생산능력지수에 대한 고찰

박효일 청주대학교 2012 産業科學硏究 Vol.30 No.1

In this study, we consider reviewing two kinds of process capability indices based on the mean which are famous and useful in the production floor to control and improve the production process in the industry. Then we introduce another definition of the process capability index which uses a median of the process distribution. Also we propose its estimate, discuss the consistency of the estimate and derive the asymptotic normality with the corresponding estimate of the limiting variance. Then we discuss some interesting features of the process capability indices with the re-sampling method as concluding remarks.

A Study on the Nonparametric Simultaneous Tests for the Location and Scale Parameters

박효일 한국자료분석학회 2013 Journal of the Korean Data Analysis Society Vol.15 No.5

In this research, we consider a nonparametric simultaneous test procedure for the location and scale parameters. For this, first of all, we formulate the null hypothesis and its alternative under the location-scale model. Then we propose three types of nonparametric tests with the three different combining functions to combine the results of the individual tests based on the well-known nonparametric tests for each parameter. We use the p-values for the results of the individual tests. Then we compare two procedures for the efficiency by obtaining the empirical powers for the five different underlying distributions through a simulation study. One procedure uses the Mood test and the other is the Ansari-Bradley one for the scale parameter. Then we discuss some interesting aspects related to the simultaneous tests with the types of alternatives which can be adopted to our procedure and obtaining the p-values for each individual test. Finally we comment briefly the use of bootstrap method in our procedure.

중앙값을 이용한 Cpk에 대한 연구

박효일 한국자료분석학회 2009 Journal of the Korean Data Analysis Society Vol.11 No.6

In this study, we propose a new process capability index(PCI) C_pk(theta) using based on median(theta) which is a modified version of C_pk and consider to obtain a consistent estimate. We derive the normal approximation as an asymptotic property and propose a consistent estimate for the limiting variance in a detailed manner with PLUG-IN method in order to furnish the statistical inferences for C_pk(theta). For the gamma family including the exponential distribution which are all asymmetric distributions, we obtain the values of C_pk(theta) and C_pk and compare both the results. Then we introduce to use the bootstrap method for obtaining an estimate for the limiting variance and applying to the statistical inferences for C_pk(theta) and briefly comment for the future research directions. 이번 연구에서 다양한 공정능력지수(PCI)에 대한 정의중의 하나인 C_pk에 대하여 평균이 아닌 중앙값(theta)을 이용하여 새로운 C_pk(theta)를 제시하고 이에 대한 일치성을 갖는 추정치를 제시한다. 점근적 성질로서 정규근사식을 도출하고 C_pk(theta)에 대한 각종 통계적 추론을 목적으로 PLUG-IN 방법을 사용하여 극한분산에 대한 일치성을 갖는 추정치를 구하는 과정을 설명한다. 좌우대칭이 아닌 지수분포를 비롯한 감마분포에 대하여 C_pk(theta)와 C_pk를 도출하여 결과를 비교하며 붓스트랩 방법을 극한분산을 비롯한 C_pk(theta)에 대한 통계적 추론에 이용하는 과정을 간단히 설명하고 장래의 연구방향에 관하여 개략적으로 언급한다.

Simultaneous Test에 대한 역사적 및 이론적 고찰

박효일 청주대학교 2017 産業科學硏究 Vol.34 No.2

In this research, we consider the historic and theoretic aspects for the simultaneous tests of the mean and variance or the location and scale parameters in the parametric and nonparametric tests. For this, first of all, we review the two types of tests for the nonparametric and parametric approaches with several combining functions. Then we discuss some interesting aspects related with the simultaneous tests including obtaining the null distributions of the combining functions. Finally, we discuss some concluding remarks with future research topics and ways.

Combined Control Charts for the Mean and Variance using Likelihood Method

박효일 한국자료분석학회 2013 Journal of the Korean Data Analysis Society Vol.15 No.6

In this study, we consider to propose combined control charts for the process mean and variance to control simultaneously assuming that the process distribution is normal. For this, first of all, we review the existing combined control charts and then propose a new chart based on the union-intersection test with the jointly likelihood ratio statistics for the mean and variance. Then we apply the Liptak combining function to propose another combined control chart. For the construction of those combined control charts, we use the fact that a series of the hypothesis tests is equivalent to the maintenance of a control chart. In order to combine the two individual tests for the respective mean and variance, we utilize the p-values for both individual tests since the two likelihood ratio statistics have different forms. Then we compare the performance of the combined charts reviewed and proposed in this study by obtaining the empirical probabilities detecting the out-of-control state when the process becomes out-of-control under the five different scenarios through a simulation study. Finally, we discuss some interesting aspects which are related with the combined charts as concluding remarks.

Bootstrap Median Control Chart

박효일 한국자료분석학회 2008 Journal of the Korean Data Analysis Society Vol.10 No.4

In this study, we propose a median control chart with the bootstrap method. In order to determine the control limits, first we consider to use the estimate of variance which can be considered as a moment estimate and then use the bootstrap confidence intervals by applying the several bootstrap methods after reviewing several bootstrap methods. Then we show an example as an illustration for our proposed method and compare several bootstrap methods through simulation study with three different distributions. Finally we discuss some interesting features in median control chart and the bootstrap methods as concluding remarks.

Nonparametric Tests for Multiple Endpoints with Grouped Observations

박효일,홍승만 한국자료분석학회 2008 Journal of the Korean Data Analysis Society Vol.10 No.1

In this paper, we consider a nonparametric test procedure for the multiple endpoints with grouped data under two sample problem setting. For the construction of the test statistic, we use the linear rank statistics which were derived based on the likelihood ratio principle for each component. Then the asymptotic distribution of the test statistic is derived under the null hypothesis. Finally, we illustrate our test procedure with an example and discuss some concluding remarks.

A Nonparametric Test Procedure for Multivariate Censored Data

박효일 한국자료분석학회 2007 Journal of the Korean Data Analysis Society Vol.9 No.4

In this paper, we consider a nonparametric test procedure for comparing two distribution functions based on the multivariate, grouped and right censored data under the two sample problem setting. For the construction of the test statistic, we use the linear rank statistics which were derived based on the likelihood ratio principle for each component. Then the asymptotic distribution of the test statistic is derived under the null hypothesis. Finally, we illustrate our test with an example and discuss some concluding remarks. In appendix, we derive the expression of the covariance.

Signed Rank Test for Two Sample Case

박효일 한국자료분석학회 2006 Journal of the Korean Data Analysis Society Vol.8 No.6

In this paper, we consider an extension of the signed rank test for the one-sample case to the two-sample problem. We make use of the fact that the distribution of the difference between any two independent random variables under the location translation model is symmetric about their location translation parameter. Then we derive the asymptotic null distribution and illustrate with an example with applying the permutation principle. Finally, we discuss its efficacy as a concluding remarks.

A Study on the Nonparametric Tests for the Two-Sample Problem

박효일 한국자료분석학회 2010 Journal of the Korean Data Analysis Society Vol.12 No.5

In this paper, we consider nonparametric test procedures based on a group of quantile test statistics. Since we do not assume any specific model, this new nonparametric tests may be useful when the underlying distributions are completely unknown. We consider the quadratic form of statistic for the general alternatives and derive the chi-square distribution as the limiting distribution for the large sample case. Then we illustrate our procedure with an example and compare the proposed tests with the individual quantile tests by obtaining empirical powers through simulation study by applying the permutation principle. Also we comment on the related discussions to this testing procedure as concluding remarks.