• Journal of Korean Society of Industrial and Systems Engineering
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• v.41 no.2
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• pp.174-183
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• 2018

In the industrial fields, the process capability index has been using to evaluate the variation of quality in the process. The traditional process capability indices such as $C_p$, $C_{pk}$, $C_{pm}$ and $C^+_{pm}$ have been applied in the industrial fields. These traditional process capability indices are mainly applied in the univariate analysis. However, the main streams in the recent industry are the multivariate manufacturing process and the multiple quality characteristics are corrected each other. Therefore, the multivariate statistical method should be used in the process capability analysis. The multivariate process indices need to be enhanced with more useful information and extensive application in the recent industrial fields. Hence, the purpose of the study is to develop a more effective multivariate process index ($MC_{pI}$) using the multivariate inverted normal loss function. The multivariate inverted normal loss function has the flexibility for the any type of the symmetrical and asymmetrical loss functions as well as the economic information. Especially, the proposed modeling method for the multivariate inverted normal loss function (MINLF) and the expected loss from MINLF in this paper can be applied to the any type of the symmetrical and asymmetrical loss functions. And this modeling method can be easily expanded from a bivariate case to a multivariate case.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.42 no.1
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• pp.106-114
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• 2019

Recently, the manufacturing process system in the industrial field has become more and more complex and has been influenced by many and various factors. Moreover, these factors have the dependent correlation rather than independent of each other. Therefore, the statistical analysis has been extended from the univariate method to the multivariate method. The process capability indices have been widely used as statistical tools to assess the manufacturing process performance. Especially, the multivariate process indices need to be enhanced with more useful information and extensive application in the recent industrial fields. The various multivariate process capability indices have been studying by many researchers in recent years. Hence, the purpose of the study is to compare the useful and various multivariate process capability indices through the simulation. Among them, we compare the useful models of several multivariate process capability indices such as $MC_{pm}$, $MC^+_{pm}$ and $MC_{pl}$. These multivariate process capability indices are incorporates both the process variation and the process deviation from target or consider the expected loss caused by the process deviation from target. Through the computational examples, we compare these process capability indices and discuss their usefulness and effectiveness.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.28 no.4
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• pp.116-123
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• 2005

The traditional process capability indices Cp, Cpk, Cpm, $Cpm^+$ have been used to characterize process performance on the basis of univariate quality characteristics. Cp, Cpk consider the process variation, Cpm considers both the process variation and the process deviation from target and Cpm+ considers economic loss for the process deviation from target. In manufacturing industry, there is growing interest in quantitative measures of process variation under multivariate duality characteristics. The multivariate process capability index incorporates both the process variation and the process deviation from target or considers expected loss caused by the process deviation from target. This paper proposes multivariate capability index based on the expected loss derived from multivariate normal distribution.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.25 no.2
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• pp.1-10
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• 2002

Process capability indices are widely used in industries and quality assurance system. In past years, process capability analysis have been used to characterize process performance on the basis of univariate quality characteristics. However, in actual manufacturing industrial, statistical process control (SPC) often entails characterizing or assessing processes or products based on more than one engineering specification or quality characteristic. Therefore, the analysis have to be required a multivariate statistical technique. This paper introduces to multivariate capability indices and then selects a multivariate process capability index incorporated both the process variation and the process deviation from target among these indices under the multivariate normal distribution. We propose a new multivariate capability index $MC_{pm}^+$ using quality loss function instead of the process variation and this index is compared with the proposed indices when quality characteristics are independent and dependent of each other.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.19 no.1
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• pp.23-45
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• 2015

We consider counterparty risk in CDS rates. To do so, we use a multivariate jump diffusion process for obligors' default intensity, where jumps (i.e. magnitude of contribution of primary events to default intensities) occur simultaneously and their sizes are dependent. For these simultaneous jumps and their sizes, a homogeneous Poisson process. We apply copula-dependent default intensities of multivariate Cox process to derive the joint Laplace transform that provides us with joint survival/default probability and other relevant joint probabilities. For that purpose, the piecewise deterministic Markov process (PDMP) theory developed in [7] and the martingale methodology in [6] are used. We compute survival/default probability using three copulas, which are Farlie-Gumbel-Morgenstern (FGM), Gaussian and Student-t copulas, with exponential marginal distributions. We then apply the results to calculate CDS rates assuming deterministic rate of interest and recovery rate. We also conduct sensitivity analysis for the CDS rates by changing the relevant parameters and provide their figures.

• Proceedings of the Safety Management and Science Conference
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• 2005.05a
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• pp.503-521
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• 2005

Process capability indices are widely used in industries and quality assurance system. When designing the parameter on the multiple quality characteristics, there has been a study for optimization of problems, but there has been few former study on the possible conflicting phenomena in considertion of the correlations among the characteristics. To solve the issue on the optimal design for muliple quality characteristics, the study propose the expected loss function with cross-product terms among the characteristics and derived range of the coefficients of terms. Therefore, the analysis have to be required a multivariate statistical technique. This paper introduces to multivariate capability indices and then selects a multivariate process capability index incorporated both the process variation and the process deviation from target among these indices under the multivariate normal distribution. We propose a new multivariate capability index $MC_{pm}^{++}$ using quality loss function instead of the process variation and this index is compared with the proposed indices when quality characteristics are independent and dependent of each other,

• Proceedings of the Safety Management and Science Conference
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• 2004.11a
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• pp.69-79
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• 2004

Process capability indices are widely used in industries and quality assurance system. When designing the parameter on the multiple quality characteristics, there has been a study for optimization of problems, but there has been few former study on the possible conflicting phenomena in considertion of the correlations among the characteristics. To solve the issue on the optimal design for multiple quality characteristics, the study propose the expected loss function with cross-product terms among the characteristics and derived range of the coefficients of terms. Therefore, the analysis have to be required a multivariate statistical technique. This paper introduces to multivariate capability indices and then selects a multivariate process capability index incorporated both the process variation and the process deviation from target among these indices under the multivariate normal distribution. We propose a new multivariate capability index $MC_{pm}^{++}$ using quality loss function instead of the process variation and this index is compared with the proposed indices when quality characteristics are independent and dependent of each other.

• Industrial Engineering and Management Systems
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• v.11 no.4
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• pp.385-389
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• 2012

With the development of computer storage and the rapidly growing ability to process large amounts of data, the multivariate control charts have received an increasing attention. The existing univariate and multivariate control charts are a single hypothesis testing approach to process mean or variance by using a single statistic plot. This paper proposes a multiple hypothesis approach to developing a new multivariate control scheme. Plotted Hotelling's $T^2$ statistics are used for computing the corresponding p-values and the procedure for controlling the false discovery rate in multiple hypothesis testing is applied to the proposed control scheme. Some numerical simulations were carried out to compare the performance of the proposed control scheme with the ordinary multivariate Shewhart chart in terms of the average run length. The results show that the proposed control scheme outperforms the existing multivariate Shewhart chart for all mean shifts.

• Journal of the Korean Data and Information Science Society
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• v.22 no.6
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• pp.1123-1135
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• 2011

This paper considers the multivariate integrated process control procedure for detecting special causes in a multivariate IMA(1, 1) process. When the multivariate control chart signals, the special cause will be detected and eliminated from the process. However, when the elimination of the special cause costs high or is not practically possible, an alternative action is to readjust the process with approximately modified adjustment scheme. In this paper, we propose the readjustment procedure after having a true signal, and show that the use of the readjustment can reduce the deviation of a process from the target.

• Communications for Statistical Applications and Methods
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• v.23 no.6
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• pp.497-515
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• 2016

Modern processes often monitor more than one quality characteristic that are referred to as multivariate statistical process control (MSPC) procedures. The MSPC is the most rapidly developing sector of statistical process control and increases interest in the simultaneous inspection of several related quality characteristics. Most multivariate detection procedures based on a multi-normality assumptions are independent, but there are many processes that assume non-normality and correlation. Many multivariate control charts have a lack of related joint distribution. Copulas are tool to construct multivariate modelling and formalizing the dependence structure between random variables and applied in several fields. From copula literature review, there are a few copula to apply in MSPC that have multivariate control charts, and represent a successful tool to identify an out-of-control process. This paper presents various types of copulas modelling for the multivariate control chart. The performance measures of the control chart are the average run length (ARL) and the average number of observations to signal (ANOS). Furthermore, a Monte Carlo simulation is shown when the observations were from an exponential distribution.