• Journal of Korean Society for Quality Management
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• v.24 no.1
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• pp.1-9
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• 1996

Ritchken(1985) analyzes free replacement and pro-rata warranty policies for products receiving renewable warranies. He shows that for constant failure rates pro-rata warranty policies are more attractive to risk-averse manufacturers than shorter term free replacement policies that result in the same average warranty cost. This paper considers the case when product lifetimes distributions are of phase-type. When this is so, Ritchken's performance measures can be simplified considerably. It is found, that irrespective of the pattern of failure rates, pro-rata warranty policies are preferable to free replacement policies. But the warranty period of the equivalent free replacement policy decreases and then increases, as product reliability(the average time between failures) increases.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1995.10a
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• pp.111-118
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• 1995

A method of determining an optimum blank shape for the non circular deep drawing process is more investigated and applied to the balnk design for multi-stage deep drawn product. The forming procedure of two-stage deep drawing process is looked over and the method of determining a blank shape is proposed. In experimental research, a optimum blank and a optional rectangular blank were considered and we measured thickness strain distributions. We could predict a strain distribution and compare with a experimental strain distribution. Also, the strain distributions for the blank shapes, optimum and rectangular, were compared.

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.847-863
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• 2023

We introduce the study of generic lightlike submanifolds of a semi-Riemannian product manifold. We establish a characterization theorem for the induced connection on a generic lightlike submanifold to be a metric connection. We also find some conditions for the integrability of the distributions associated with generic lightlike submanifolds and discuss the geometry of foliations. Then we search for some results enabling a generic lightlike submanifold of a semi-Riemannian product manifold to be a generic lightlike product manifold. Finally, we examine minimal generic lightlike submanifolds of a semi-Riemannian product manifold.

• Journal of the Korean Mathematical Society
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• v.47 no.3
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• pp.601-631
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• 2010

In [6] and [7], we introduced graph von Neumann algebras which are the (groupoid) crossed product algebras of von Neumann algebras and graph groupoids via groupoid actions. We showed that such crossed product algebras have the graph-depending amalgamated reduced free probabilistic properties. In this paper, we will consider a scalar-valued $W^*$-probability on a given graph von Neumann algebra. We show that a diagonal graph $W^*$-probability space (as a scalar-valued $W^*$-probability space) and a graph W¤-probability space (as an amalgamated $W^*$-probability space) are compatible. By this compatibility, we can find the relation between amalgamated free distributions and scalar-valued free distributions on a graph von Neumann algebra. Under this compatibility, we observe the scalar-valued freeness on a graph von Neumann algebra.

• Journal of the Korean Operations Research and Management Science Society
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• v.6 no.2
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• pp.51-55
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• 1981

In both continuous-review and periodic-review non-stationary inventory systems, the non-stationary Poisson demand process and the associated inventory position processes were proved being mutually independent of each other, which lead to the probability distribution of the corresponding net inventory position process in the form of a finite product sum of those two process distributions. It is also discussed how these results can correspond to analytical stochastic inventory cost function formulations in terms of the probability distributions of the processes.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.221-230
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• 2007

The exponential and the gamma distributions have been the traditional models for drought duration and drought intensity data, respectively. However, it is often assumed that the drought duration and drought intensity are independent, which is not true in practice. In this paper, an application of the bivariate gamma exponential distribution is provided to drought data from Nebraska. The exact distributions of R=X+Y, P=XY and W=X/(X+Y) and the corresponding moment properties are derived when X and Y follow this bivariate distribution.

• International Journal of Reliability and Applications
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• v.1 no.2
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• pp.133-143
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• 2000

Data from weighted distributions appear, among other situations, when some of the data are missing or are damaged, a case that is important in reliability and life testing. The kernel method for hazard rate estimation is discussed for these data where the basic large sample properties are given. As a by product, the basic properties of the kernel estimate of the distribution function for data from weighted distribution are presented.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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• pp.687-704
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• 2017

Using a simple formula for conditional expectations over an analogue of Wiener space, we calculate a generalized analytic conditional Fourier-Feynman transform and convolution product of generalized cylinder functions which play important roles in Feynman integration theories and quantum mechanics. We then investigate their relationships, that is, the conditional Fourier-Feynman transform of the convolution product can be expressed in terms of the product of the conditional FourierFeynman transforms of each function. Finally we establish change of scale formulas for the generalized analytic conditional Fourier-Feynman transform and the conditional convolution product. In this evaluation formulas and change of scale formulas we use multivariate normal distributions so that the orthonormalization process of projection vectors which are essential to establish the conditional expectations, can be removed in the existing conditional Fourier-Feynman transforms, conditional convolution products and change of scale formulas.

• Communications for Statistical Applications and Methods
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• v.16 no.2
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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.