• Journal of the Korean Data and Information Science Society
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• v.14 no.4
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• pp.1031-1044
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• 2003

In this paper, we establish some recurrence relations of the moments, product moments, percentage points, and modes of order statistics from the transformed exponential distribution.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.22 no.52
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• pp.337-345
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• 1999

The long-tailed, positively skewed exponential distribution can be made into an almost symmetric distribution by taking the exponent of the data. In these situations, to use the traditional shewhart control limits on an individuals chart would be impractical and inconvenient. The transformed data, approximately bell-shaped, can be plotted conveniently on the individuals chart and exponentially weighted moving average chart. In this paper, using modifying statistics with transformed exponential of the data, we give a method for constructing control charts. Selecting method of exponent for individual chart is evaluated. And consider that smaller weight being assigned to the older data as time process and properties and taking method of exponent($\theta$), weighting factor($\alpha$) are suggested. Our recommendation, on the basis result of simulation, is practical method for EWMA chart.

• Geomechanics and Engineering
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• v.15 no.3
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• pp.919-925
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• 2018

Stress-strain responses of weak-to-strong carbonate rocks used for tunnel construction were studied. The analysis of applicability of exponential stress-strain models based on Haldane's distribution function is presented. It is revealed that these exponential equations presented in transformed forms allow us to predict stress-strain relationships over the whole pre-failure strain range without mechanical testing of rock samples under compression using a press machine and to avoid measurements of axial failure strains for which relatively large values of compressive stress are required. In this study, only one point measurement (small strain at small stress) using indentation test and uniaxial compressive strength determined by a standard Schmidt hammer are considered as input parameters to predict stress-strain response from zero strain/zero stress up to failure. Observations show good predictive capabilities of transformed stress-stress models for weak-to-strong (${\sigma}_c$ <100 MPa) heterogeneous carbonate rocks exhibiting small (< 0.5 %), intermediate (< 1 %) and large (> 1 %) axial strains.

• Communications for Statistical Applications and Methods
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• v.7 no.1
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• pp.277-284
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• 2000

The transformed sample Lorenz curve provides a powerful and easily computed goodness-of-fit test for exponentiality which does not depend on the unknown scale parameter. We compare the power of the transformed sample Lorenz curve statistic with the other goodness-of-fit tests for exponentiality against various alternatives through Monte Carlo methods and discuss the results.

• Journal of Korean Institute of Industrial Engineers
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• v.17 no.1
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• pp.95-108
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• 1991

For the case where the lifetime at a constant stress level has exponential distribution, optimal accelerated life test plans are developed under the assumptions of intermittent inspection and Type I censoring. In a optimal plan, the low and high stress levels, the proportion of test units allocated and the inspection times at each stress are determined such that the asymptotic variance of the maximum likelihood estimator of logarithmic transformed mean at the use condition is minimized. In addition to the optimal plan in which numerical technique to solve the set of nonlinear equations must be employed to determine inspection times at each stress level, we also propose another plans which employ equally-spaced or equal probability inspection schemes at two overstress levels of corresponding optimal one. For both optimal and proposed plans, computational results indicate that the asymptotic variance of the estimated mean at the use stress is insensitive to number of inspections at overstress levels for the range of parameter values considered.

• 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.

• The Korean Journal of Applied Statistics
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• v.8 no.2
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• pp.87-97
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• 1995

When there is no main effcts or only one main effect in a $2 \times 2$ factorial design, Type I error rates and power for the rank transformed F test (FR test) for interaction are nearly equal to those of the classical F test. However the power of FR test is quite superior under the exponential distribution rather than the of FR test is quite superior under the exponential distribution rather than the normal distribution. Meanwhile when both main effects are in the model, Type I error rates of FR test, compared with those of F test, decrease as the effect size increases and are dependent on the fashion in which main effects are constructed. In addition, the power of FR test increases as the effect size and the sample size increase and is highly dependent on the manner in which main effects are constructed and the type of population distribution.

• The Korean Journal of Applied Statistics
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• v.19 no.1
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• pp.111-120
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• 2006

In a two-stage two-level balanced nested design, type I error rates for the parametric tests and the rank transformed tests for the main effects and the nested effects are in overall similar to each other. Furthermore, powers for the rank transformed statistic for the main effects and the nested effects in a two-stage two-level balanced nested design are generally superior to powers for the parametric statistic When the effect size and the sample size are increased, we can find that powers increase for the parametric statistic and the rank transformed statistic are dramatically improved. Especially for the case of the fixed effects in the asymmetric distributions such as an exponential distribution, powers for the rank transformed tests are quite high rather than powers for the parametric tests.

• Journal of the Korean Data and Information Science Society
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• v.23 no.4
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• pp.683-691
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• 2012

In $4{\times}4$ graeco-latin square design, powers of rank transformed statistic for testing the main effect are superior to powers of parametric statistic without regard to the effect structure with equally or unequally spaced effect levels as well as the type of population distributions such as exponential, double exponential, normal and uniform distribution. As numbers of block effect or effect sizes are decreased, powers of rank transformed statistic are much higher than powers of parametric statistic. In case that block effects are smaller than a main effect or one block effect is higher than other block effects, powers of rank transformed statistic are much higher than powers of parametric statistic in $4{\times}4$ graeco-latin square design with three block effects and one main effect.

• Journal of Korean Institute of Industrial Engineers
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• v.14 no.2
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• pp.91-97
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• 1988

In accelerated life testing, a relationship is usually assumed between the stress and a parameter of the lifetime distribution. However, the true relationship is not usually known, and therefore, the experimenter may wish to provide protections against the likely departures from the assumed relationship. This paper considers an accelerated life test in which two stress levels are involved, and the lifetime of each test item at a stress level is assumed to have an independent, identical, exponential distribution. For the case where a first order relationship is assumed while the true one is quadratic, a procedure is developed for allocating test items to stress levels such that the bias and/or the variance of the estimated(log-transformed) mean lifetime at the use condition is minimized.