• 품질경영학회지
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• 제30권3호
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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 $C_{pm}$ $^{+}$.>.+/./.

• 산업경영시스템학회지
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• 제36권4호
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• pp.109-115
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• 2013

Process Capability Index (PCI) is useful Statistical Process Control (SPC) tool that is measure of process diagnostic and assessment tools widely use in industrial field. It has advantage of easy to calculate and easy to use in the field. $C_p$ and $C_{pk}$ are traditional PCIs. These are only considers of process variation. These are not given information about the characteristic value does not match the target value of the process. Studies of this process capability index by many scholars actively for supplement of its disadvantage. These studies to evaluate the capability of situation of various field has presented a new process capability index. $C_{pm}$ is considers both the process variation and the process deviation from target value. And $C_{pm}{^+}$ is considers economic loss for the process deviation from target value. In this paper development of new process capability index that is Taguchi's quadratic loss function by applying the expected loss. And check the correlation between existing traditional process capability index ($C_{pk}$) and new one. Finally, we propose the criteria for classification about developed process capability index.

• 산업경영시스템학회지
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• 제41권2호
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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.

• 산업경영시스템학회지
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• 제39권2호
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• pp.37-45
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• 2016

Control chart is representative tools of statistical process control (SPC). It is a graph that plotting the characteristic values from the process. It has two steps (or Phase). First step is a procedure for finding a process parameters. It is called Phase I. This step is to find the process parameters by using data obtained from in-controlled process. It is a step that the standard value was not determined. Another step is monitoring process by already known process parameters from Phase I. It is called Phase II. These control chart is the process quality characteristic value for management, which is plotted dot whether the existence within the control limit or not. But, this is not given information about the economic loss that occurs when a product characteristic value does not match the target value. In order to meet the customer needs, company not only consider stability of the process variation but also produce the product that is meet the target value. Taguchi's quadratic loss function is include information about economic loss that occurred by the mismatch the target value. However, Taguchi's quadratic loss function is very simple quadratic curve. It is difficult to realistically reflect the increased amount of loss that due to a deviation from the target value. Also, it can be well explained by only on condition that the normal process. Spiring proposed an alternative loss function that called reflected normal loss function (RNLF). In this paper, we design a new control chart for overcome these disadvantage by using the Spiring's RNLF. And we demonstrate effectiveness of new control chart by comparing its average run length (ARL) with ${\bar{x}}-R$ control chart and expected loss control chart (ELCC).

• 산업경영시스템학회지
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• 제28권4호
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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.

• 품질경영학회지
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• 제31권1호
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• pp.109-122
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• 2003

This paper presents a robust process capability index(PCI) based on the expected loss derived from the empirical distribution function(EDF). We propose the EDF expected loss in order to develop a PCI that does not depends on the underlying process distribution. The EDF expected loss depends only on the sample data, so the PCI based on it is robust and it does nor require complex calculations. The inverted normal loss function(INLF) is employed in order to overcome the drawback of the quadratic loss which may Increase unboundedly outside the specification limits. A comprehensive simulation study was performed under various process distributions, in order to compare the accuracy and the precision of the proposed PCI with those of the PCI based on the expected loss derived from the normal distribution. The proposed PCI turned out to be more accurate than the normal PCI in most cases, especially when the process distribution has high kurtosis or skewness. It is expected that the proposed PCI can be utilized In real processes where the true distribution family may not be known.

• 산업경영시스템학회지
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• 제40권1호
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• pp.41-49
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• 2017

Process quality control, which prevents problems and risks that may occur in products and processes, has been recognized as an important issue, and SPC techniques have been used for this purpose. Process Capability Index (PCI) is useful Statistical Process Control (SPC) tool that is measure of process diagnostic and assessment tools widely use in industrial field. It has advantage of easy to calculate and easy to use in the field. $C_p$ and $C_{pk}$ are traditional PCIs. These traditional $C_p$ and $C_{pk}$ were used only as a measure of process capability, taking into account the quality variance or the bias of the process mean. These are not given information about the characteristic value does not match the target value of the process and this has the disadvantage that it is difficult to assess the economic losses that may arise in the enterprise. Studies of this process capability index by many scholars actively for supplement of its disadvantage. These studies to evaluate the capability of situation of various field has presented a new process capability index. $C_{pm}$ is considers both the process variation and the process deviation from target value. And $C_{pm}{^+}$ is considers economic loss for the process deviation from target value. In this paper we developed an improved Expected Loss Capability Index using Reflected Normal Loss Function of Spring. This has the advantage that it is easy to realistically reflect the loss when the specification is asymmetric around the target value. And check the correlation between existing traditional process capability index ($C_{pk}$) and new one. Finally, we propose the criteria for classification about developed process capability index.

• International Journal of Quality Innovation
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• 제9권1호
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• pp.41-54
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• 2008

The process capability indices have been widely used to measure process capability and performance. In this paper, we proposed a new process capability index which is based on an actual dollar loss by defects. The new index is similar to the Taguchi's loss function and fully incorporates the distribution of quality attribute in a process. The strength of the index is to apply itself to non-normal or asymmetric distributions. Numerical examples were presented to show superiority of the new index against $C_p$, $C_{pk}$, and $C_{pm}$ which are the most widely used process capability indices.

• 산업공학
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• 제21권4호
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• pp.365-377
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• 2008

In this paper, for constructing the Korean Hazard Information System (KHIS), we conceptually design a hazard evaluation process. We first deal with a hazard evaluation process focused on flood hazard to give the most immense damage and loss. The hazard evaluation process is consist of a damage evaluation process and a loss evaluation process, and is used for transforming hazards from natural disasters into economic measures. The proposed process is developed based on the famous FEMA (Federal Emergency Management Agency)'s $HAZAS^{@MH}$methodology. We modify the FEMA's process to be mutually exclusive and collectively exhaustive, that is all losses from the hazards are included into the estimation process but the losses are not duplicated in the process. In addition to this, we define the loss process specifically by considering the characteristics from the hazard environments of Korea. We can expect that KHIS for evaluating economic losses from natural hazards can be developed based on the conceptual design for the economic loss evaluation process, and KHIS can be used as a useful tool for analyzing the feasibilities of mitigation plans in central/local governments.

• 산업경영시스템학회지
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• 제36권2호
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• pp.56-62
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• 2013

Control chart is representative tool of Statistical Process Control (SPC). But, it is not given information about the economic loss that occurs when a product is produced characteristic value does not match the target value of the process. In order to manage the process, we should consider not only stability of the variation also produce products with a high degree of matching the target value that is most ideal quality characteristics. There is a need for process control in consideration of economic loss. In this paper, we design a new control chart using the quadratic loss function of Taguchi. And we demonstrate effectiveness of new control chart by compare its ARL with ${\overline{x}}-R$ control chart.