• 대한기계학회:학술대회논문집
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• 대한기계학회 2008년도 추계학술대회A
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• pp.1069-1074
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• 2008

Tool condition monitoring (TCM) is crucial for improvement of productivity in manufacturing process. However, TCM techniques have not been applied to monitor tool failure in an industrial gear shaving application. Therefore, this work studied a statistical TCM method for monitoring gear shaving tool condition. The method modeled the shaving process using beta probability distribution in order to extract the effective features. Modeling includes rectifying for converting a bi-modal distribution into a unimodal distribution, estimating parameters of beta probability distribution based on method of moments. The usefulness of features obtained from the proposed method was evaluated and discussed.

• 호남수학학술지
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• 제33권2호
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• pp.187-206
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• 2011

The main object of this paper is to present generalization of extended beta function, extended hypergeometric and confluent hypergeometric function introduced by Chaudhry et al. and obtained various integral representations, properties of beta function, Mellin transform, beta distribution, differentiation formulas transform formulas, recurrence relations, summation formula for these new generalization.

• Communications for Statistical Applications and Methods
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• 제16권2호
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• pp.389-396
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• 2009

Approximations for the null distribution of a test statistic arising in multivariate analysis to test homogeneity of variances and a mixture of two beta distributions by making use of a product of beta baseline density function and a polynomial adjustment, so called beta-polynomial density approximant, are discussed. Explicit representations of density and distribution approximants of interest in each case can easily be obtained. Beta-polynomial density approximants produce good approximation over the entire range of the test statistic and also accommodate even the bimodal distribution using an artificial example of a mixture of two beta distributions.

• 품질경영학회지
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• 제21권1호
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• pp.171-180
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• 1993

Variables, x and y are said to have a linear relation if $y={\beta}_0+{\beta}_1\;x$, and ${\beta}_0$ and ${\beta}_1$ are constants. The relationship is called a structural relationship if x has positive variance (i.e., x is not fixed) and only error-prone measurements of x and y can be obtained. This paper derives (to order $n^{+1/2}$) an approximate distribution of the Studentized test statistic for testing hypotheses about the slope parameter, ${\beta}_1$ in a simple linear structural model. A simulation study suggests our approximate distribution is more accurate approximation to the exact distributions of the Studentized statistic than is the limiting distribution.

• Journal of Mechanical Science and Technology
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• 제16권1호
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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 applied mathematics & informatics
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• 제27권3_4호
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• pp.955-961
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• 2009

In this paper, we establish some characterizations which is satisfied by the independence of the upper record values from the Pareto distribution. We prove that $X\;{\in}\;PAR(1,\;{\beta})$, $\beta$ > 0, if and only if $\frac{X_{U(n)}}{X_{U(m)}}$ and $X_{U(m)}$, $1\;{\le}\;m\;<\;n$ are independent. We show that $X\;{\in}\;PAR(1,\;{\beta})$, $\beta$ > 0 if and only if $\frac{X_{U(n)}+X_{U{(n+1)}}}{X_{U(n)}}$ and $X_{U(n)}$, $n\;{\ge}\;1$ are independent. And we characterize that $X\;{\in}\;PAR(1,\;{\beta})$, $\beta$ > 0, if and only if $\frac{X_{U(n)}}{X_{U(n)}+X_{U{(n+1)}}}$ and $X_{U(n)}$, $n\;{\ge}\;1$ are independent.

• 산업경영시스템학회지
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• 제35권2호
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• pp.98-105
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• 2012

This paper describes the Bayesian approach for reliability demonstration test based on the samples from a finite population. The Bayesian approach involves the technical method about how to combine the prior distribution and the likelihood function to produce the posterior distribution. In this paper, the hypergeometric distribution is adopted as a likelihood function for a finite population. The conjugacy of the beta-binomial distribution and the hypergeometric distribution is shown and is used to make a decision about whether to accept or reject the finite population judging from a viewpoint of faulty goods. A numerical example is also given.

• 경영과학
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• 제24권1호
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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.

• 한국물환경학회지
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• 제33권3호
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• pp.256-272
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• 2017

Extreme rainfall has become more frequent over the Korean peninsula in recent years, causing serious damages. In a changing climate, traditional approaches based on historical records of rainfall and on the stationary assumption can be inadequate and lead to overestimate (or underestimate) the design rainfalls. A main objective of this study is to develop a stochastic disaggregation method of seasonal rainfall to hourly extreme rainfall, and offer a way to derive the nonstationary IDF curves. In this study, we propose a novel approach based on a Four-Parameter Beta (4P-beta) distribution to estimate the nonstationary IDF curves conditioned on the observed (or simulated) seasonal rainfall, which becomes the time-varying upper bound of the 4P beta distribution. Moreover, this study employed a Bayesian framework that provides a better way to take into account the uncertainty in the model parameters. The proposed model showed a comparable design rainfall to that of GEV distribution under the stationary assumption. As a nonstationary rainfall frequency model, the proposed model can effectively translate the seasonal variation into the sub-daily extreme rainfall.

• 충청수학회지
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• 제25권3호
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• pp.501-505
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• 2012

In this paper, general classes of continuous distributions are characterized by considering the conditional expectations of functions of upper record statistics. The specific distribution considered as a particular case of the general class of distribution are Exponential, Exponential Power(EP), Inverse Weibull, Beta Gumbel, Modified Weibull(MW), Weibull, Pareto, Power, Singh-Maddala, Gumbel, Rayleigh, Gompertz, Extream value 1, Beta of the first kind, Beta of the second kind and Lomax.