• Journal of the Korean Data and Information Science Society
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• v.21 no.4
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• pp.813-818
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• 2010

The least squares estimation method for model parameters under failure step-stress accelerated life tests is studied and a numerical example will be given to illustrate the proposed inferential procedures under the compound linear plans proposed as an alternative to the optimal quadratic plan, assuming that the exponential distribution with a quadratic relationship between stress and log-mean lifetime. The proposed compound linear plan for constant stress accelerated life tests and 4:2:1 plan are compared for various situations. Even though the compound linear plan was proposed under constant stress accelerated life tests, we found that this plan did well relatively in failure step-stress accelerated life tests.

• 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 Korean Data and Information Science Society
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• v.17 no.3
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• pp.945-952
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• 2006

Several accelerated life test plans use tests at only two levels of stress and thus, have practical limitations. They highly depend upon the assumption of a linear relationship between stress and time-to-failure and use only two extreme stresses that can cause irrelevant failure modes. Thus 3-level stress plans are preferable. When the lifetime distribution of test unit is exponential with mean lifetime $\theta_i$ at stress $x_i$, i=0, 1, 2, 3, we derive the optimum quadratic plan under the assumption that a quadratic relationship exists between stress and log(mean lifetime), and propose the compound linear plans, as an alternative to the optimum quadratic plan. The proposed compound linear plan is better than two other compromise plans for constant stress testing and nearly as good as the optimum quadratic plan, and has the advantage of simplicity.

• Journal of the Korean Operations Research and Management Science Society
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• v.23 no.3
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• pp.153-168
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• 1998

In this study we consider a CONWIP system in which the processing times at each station follow an exponential distribution and the demands for the finished Products arrive according to a compound Poisson process. The demands that are not satisfied instantaneously are assumed to be backordered. For this system we develop an approximation method to obtain the performance measures such as steady state probabilities of the number of parts at each station, the proportion of backordered demands, the average number of backordered demands and the mean waiting time of a backordered demand. For the analysis of the proposed CONWIP system, we model the CONWIP system as a closed queueing network with a synchronization station and analyze the closed queueing network using a product form approximation method. A matrix geometric method is used to solve the subnetwork in the application of the product-form approximation method. To test the accuracy of the approximation method, the results obtained from the approximation method were compared with those obtained by simulation. Comparisons with simulation have shown that the approximate method provides fairly good results.

• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.979-991
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• 2022

A special class of exponential dispersion models is the class of Tweedie distributions. This class is very significant in statistical modeling as it includes a number of familiar distributions such as Gaussian, Gamma and compound Poisson. A Tweedie distribution has a power parameter p, a mean m and a dispersion parameter 𝜙. The value of the power parameter lies in identifying the corresponding distribution of the Tweedie family. The basic objective of this research work resides in investigating the existence of the implicit estimator of the power parameter of the Tweedie distribution. A necessary and sufficient condition on the mean parameter m, suggesting that the implicit estimator of the power parameter p exists, was established and we provided some asymptotic properties of this estimator.

• Journal of the Korean Data and Information Science Society
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• v.22 no.6
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• pp.1089-1096
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• 2011

We consider an infinite dam with inputs formed by a compound Poisson process and adopt a $P^M_{\lambda}$-policy to control the level of water, where the water is released at rate M when the level of water exceeds threshold ${\lambda}$. We obtain interesting stationary properties of the level of water, when the amount of each input independently follows an exponential distribution. After assigning several managing costs to the dam, we derive the long-run average cost per unit time and show that there exist unique values of releasing rate M and threshold ${\lambda}$ which minimize the long-run average cost per unit time. Numerical results are also illustrated by using MATLAB.

• Mass Spectrometry Letters
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• v.10 no.3
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• pp.88-92
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• 2019

A sensitive analytical method of rhodanthpyrone A in rat plasma was developed using a liquid chromatography-tandem mass spectrometry (LC-MS/MS). Rhodanthpyrone A and rhodanthpyrone B (internal standard) in rat plasma were extracted by a liquid-liquid extraction method with ethyl acetate. This extraction method gave results in high and reproducible extraction recovery in the range of 73.75-79.90% with no interfering peaks around the peak elution time of rhodanthpyrone A and B. The standard calibration curves for rhodanthpyrone A ranged from 0.5 to 2000 ng/mL were linear with $r^2$ > 0.994 and the inter- and intra-day accuracy and precision and the stability were within acceptance criteria. Using this validated analytical method, pharmacokinetics of rhodanthpyrone A following intravenous and oral administration of rhodanthpyrone A at doses of 2 mg/kg and 30 mg/kg, respectively, were investigated. Rhodanthpyrone A in rat plasma showed multi-exponential elimination pattern with high clearance and volume of distribution values. The absolute oral bioavailability of this compound was calculated as 3.7%. Collectively, the newly developed sensitive LC-MS/MS analytical method of rhodanthpyrone A could be successfully applied to investigate the pharmacokinetic properties of this compound and would be useful for the further studies on the efficacy, toxicity, and biopharmaceutics of rhodanthpyrone A.

• IE interfaces
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• v.11 no.3
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• pp.55-63
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• 1998

In this study we consider a CONWIP system in which the processing times at each station follow an exponential distribution and the demands for the finished products arrive according to a compound Poisson process. The demands that are not satisfied instantaneously are assumed to be lost. We assume that the lot size at each station is greater than one. For this system we develop an approximation method to obtain the performance measures such as steady state probabilities of the number of parts at each station, average number of parts at each station and the proportion of lost demands. For the analysis of the proposed CONWIP system, we model the CONWIP system as a closed queueing network with a synchronization station and analyze the closed queueing network using a product form approximation method. A recursive technique is used to solve the subnetwork in the application of the product-form approximation method. To test the accuracy of the approximation method, the results obtained from the approximation method were compared with those obtained by simulation. Comparisons with simulation have shown that the accuracy of the approximate method is acceptable.

• Structural Engineering and Mechanics
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• v.44 no.2
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• pp.139-161
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• 2012

In this paper, the static behavior of bi-directional functionally graded (FG) non-uniform thickness circular plate resting on quadratically gradient elastic foundations (Winkler-Pasternak type) subjected to axisymmetric transverse and in-plane shear loads is carried out by using state-space and differential quadrature methods. The governing state equations are derived based on 3D theory of elasticity, and assuming the material properties of the plate except the Poisson's ratio varies continuously throughout the thickness and radius directions in accordance with the exponential and power law distributions. The stresses and displacements distribution are obtained by solving state equations. The effects of foundation stiffnesses, material heterogeneity indices, geometric parameters and loads ratio on the deformation and stress distributions of the FG circular plate are investigated in numerical examples. The results are reported for the first time and the new results can be used as a benchmark solution for future researches.

• The Korean Journal of Applied Statistics
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• v.24 no.4
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• pp.575-586
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• 2011

In this paper, we study an asymptotic behavior of the finite-time ruin probability of the compound Poisson model in the case that the initial surplus is large. To compare an exact ruin probability with an approximate one, we place the focus on the exact calculation for the ruin probability when the claim size distribution is regularly varying tailed (i.e. exponential claims and inverse Gaussian claims). We estimate an adjustment coefficient in these examples and show the relationship between the adjustment coefficient and the safety premium. The illustration study shows that as the safety premium increases so does the adjustment coefficient. Larger safety premium means lower "long-term risk", which only stands to reason since higher safety premium means a faster rate of safety premium income to offset claims.