• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.479-488
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• 2007

A sequential procedure is proposed in order to construct one-sided confidence intervals for a normal mean with guaranteed coverage probability and ${\beta}-protection$ when the normal mean and variance are identical. First-order asymptotic properties on the sequential sample size are found. The derived results hold with uniformity in the total parameter space or its subsets.

• Journal of Mechanical Science and Technology
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• v.16 no.1
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• pp.60-74
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• 2002

In this study, normal, log-normal, triangular, uniform. Weibull, Erlang and unit beta probability density functions are tried to represent the behaviour of frequency distributions of workpiece dimensions collected from various manufacturing firms. Among the distribution functions, the unit beta distribution function is found to be the best fit using the chi-square test of fit. An attempt is made for the adoption of the unit beta model to x-bar charts of quality control in manufacturing. In this direction, upper and lower control limits (UCL and LCL) of x-bar control charts of dimension measurements are estimated for the beta model, and the observed differences between the beta and normal model control limits are discussed for the measurement sets.

• Journal of the Korean Data and Information Science Society
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• v.16 no.2
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• pp.451-456
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• 2005

We introduce the standard two-sided power normal distribution and consider the relation between the probability in standard two-sided power distribution and the probability in standard two-sided power normal distribution and obtain the even moment of the special two-sided power normal distribution including the cases considered by Gupta and Nadarajah(2004)

• Journal of the Korean Statistical Society
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• v.31 no.3
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• pp.379-389
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• 2002

For two normal distribution with unknown means and unknown variances, a sequential procedure for estimating the difference of two normal means which satisfies both the coverage probability condition and the $\beta$-protection is proposed under some smoothness of variable imprecision function, and the asymptotic normality of the proposed stopping time after some centering and scaling is given.

• Korean Management Science Review
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• v.24 no.1
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• pp.77-90
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• 2007

Taguchi assumed that a product characteristic has the uniform distribution in its preventive maintenance limit when deriving the expected loss generated by the quality deviation. But it is reasonable to assume that a product characteristic has the normal distribution than the uniform distribution. On this paper, we first find the optimum inspection interval and the optimum preventive maintenance limit under the truncated triangular distribution. Secondly we use the beta-general distribution and compare with the truncated triangular distribution. By using the numerical examples, we find the optimum inspection interval and the optimum preventive maintenance limit under their distributions. As a result, we find that the beta-general distribution gives the best solution and easy calculation.

• The Korean Journal of Applied Statistics
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• v.28 no.6
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• pp.1245-1255
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• 2015

In this paper, we investigated the major 8 companies of Korean stock market, and carried out the goodness of fit and independence tests. We found out the distributions of absolute returns are closed to compressed exponential distribution. The parameters are dominant that 1 < ${\beta}$ < 2, followed by ${\beta}=1$(exponential distribution) and ${\beta}=2$(normal distribution). Meanwhile, we assured that most of the absolute returns for major 8 companies have relevance to each other by chi-square independence test.

• Communications for Statistical Applications and Methods
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• v.6 no.1
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• pp.275-283
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• 1999

In order to estimate a parameter $(\alpha,\beta^r), r\epsilonN$, in a distribution belonging to a location-scale family we usually use best invariant estimator (BIE) and best unbiased estimator (BUE). But in some conditions Ryu (1996) showed that BIE is better than BUE. In this paper we calculate risks of BIE and BUE in a normal and an exponential distribution respectively and calculate a percentage risk improvement exponential distribution respectively and calculate a percentage risk improvement (PRI). We find the sample size n which make no significant differences between BIE and BUE in a normal distribution. And we show that BIE is always significantly better than BUE in an exponential distribution. Also simulation in a normal distribution is given to convince us of our result.

• Journal of Korean Society for Quality Management
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• v.44 no.1
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• pp.167-180
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• 2016

Purpose: The problem for the traditional control chart is that it is unable to monitor the very small fraction of nonconforming and the underlying distribution is the normal distribution. $Z_p$ control chart is useful where it controls the vert small fraction on nonconforming. In this study, we will design the $Z_p$ control chart in order to use under non-normal process. Methods: $Z_p$ is calculated not by failure rate based on attribute data but using variable data. Control limit for non-normal $Z_p$ control chart is designed based on ${\alpha}$-risk calculated by cumulative distribution function of Burr distribution. ${\beta}$-risk, which is for performance evaluation, obtains in the Burr distribution's cumulative distribution function and control limit. Results: The control limit for non-normal $Z_p$ control chart is designed based on Burr distribution. The sensitivity can be checked through ARL table and OC curve. Conclusion: Non-normal $Z_p$ control chart is able to control not only the very small fraction of nonconforming, but it is also useful when $Z_p$ distribution is non-normal distribution.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.1
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• pp.29-36
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• 2013

In the treatment of the sequential beta-protection procedure, we define the reasonable stopping time and investigate that for the stopping time Wijsman's requirements, coverage probability and beta-protection conditions, are satisfied in the estimation for the mean vector ${\mu}$ by the sample from the multivariate normal distributed population with unknown mean vector ${\mu}$ and a positive definite variance-covariance matrix ${\Sigma}$.

• Journal of Institute of Control, Robotics and Systems
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• v.20 no.8
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• pp.854-867
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• 2014

This paper deals with the performance comparison of a PSO algorithm inspired in the process of simulating the behavior pattern of the organisms. The PSO algorithm finds the optimal solution (fitness value) of the objective function based on a stochastic process. Generally, the stochastic process, a random function, is used with the expression related to the velocity included in the PSO algorithm. In this case, the random function of the normal distribution (Gaussian) or uniform distribution are mainly used as the random function in a PSO algorithm. However, in this paper, because the probability distribution which is various with 2 shape parameters can be expressed, the performance comparison of a PSO algorithm using the beta probability distribution function, that is a random function which has a high degree of freedom, is introduced. For performance comparison, 3 functions (Rastrigin, Rosenbrock, Schwefel) were selected among the benchmark Set. And the convergence property was compared and analyzed using PSO-FIW to find the optimal solution.