.

• The Korean Journal of Applied Statistics
• /
• v.14 no.1
• /
• pp.13-24
• /
• 2001

In this paper, we investigated mean estimation methods in two-phase sampling. Under the fixed expected cost we reviewed the optimal sample sizes, minimum variances and approximate unbiased variance estimators for usual ratio estimator, stratified sample mean with proportional allocation and Rao's allocation of the second phase sample. Also we proposed combined ratio estimator, which uses both ratio estimation and stratification and derived optimal sample size, minimum variance and unbiased variance estimator. Through a limited simulation study, we compared estimators by design effects and came to know that ratio estimator is more efficient than stratified sample mean in some cases and inefficient in the other cases, but combined ratio estimator is more efficient than others in most cases.

• Journal of Korean Society for Quality Management
• /
• v.22 no.1
• /
• pp.82-95
• /
• 1994

When independent individual measurements are taken both $S/c_4$ and $\bar{R}/d_2$ are unbiased estimators of the process standard deviation. However, with dependent data $\bar{R}/d_2$ is not an unbiased estimator of the process standard deviation. On the other hand $S/c_4$ is an asymptotic unbiased estimator. If there exists correlation in the data, positive(negative) correlation tends to increase(decrease) the ARL. The effect of using $\bar{R}/d_2$ is greater than $S/c_4$ if the assumption of independence is invalid. Supplementary runs rule shortens the ARL of X control charts dramatically in the presence of correlation in the data.

• The Korean Journal of Applied Statistics
• /
• v.6 no.1
• /
• pp.95-103
• /
• 1993

Necessary and sufficient conditions for the equality between the best linear unbiased estimators in two linear models with different covariance matrices, $V_1 and V_2$, say, are derived. Various applications of this discovery are also given. Necessary and sufficient conditions for the equality between the best linear unbiased estimator and the ordinary least squares estimator are discussed related to this topic.

• Journal of Korean Society for Quality Management
• /
• v.22 no.1
• /
• pp.205-213
• /
• 1994

We construct a new lower bound of Cramer-Rao type for the median-unbiased estimator in the presence a nuisance parameter. We also identify useful necessary and sufficient conditions for the attainability of the lower bound. Some applications including the analysis of censored reliability data are considered as examples.

• IE interfaces
• /
• v.22 no.3
• /
• pp.214-222
• /
• 2009

In the early design stage, system reliability must be estimated from life testing data at the component level. Previously, a point estimate of system reliability was obtained from the unbiased estimate of the component reliability after assuming that the number of failed components for a given time followed a binomial distribution. For deriving the confidence interval of system reliability, either the lognormal distribution or the normal approximation of the binomial distribution was assumed for the estimator of system reliability. In this paper, a new estimator is used for the component level reliability, which is biased but has a smaller mean square error than the previous one. We propose to use the beta distribution rather than the lognormal or approximated normal distribution for developing the confidence interval of the system reliability. A numerical example based on Monte Carlo simulation illustrates advantages of the proposed approach over the previous approach.