• International Journal of Reliability and Applications
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• v.2 no.3
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• pp.189-197
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• 2001

The estimation of mean lifetimes in presence of interval censoring with mixed replacement procedure is examined when the distributions of lifetimes are exponential. It is assumed that, due to physical restrictions and/or economic constraints, the number of failures is investigated only at several inspection times during the lifetime test; thus there is interval censoring. The maximum likelihood estimator is found in an implicit form. The Cramor-Rao lower bound, which is the asymptotic variance of the estimator, is derived. The estimation of mean lifetimes for competing failures model has been expanded.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.3
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• pp.491-497
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• 2015

In this paper, we have suggested an extended double Newton's method with sixth-order convergence by considering a control parameter ${\gamma}$ and a weight function H(s, u). We have determined forms of ${\gamma}$ and H(s, u) in order to induce the greatest order of convergence and established the main theorem utilizing related properties. The developed theory is ensured by numerical experiments with high-precision computation for a number of test functions.

• Communications for Statistical Applications and Methods
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• v.22 no.6
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• pp.605-613
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• 2015

A three-arm parallel design has been proposed to assess the biosimilarity between a biological product and a reference product using relative distance (Kang and Chow, 2013). The three-arm parallel design consists of two arms for the reference product and one arm for the biosimilar product. This paper extended the three-arm parallel design to a (k + 1)-arm parallel design composed of k (${\geq}3$) arms for the reference product and one arm for the biosimilar product. A new relative distance was defined based on Euclidean distance; consequently, a corresponding test procedure was developed based on asymptotic distribution. Type I error rates and powers were investigated both theoretically and empirically.

• Journal of the Korean Data and Information Science Society
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• v.7 no.1
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• pp.21-35
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• 1996

In this paper, estimation and prediction procedures are discussed for grneral situation in which the failure time follows the independent density $f_{i}({\varepsilon}_{i})$ for the accelerated life testing under Type II censoring. In the context of accelerated life test experiment, procedures are given for estimating the parameters in the Eyring model, and for estimating mean life at a given future stress level. The procedures given are conditional confidence interval procedures, obtained by conditioning on ancillary statistics. A comparison is made of these procedures and procedures based on asymptotic properties of the maximum, likelihood estimates.

• Journal of the Korean Data and Information Science Society
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• v.13 no.2
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• pp.87-95
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• 2002

In this paper we consider optimal designs of partially accelerated life testing which is devised for multi-component mixed systems with the considerably long lifetime. Test items are run at both use condition and accelerated condition until a specified censoring time. The optimal criterion for the sample-proportion allocated to accelerated condition is to minimize asymptotic variance of the maximum likelihood estimators of the acceleration factor and hazard rates.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.22 no.8
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• pp.1141-1151
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• 1998

An effective thermal conductivity measurement for suspensions of microparticles in oil mixture is conducted in order to evaluate the shear rate-dependence of the thermal conductivity of suspensions. Measurements are made for rotating Couette flows between two concentric cylinders. The rotating outer cylinder is immersed into a constant temperature water bath while the stationary inner cylinder is subject to a uniform heat fluff. Test fluids are made to be homogeneous suspensions, in which neutrally buoyant microparticles ($d=25{\sim}300{\mu}m$) are uniformly dispersed. The present measurements show strong shear-rate dependent thermal conductivities for the suspensions, which are higher than those at zero shear rate. The shear rate dependent thermal conductivity increases with the particle size and volume concentration.4 new model for shear rate-dependent thermal conductivity of microparticle suspensions is proposed; the correlation covers from zero shear rate value to asymptotic plateau value at moderately high shear rates.

• Journal of the Korean Statistical Society
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• v.30 no.1
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• pp.1-20
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• 2001

We present how bootstrap methods can be used to conduct inference on the rates of Poisson distributions when only the grouped data are available. A theoretical justification for the validity of bootstrap is given with an illustration of proposed method using a data set obtained fro ma pathology laboratory test. Traditional asymptotic methods are compared with bootstrap methods in computing the estimated standard errors and achieved significance levels for one sample and two sample tests. Bootstrap methods are shown to possess a nice property that he small sample distribution of the relevant statistics can be readily obtained from the bootstrap copies.

• Food Science and Biotechnology
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• v.18 no.4
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• pp.1013-1018
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• 2009

Several rheological terms were introduced to estimate the properties of cooked noodles with different starch content using tensile tests. Ring-shaped specimens were prepared by connecting both ends of the noodle strip before cooking. Hencky strain and rate, as well as true stress were applied in constant deformation tests. The elastic region on the curves of strain vs. stress was not clearly identified. Strain hardening in the subsequent plastic region was more prominent in low-starch noodles. Elongational viscosities at lower strain rates were used to differentiate noodles with different starch content, representing the dominant effect of protein content in the range of lower strain rates. In stress relaxation tests, the reciprocal of Peleg's constant $K_1$ (initial decay rate) and $K_2$ (asymptotic level) increased and decreased respectively, with an increase in starch content. This indicated that addition of starch contributed to the noodles becoming viscous liquid rather than elastic solid.

• Journal of applied mathematics & informatics
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• v.36 no.3_4
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• pp.331-348
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• 2018

In this paper, an initial value method for solving a class of singularly perturbed delay differential equations with layer behavior is proposed. In this approach, first the given problem is modified in to an equivalent singularly perturbed problem by approximating the term containing the delay using Taylor series expansion. Then from the modified problem, two explicit Initial Value Problems which are independent of the perturbation parameter, ${\varepsilon}$, are produced: the reduced problem and boundary layer correction problem. Finally, these problems are solved analytically and combined to give an approximate asymptotic solution to the original problem. To demonstrate the efficiency and applicability of the proposed method three linear and one nonlinear test problems are considered. The effect of the delay on the layer behavior of the solution is also examined. It is observed that for very small ${\varepsilon}$ the present method approximates the exact solution very well.

• Journal of Korean Society for Quality Management
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• v.24 no.3
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• pp.37-49
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• 1996

For highly reliable devices it is often defined to "fail" when its performance degrades below a specified value. In this paper we consider a method for optimally designing accelerated degradation tests(ADTs) in which the performance over exposure time and stress has Weibull distribution. For the product whose performance has Weibull distribution, the optimum plan - low stress level and sample proportions allocated to each test condition - is obtained, which minimize the asymptotic variance of maximum likelihood estimator of a stated quantile at design stress. We also present compromise ADTs plan that can be used for the practical purpose.