This study is about the process capability index (PCI). In this study, we introduce several indices including the index CPR and present the characteristics of the CPR as well as its validity. The difference between the other indices and the CPR is the way we use to estimate the standard deviation. Calculating the index, most indices use sample standard deviation while the index CPR uses range R. The sample standard deviation is generally a better estimator than the range R . But in the case of the panel process, the CPR has more consistency than the other indices at the point of non-conforming ratio which is an important term in quality control. The reason why the CPR using the range has better consistency is explained by introducing the concept of ‘flatness ratio’. At least one million cells are present in one panel, so we can’t inspect all of them. In estimating the PCI, it is necessary to consider the inspection cost together with the consistency. Even though we want smaller sample size at the point of inspection cost, the small sample size makes the PCI unreliable. There is ‘trade off’ between the inspection cost and the accuracy of the PCI. Therefore, we should obtain as large a sample size as possible under the allowed inspection cost. In order for CPR to be used throughout the industry, it is necessary to analyze the characteristics of the CPR . Because the CPR is a kind of index including subgroup concept, the analysis should be done at the point of sample size of the subgroup. We present numerical analysis results of CPR by the data from the random number generating method. In this study, we also show the difference between the CPR using the range and the CP which is a representative index using the sample standard deviation. Regression analysis was used for the numerical analysis of the sample data. In addition, residual analysis and equal variance analysis was also conducted.

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 Cp, Cpk, Cpm, 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 (MCpI ) 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.

This study is concerned about the process capability index in single process. Previous process capability indices have been developed for the consistency with the nonconforming rate due to the process target value and skewness. These indices calculate the process capability by measuring one spot in an item. But the only one datum in an item reduces the representativeness of the item. In addition to the lack of representativeness, there are many cases that the uniformity of the item such as flatness of panel is absolutely important. In these cases, we have to measure several spots in an item. Also the nonconforming judgment to an item is mainly due to the range not due to the standard variation or the shift from the specifications. To imply the uniformity concept to the process capability index, we should consider only the variation in an item. It is the within subgroup variation. When the universe is composed of several subgroups, the sample standard deviation is the sum of the within subgroup variation and the between subgroup variation. So the range R which represents only the within subgroup variation is the much better measure than that of the sample standard deviation. In general, a subgroup contains a couple of individual items. But in our cases, a subgroup is an item and R is the difference between the maximum and the minimum among the measured data in an item. Even though our object is a single process index, causing by the subgroups, its analytic structure looks like a system process capability index. In this paper we propose a new process capability index considering the representativeness and uniformity.

This study is concerned with process capability index in single process. We enumerated issues on the calculation of process capability index and described the effects of these issues. We explained the development process and the reason of the representative existing process capability indices. We investigated whether the indices agree with the concept of process capability and drew the problems from those results. In addition, we proposed alternative and direction to seize the process capability necessary to the field.

Process capability indices (PCIs) have been widely used in manufacturing industries to provide a quantitative measure of process potential and performance. The previous studies have measured only one location on each part in the case of single variate. To

This research presents an implementation strategy of Process Capability Index ( PCI) according to the types of process characteristics. The types of process feature are classified as four perspectives of variation range, time period, error position, and process stage. The paper examines short-term or long-term PCI, within or between variation, position of precision or accuracy, and inclusion of measurement or calibration stage. Moreover, the study proposes normality test of unilateral PCI.

We develop methods for propagating and analyzing EPCI(Extended Process Capability Index) by using the error type that classifies into accuracy and precision. EPCI developed in this study can be applied to the three combined processes that consist of production, measurement and calibration. Little calibration work discusses while a great deal has been studied about SPC(Statistical Process Contol) and MSA(Measurement System Analysis). EPCI can be decomposed into three indexes such as PPCI(Production Process Capability Index), PPPI(Production Process Performance Index), MPCI(Measurement PCD, and CPCI(Calibration PCI). These indexs based on the type of error classification can be used with various statistical techniques and principles such as SPC control charts, ANOVA(Analysis of Variance), MSA Gage R&R, Additivity-of-Variance, and RSSM(Root Sum of Square Method). As the method proposed is simple, any engineer in charge of SPC. MSA and calibration can use efficientily in industries. Numerical examples are presentsed. We recommed that the indexes can be used in conjunction with evaluation criteria.

  Process Capability indices (PCIs) have been widely used in manufacturing industries to provide a quantitative measure of process performance. PCIs have been developed to represent process capability more exactly. In the previous studies, only one design

It is necessary to deal with the process capability index carefully because it has been developed with certain assumptions. Companies make a decision on processes through the results obtained by using and treating data extracted from the processes. However if they have incorrect or wrong results, they cannot lead to proper outputs but also bring to loss of the competition in quality. Therefore, this study will show a method to analysis Cp (process capability ; CP) and an idea of mass-production on Pp (process performance ; PP) based on the Sigma Estimate which is one of the uncertainty in the process capability index and makes a lot of error. To apply this method, it is essential to understand and to analyze the processes exactly. Especially, it is required to establish the more accurate process capability index that can quickly and properly respond to changes on processes to recognize the small changes on the process which lies in specification in mass production system that the continual monitoring of quality managers is required.

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 p

Recently, a couple of process capability indices are used to evaluate that the outputs of the process satisfy the specifications. An assumption of those indices is that the specifications of the characteristics are given single constant value. The display

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 MCpm 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,

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 MCpm 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.

As we understand it, Process Capability indices are intended to provide single-number assessments of ability to meet specification limits on quality characteristics of interest. As a consequence of the varied ways in which PCIs are used, there have been two natural lines of research work: ① studies on the properties of PCIs and their estimators in many different environments; ② construction of new PCIs purporting to have better properties in certain circumstances. The most of existing process capability indices are concerned with the single variable. But, in many cases, a quality characteristic is composed with several factors. In that case, we want to know the integrated process capability of a quality characteristic not those of each factor. In this paper, we proposed a new multivariate system process capability index called MSPCI:SCpsk which is the geometric mean of performance measure Cpsk'S, and will be used as the criterion to assess multiple response process designs. Numerical illustration is done for SCpsk, Cp(f), Cp, Cpk, Cpm, and Cpsk.