• Journal of Korean Society for Quality Management
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• v.30 no.3
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• pp.66-78
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• 2002

Process capability indices are being used as indicators for measurements of process capability for SPC of quality assurance system in industries. In view of the enhancement of customer satisfaction, process capability indices in which loss functions are used to deal with the economic loss In the processes deviated from the target, are in an adequate representation of the customer's perception of quality In this connection, the loss function has become increasingly important in quality assurance. Taguchi uses a modified form of the quadratic loss function to demonstrate the need to consider the proximity to the target while assessing its quality. But this traditional quadratic loss function is inadequate to assessing the quality and quality improvement since different processes have different sets of economic consequences on the manufacturing, Thereby, a flexible approach to the development of the loss function needs to be desired. In this paper, we introduce an easily understood loss function, based on reflection of probability density function of the normal distribution. That is, the Reflected Normal Loss function can be adapted to an asymmetric loss as well as to a symmetric loss around the target. We propose that, instead of the process variation, a new capability index, CpI using the Reflected Normal Loss Function that can accurately reflect the losses associated with the process and a new capability index CpI Is compared with the classical indices as $C_{p}$ , $C_{pk}$, $C_{pm}$ and $C_{pm}$ $^{+}$.>.+/./.

• International journal of advanced smart convergence
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• v.5 no.3
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• pp.56-60
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• 2016

Body physical technique is to pursuit the dynamic motion by the physical index(PI) and sensory index(SI) on the physical body function. Function of the physical body by the motor condition is organized the dynamic physical system. For the physical motion of signal, we is defined a runout value of the body function by the physical index on the dynamic state. The concept of body physical index was identified the reference of physical index and sensory index by the body technique. As to detect a variation of the body physical technique-runout physical index(BPT-RPI) of the maximum and average and minimum in terms of physical motion, and the dynamic sensory value that was a runout function of the vision variation of the $Vi-{\xi}_{MAX-AVG-MIN}$ with $2.53{\pm}4.85$ units, that was a runout function of the vestibular variation of the $Ve-{\xi}_{MAX-AVG-MIN}$ with ($-0.69{\pm}2.32$)units, that was a runout function of the somatosensory variation of the $So-{\xi}_{MAX-AVG-MIN}$ with ($-1.43{\pm}-1.36$) units. The dynamic physical motion will be to confirm at the variable function of the runout motion for the body function values of dynamic physical index on the BPT-RPI that was identified an evaluation of the physical sensory function by the dynamic physical system. Runout body system was mentioned of a physical body situation by the mild moving and was refer a runout data of dynamic physical nervous index.

• Structural Engineering and Mechanics
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• v.67 no.4
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• pp.327-336
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• 2018

In this study, an efficient damage index is proposed to identify multiple damage cases in structural systems using the concepts of frequency response function (FRF) matrix and strain energy of a structure. The index is defined based on the change of strain energy of an element due to damage. For obtaining the strain energy stored in elements, the columnar coefficients of the FRF matrix is used. The new indicator is named here as frequency response function strain energy based index (FRFSEBI). In order to assess the performance of the proposed index for structural damage detection, some benchmark structures having a number of damage scenarios are considered. Numerical results demonstrate that the proposed index even with considering noise can accurately identify the actual location and approximate severity of the damage. In order to demonstrate the high efficiency of the proposed damage index, its performance is also compared with that of the flexibility strain energy based index (FSEBI) provided in the literature.

• International Journal of Industrial Entomology and Biomaterials
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• v.5 no.1
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• pp.37-43
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• 2002

Eighteen new bivoltine silkworm (Bombyx mori L.) hybrids developed at Andhra Pradesh State Sericul-ture Research and Development Institute, Hindupur are evaluated for 10 economic traits by following two multiple trait index methods, i.e., Subordinate Function and Evaluation Index for their economic merit. The hybrid genotype, APS6${\times}$APS11 with highest Subordinate function value of 8.2432 and highest average Evaluation Index of 61.67 ranked first. This hybrid is adjudicated as most promising hybrid and recommended for commercial use. Further, applicability of Subordinate Function Index Method is tested and recommended for application of multiple trait evaluation similar to Evaluation Index Method as the results obtained are comparable. Further, both these methods can be applied for confirmation of results.

• East Asian mathematical journal
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• v.35 no.1
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• pp.23-30
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• 2019

Since Mittag-Leffler introduced the so-called Mittag-Leffler function, a number of its extensions have been investigated due mainly to their applications in a variety of research subjects. Shukla and Prajapati presented a lot of formulas involving a generalized Mittag-Leffler function in a systematic manner. Motivated mainly by Shukla and Prajapati's work, we aim to investigate a generalized multi-index Mittag-Leffler function and, among possible numerous formulas, choose to present several formulas involving this generalized multi-index Mittag-Leffler function such as a recurrence formula, derivative formula, three integral transformation formulas. The results presented here, being general, are pointed out to reduce to yield relatively simple formulas including known ones.

• International Journal of Quality Innovation
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• v.6 no.2
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• pp.31-45
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• 2005

The target costing technique, mathematically discussed by Sauers, only uses the $C_p$ index along with Taguchi loss function and ${\bar{X}}-R$ control charts to set up goal control limits. The new specification limits derived from Taguchi loss function is linked through the $C_p$ value to ${\bar{X}}-R$ control charts to obtain goal control limits. This study further considers the reflected normal loss function as well as the $C_{pk}$ index along with its lower confidence interval in forming goal control limits. With the use of lower confidence interval to replace the point estimator of the $C_{pk}$ index and reflected normal loss function proposed by Spiring to measure the loss to society, this modified and improved target costing technique would become more robust and applicable in practice. Finally, an example is provided to illustrate how this modified and improved target costing technique works.

• Korean Journal of Clinical Laboratory Science
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• v.41 no.3
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• pp.135-139
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• 2009

Pulmonary function test has been know to be greatly affected by body indices, such as sex, age, height, body weight, body surface area (BSA) and body mass index (BMI), so hat this study was focused to see the relationship between body index and flow-volume curves. Subjects were 156 (male 90, female 66) and they were examined for pulmonary function test in terms of body index and correlation/multiple regression analysis of flow-volume curves at Presbyterian Medical Center from March to August, 2009. The followings results after analyzing the correlation between body index and flow-volume curves. Although flow-volume curve FEF25-75% showed close correlation with age, body weight, and body surface area, but not with body mass index. In addition, multiple regression analysis was performed to see how each body index affects flow-volume curve FEF25-75%, and FEF25-75% dispersion was explained as 74.5% with age only, 94.2% with age and height, and 96% with age, height, and sex. Therefore, sex, age and height that are mainly used for predictive formular of pulmonary function test and nomogram were important factors for pulmonary function test itself, and further study must be done for other body index.

• Structural Engineering and Mechanics
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• v.62 no.3
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• pp.365-372
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• 2017

Reliability analysis is a probabilistic approach to determine a safety level of a system. Reliability is defined as a probability of a system (or a structure, in structural engineering) to functionally perform under given conditions. In the 1960s, Basler defined the reliability index as a measure to elucidate the safety level of the system, which until today is a commonly used parameter. However, the reliability index has been formulated based on the pivotal assumption which assumed that the considered limit state function is normally distributed. Nevertheless, it is not guaranteed that the limit state function of systems follow as normal distributions; therefore, there is a need to define a new reliability index for no-normal distributions. The main contribution of this paper is to define a sophisticated reliability index for limit state functions which their distributions are non-normal. To do so, the new definition of reliability index is introduced for non-normal limit state functions according to the probability functions which are calculated based on the convolution theory. Eventually, as the state of the art, this paper introduces a simplified method to calculate the reliability index for non-normal distributions. The simplified method is developed to generate non-normal limit state in terms of normal distributions using series of Gaussian functions.

• Communications for Statistical Applications and Methods
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• v.11 no.1
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• pp.161-168
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• 2004

A single-index model is useful in fields which employ multidimensional regression models. Many methods have been developed in parametric and nonparametric approaches. In this paper, posterior inference is considered and a wavelet series is thought of as a function approximated to a true function in the single-index model. The posterior inference needs a prior distribution for each parameter estimated. A prior distribution of each coefficient of the wavelet series is proposed as a hierarchical distribution. A direction $\beta$ is assumed with a unit vector and affects estimate of the true function. Because of the constraint of the direction, a transformation, a spherical polar coordinate $\theta$, of the direction is required. Since the posterior distribution of the direction is unknown, we apply a Metropolis-Hastings algorithm to generate random samples of the direction. Through a Monte Carlo simulation we investigate estimates of the true function and the direction.

• Journal of Urban Science
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• v.11 no.2
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• pp.9-17
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• 2022

The purpose of this study is to develop an index for evaluating the function of a new motorway using the travel distance frequency distribution (TLFD) calculated using the vehicle travel route big data, and to overcome the limitations of the evaluation through the existing traffic volume. The mobility evaluation index of motorways was developed by applying it to the TLFD data table in 2019. The smaller the value of the mobility evaluation index of the link is calculated, the more it is a link with mainly short-distance travel, and the higher the value of the mobility evaluation index, the more it means a link with mainly long-distance travel. The accessibility evaluation index was calculated through the result of the mobility evaluation index of all motorways developed, and all motorways were grouped into three groups using K-means clustering. Group A was found to exist inside a large city and consisted of motorways with many short-distance traffic, Group B was investigated as acting as an arterial between groups, and Group C was classified as a motorway consisting mainly of long-distance traffic connecting large cities and large cities. This study is significant in developing a new motorway function evaluation index that can overcome the limitations of motorway function evaluation through the existing traffic volume. It is expected that this study can be a reasonable comprehensive indicator in the operation and planning process of motorways.