• Communications for Statistical Applications and Methods
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• v.15 no.3
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• pp.451-464
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• 2008

Six sigma is the rating that signifies "best in clas", with only 3.4 defects per million units or operations. Higher sigma quality level is generally perceived by customers as improved performance by assigning a correspondingly higher satisfaction score. The process capability indices and the sigma level $Z_{st}$ have been widely used in six sigma industries to assess process performance. Most evaluations on process capability indices focus on point estimates, which may result in unreliable assessments of process performance. In this paper, we consider statistical inference for process capability indices $C_p$, $C_{pk}$ and $C_{pm}$. Also, we study better testing procedure on assessing sigma level $Z_{st}$ and capability index $C_{pm}$, for practitioners to use in determining whether a given process is capable. The proposed method is easy to use and the decision making is more reliable. Whether a process is clearly normal or nonnormal, our bootstrap testing procedure could be applied effectively without the complexity of calculation. A numerical result based on our proposed method is illustrated.

• Journal for History of Mathematics
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• v.25 no.4
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• pp.53-67
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• 2012

Today, it is necessary to calculate orbits with high accuracy in space flight. The key words of Poincar$\acute{e}$ in celestial mechanics are periodic solutions, invariant integrals, asymptotic solutions, characteristic exponents and the non existence of new single-valued integrals. Poincar$\acute{e}$ define an invariant integral of the system as the form which maintains a constant value at all time $t$, where the integration is taken over the arc of a curve and $Y_i$ are some functions of $x$, and extend 2 dimension and 3 dimension. Eigenvalues are classified as the form of trajectories, as corresponding to nodes, foci, saddle points and center. In periodic solutions, the stability of periodic solutions is dependent on the properties of their characteristic exponents. Poincar$\acute{e}$ called bifurcation that is the possibility of existence of chaotic orbit in planetary motion. Existence of near exceptional trajectories as Hadamard's accounts, says that there are probabilistic orbits. In this context we study the eigenvalue problem in early 20th century in three body problem by analyzing the works of Darwin, Bruns, Gyld$\acute{e}$n, Sundman, Hill, Lyapunov, Birkhoff, Painlev$\acute{e}$ and Hadamard.

• Journal of the Korean Geotechnical Society
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• v.25 no.10
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• pp.111-122
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• 2009

Dissolution of some of geo-materials may yield the loss of the soil strength and the settlement of earth structures. The goal of this study is to monitor the several physical behaviors of soluble mixtures during dissolution. Sand-salt mixtures are used to monitor the meso to macro response including the settlements and shear waves. The mixtures of photoelastic and ice disks are used to monitor micro to meso behavior of soluble mixture including the void ratio, force chain, coordination number and horizontal force changes. In the sand-salt mixtures, shear waves are measured by using bender elements in conventional oedometer cells. In the photoelastic disk - ice disk mixtures, micro to meso response are measured by digital images and load cells. The shear wave velocity decreases at the initial stage of the dissolution, and then increases and approaches to asymptotic value. The larger dissoluble particle and the more random packing produces the severe horizontal fore change. After dissolution, the void increases and the coordination number decreases. This study demonstrates that the particle level behavior such as the changes of the force chain, void ratio, and coordination number affects the global behavior such as the change of the shear wave velocity and horizontal force of the system.

• Journal of Korean Society of Forest Science
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• v.86 no.2
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• pp.135-145
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• 1997

This study aimed at evaluating one curvilinear equation and nine non-linear equations for estimating stand growth characteristics(mean dbh, mean height and volume per ha) for the plantations of Pinus koraiensis and the natural stands of Quercus mongolica. The data were collected from 92 plots in Pines koraiensis stands and 83 plots in Quercus mongolica stands, and the site index of all the stands is 14. The curvilinear equation, $Y=at^be^{-c/t}$, used in preparing the yield tables was well fitted within the range of data, but was likely to give overestimates when extrapolating in old stage due to the tendency of linear increase. Among the non-linear equations, logistic equation and Sloboda equation gave overestimates in young stands and reached the asymptotic status early which means underestimates in old stage. Extrapolating in old stage, Hossfeld equation generally gave larger values than others due to its large estimates of parameter a, the maximum value. On the other hand, Bertalanffy equation gave underestimates in young and old stands and overestimates in middle-aged stands. The estimates with Korf equation was relatively low for Pinus koraiensis stands, and this tendency was more obvious in dbh growth of Quercus mongolica stands. Ueno-Ohzaki equation was liable to give over or underestimates depending on the value of parameter b when extrapolating in old stands. Considering the accuracy of estimates and the biological base of the growth equations, Gompertz equation, Chapman-Richards equation and Weibull equation were generally applicable for estimating the stand growth characteristics of both species in the whole range of stand ages including extrapolated range. To get more accurate and precise parameter estimates, more data, especially in old stands, should be required in further study.