• International Journal of Reliability and Applications
• /
• v.17 no.1
• /
• pp.51-63
• /
• 2016

Stress function of ball bearing is function of multiple stochastic factors and this system is so complex that analytical expression for reliability is difficult to obtain. To address this pressing problem, in this article, we have made an attempt to approximate system reliability of this important item based on reliability bounds under the stress strength setup. This article also provides level of error of this item. Numerical analysis has been adopted to show the closeness between the upper and lower bounds of this item.

• Journal of the Korean Statistical Society
• /
• v.20 no.2
• /
• pp.108-117
• /
• 1991

A parametric empirical Bayes procedure is proposed and studied to compare treatments simultaneously with the best. Minimum Bayes risk lower bounds are derived for an additive loss function, and their relationship with Bayesian simultaneous confidence lower bounds is given. For the proposed empirical Bayes procedure, the nominal confidence level both in Bayesian sense and in frequentist's sense is shown to be controlled asymptotically. For practical implementation, a measure of significance similar to f-value is suggested with an illustrative example.

• Bulletin of the Korean Mathematical Society
• /
• v.35 no.2
• /
• pp.209-225
• /
• 1998

In this paper we obtain sharp upper and lower bounds of small ball oprobabilities for Gaussian processes with stationary increments, whose results are essential to estabilish Chung type laws of iterated logarithm.

• Journal of the Korean Operations Research and Management Science Society
• /
• v.16 no.2
• /
• pp.164-176
• /
• 1991

This paper considers the model of a k-out-of-n :G system with non-identical components which are subject to both forced and planned outages. For the forced outages, it assumes that there are the independent and common-cause outage events causing component failures. Then, the objective is to derive the upper and lower bounds on the mean operating time between system failures in the ample-server model. In addtion, the mean system failure times are also considered.

• Bulletin of the Korean Mathematical Society
• /
• v.50 no.5
• /
• pp.1725-1736
• /
• 2013

In this paper, we compute the images of homotopy groups of various classical Lie groups under the homomorphisms induced by the natural projections from those groups to irreducible symmetric spaces of classical type. We identify that those computations are certain lower bounds of Gottlieb groups of irreducible symmetric spaces. We use the lower bounds to compute some Gottlieb groups.

• Journal of the Chungcheong Mathematical Society
• /
• v.22 no.2
• /
• pp.171-175
• /
• 2009

Let $A_1,\;A_2,\;{\cdots},\;A_n$ be a sequence of events on a given probability space. Let $m_n$ be the number of those $A_{i}{^{\prime}}s$ which occur. We establish an improved lower bounds of Univariate Bonferroni-Type inequality by using the linearity of binomial moments $S_1,\;S_2,\;S_3,\;S_4$ and$S_5$.

• Journal of the Korean Operations Research and Management Science Society
• /
• v.10 no.2
• /
• pp.45-53
• /
• 1985

In the present paper, the capacitated solid transportation problem (planar constraints) is considered with upper and lower bounds on the rim conditions. The considered model has been shown to be equipvalent to a standard capacitated 3-index transportation problem. A procedure to solve any capacitated 3-index transportion problem is also suggested. Some special cases of the considered model have been shown to conform to possible practical situations.

• Kyungpook Mathematical Journal
• /
• v.49 no.2
• /
• pp.321-348
• /
• 2009

In this paper, we give two lower bounds on the diameter of the boundary slope set of a Montesinos knot. One is described in terms of the minimal crossing numbers of the knots, and the other is related to the Euler characteristics of essential surfaces with the maximal/minimal boundary slopes.

• Korean Journal of Mathematics
• /
• v.10 no.1
• /
• pp.67-74
• /
• 2002

Suppose linear forms whose coefficients are arithmetic progressions are given. In this paper, we will find the upper and lower bounds of the minimal ranks of subforms of these forms which left the Frobenius numbers invariant. This is an improvement of Ritter's bounds.

• Kyungpook Mathematical Journal
• /
• v.61 no.3
• /
• pp.583-590
• /
• 2021

In this work we give new upper and lower bounds for the numerical radius of a complex square matrix A using the entries and the trace of A.