Multivariate Process Capability Indices Research Articles

Multivariate process capability analysis with decision-maker preferences

A process capability analysis is an invaluable technique for assessing the efficacy of a system by determining its alignment with customer expectations. In the context of a manufacturing process with multiple correlated variables, the use of multivariate methods is essential for the analysis of quality characteristics. In the literature, there have been various proposals for MPCI (multivariate process capability indices) based on different approaches, including the proportion of non-conforming items or PCA (principal component analysis). In this context, a novel approach to capability analysis with multiple responses of varying degrees of importance has been proposed, termed WAMP (Weighted Arithmetic Mean with Prioritization). The findings indicated that the WAMP method demonstrated greater robustness than the SAM (simple arithmetic mean) and SGM (simple geometric mean) approaches. However, the WAM (weighted arithmetic mean) and WGM (weighted geometric mean) methods also exhibited satisfactory performance in accordance with the established acceptance criteria. The method was evaluated using both simulated and experimental data, demonstrating its efficacy in scenarios with varying degrees of correlation. When a greater weight is assigned to a single original variable, the MPCI is observed to be similar in value to that of the original variable with the highest weight when considered univariately. When equal weights are assigned to two original variables, the MPCI is situated within the capability indices of the original variables with the highest weight. Furthermore, it was observed that the performance of the MPCI improves with an increase in correlation. In conclusion, WAMP has been demonstrated to be a valuable and effective tool for capability analysis in systems with multiple correlated responses of varying degrees of importance.

Multivariate process capability analysis for evaluating metal additive manufacturing via electron beam melting

Abstract Electron beam melting (EBM) as one of the relatively new metal AM techniques showed promising and increasing applications. Therefore, there is a need to evaluate the quality of the EBM process using its critical quality characteristics. However, EBM and different AM process parts have many functionally or statistically correlated quality characteristics. Consequently, the quality characteristics of the EBM process should be evaluated together. Therefore, this research aims to evaluate the quality of the EBM process using a multivariate process capability index (MPCI). In this study, the dimensional accuracy in different directions is considered as a quality characteristics. The proposed methodology involves producing a large sample of small specimens of square shape using EBM technology. Three critical dimensions of the specimen in the X, Y, and Z axis are investigated as quality characteristics. The dimensions of quality characteristics are measured using a precise measurement device. The normality and stability assumptions of the collected data are investigated using skewness measure, and multivariate process control chart respectively. Then a large sample of the multivariate normal data is simulated using computer software to estimate the percent of nonconforming (PNC) from the established specification limits, which is used to estimate MPCI. Finally, the capable tolerance of the process is estimated and the sensitivity analysis of variation is investigated. The results show the capability of the EBM process under different specification limits designations. Estimating MPCI revealed that the EBM process is capable under very coarse limits only. Moreover, the sensitivity analysis showed that variation in quality characteristics data is very sensitive for MPCI estimation, especially variation in width quality characteristic.

New Approach for Process Capability Analysis Using Multivariate Quality Characteristics

The evaluation of manufacturing processes aims to ensure that the processes meet the desired requirements. Therefore, process capability indexes are used to measure the capability of a process to meet customer requirements and/or engineering specifications. However, most of the manufacturing products have more than one quality characteristic (QC), in which case, the multivariate QCs should be evaluated together using a single capability index. The research in this article proposes a methodology for estimating the multivariate process capability index (PCI). First, the dimensions of the multivariate QCs are reduced into a new single variable using the proportion of the process specification region, by comparing each variable datapoint to its specification limits. Moreover, nonnormal data are transformed to normality using a root transformation algorithm. Then, a large data sample is generated using the parameters of the new variable. The generated data are compared to the specification limits to estimate the percent of nonconforming (PNC). Finally, the capability index of a given process datapoints is estimated using the PNC. Accordingly, managerial insights for the implementation of the proposed methodology in real industry are presented. The methodology was assessed by well-known multivariate samples from four different distributions, in which an algorithm was developed for generating these samples with their given correlations. The results show the effectiveness of the proposed methodology for estimating multivariate PCIs. Also, the results from this research outperform the previous published results in most cases.

Four critical engineering and technical problems in manufacturing measurement of traditional Chinese medicine

Focusing on the development and quality improvement strategy of the traditional Chinese medicine(TCM) industry, the scientific and technological innovation of the new engineering of TCM should be paid attention to solve the "stuck neck" dilemma. Under the background of the ecological and industrial revolution of the scientific and technological innovation system, the super-scale information interaction and multi-dimensional integration will inevitably lead to profound changes in the manufacturing mode of TCM. Manufacturing measurement of TCM is formed on the basis of the reliability engineering theory of process control of TCM production. It is the development extension of system theory and system science ideas and a cross-fertilization discipline that combines theory with practice and adheres to the "four-oriented" re-epistemology improvement of the TCM discipline. In response to the problems of complex raw material sources, coarse process technology, unclear material basis, and poor applicability of equipment and technology in the manufacture of TCM, the transformation research mode of "aiming at the integration of pharmaceutical industry-developing intelligent production line-enabling industrial transformation" has been developed. This paper proposed the four key engineering technical problems, i.e., the identification of critical quality attributes(CQA) in the manufacture of TCM, the quality by design(QbD) and product development of the manufacturing process of TCM, the quality transfer principle and multivariate process capability index of TCM manufacturing, and the development of measurement technology and equipment of the manufacturing measurement of TCM, to achieve the systematization of quality control indicators, real-time process control, digitalization of manufacturing process, transparency of quality transfer, and intelligent whole-process control. In this paper, the new concepts, new theories, and new technologies provide a reference for the industrialization of TCM.

A bibliography of the literature on process capability indices (PCIs): 2010–2021, Part II: Multivariate PCI‐ and functional PCI‐related papers, special applications, software packages, and omitted papers

AbstractThis is the second part of the bibliography on process capability indices (PCIs) for the period 2010–2021, and includes multivariate and functional PCI‐related papers, special applications, software packages, and papers omitted in the author's previous bibliography.

The effects of measurement errors on estimating and assessing the multivariate process capability with imprecise characteristic

In industrial environments, process capability indices are daily employed as numerical metrics to summarize the performance of a process according to a predefined set of specification limits. Neglecting gauge measurement errors is a common phenomenon in process capability evaluations by researchers in laboratory investigations and by practitioners in daily operations. However, this common negligence is far from reality regardless of the employment of highly modern measuring tools, and may notably influence the efficiency of the measuring method for assessing the performance of a manufacturing process. In this paper, a linear covariate error model is applied to investigate the effects of gauge measurement errors on the classical and fuzzy estimation approaches of the multivariate process capability index SpkT for univariate and multivariate normally distributed quality characteristics with precise specification limits. Moreover, lower confidence bounds are also derived for the yield index SpkT in the presence of measurement errors and based on a fuzzy approach. In addition to the theoretical results, extensive simulations have been conducted to analyze how the behavior of the test statistic and lower confidence bound (LCB) for assessing the performance of the process is affected by different sources of the measurement errors. The obtained results indicate that a serious underestimation of the process capability occurs when the data is contaminated with measurement errors. It is also shown that the underestimation problem is somewhat solved by taking multiple measurements from the identical item. Moreover, comparative analyses show that the proposed method is superior to Scagliarini’s method and Wang’s way such that the negative effects of errors on underestimating the LCB are reduced in the proposed plan. This paper also extends the application of the introduced method to correlated variables. Finally, three practical examples are discussed to demonstrate the use of the proposed method in industrial applications.

Two‐phase multivariate supplier selection for symmetric specification region and correlated quality characteristics

AbstractAmong different yardsticks of assessing a supplier's performance and comparing the same with other competing suppliers, quality is often considered as one of the most important criteria. The problem becomes even more complicated for multivariate processes having more than one correlated quality characteristics. Unfortunately, very few research work has been carried out in literature, to compare performances of two suppliers having multivariate processes with correlated quality characteristics and symmetric specification region. In the present article, a two‐phase hypothesis testing‐based supplier selection process using multivariate process capability indices (MPCIs) called and is proposed to address this issue. While measures potential capability of a multivariate process, measures its actual capability. The proposed method is easy to implement in practice and hence is suitable for practical applications. A real‐life example and a simulated example are discussed to supplement the theory developed in this article.

A new probability-based multivariate process capability index

Multivariate process capability indices (MPCIs) MCp, MCpk and MCpm have been proposed in literature to measure multivariate process capability. From a practitioner's view, the intention of this paper is to propose a new probability-based MPCI MSpmk which takes into account process variability, departure of the process mean from target and proportion of conformity when assessing multivariate process performance. The MSpmk is the extension in multivariate setup of univariate process capability index Spmk. The Spmk is smooth version of widely used univariate process capability index Cpmk. The MSpmk is very easy to compute and combines the merits of MPCIs MCp, MCpk and MCpm. Proposed MPCI assumes that production process is multivariate normal and specification region is rectangular. Proposed MPCI is recommendable with respect to its performance in various scenarios and its natural estimator statistical properties for real world usage.

A new probability-based multivariate process capability index

Multivariate process capability indices (MPCIs) MCp, MCpk and MCpm have been proposed in literature to measure multivariate process capability. From a practitioner's view, the intention of this paper is to propose a new probability-based MPCI MSpmk which takes into account process variability, departure of the process mean from target and proportion of conformity when assessing multivariate process performance. The MSpmk is the extension in multivariate setup of univariate process capability index Spmk. The Spmk is smooth version of widely used univariate process capability index Cpmk. The MSpmk is very easy to compute and combines the merits of MPCIs MCp, MCpk and MCpm. Proposed MPCI assumes that production process is multivariate normal and specification region is rectangular. Proposed MPCI is recommendable with respect to its performance in various scenarios and its natural estimator statistical properties for real world usage.

Distributional and inferential properties of some new multivariate process capability indices for symmetric specification region

AbstractStatistical quality control is used to improve performance of processes. Since most of the processes are multivariate in nature, multivariate process capability indices (MPCIs) have been developed by many researchers depending on the context. However, it is generally difficult to understand and calculate MPCIs, compared to their univariate counterparts like , , and so on. This paper discusses a relatively new development in MPCIs, namely, , which is a multivariate analogue of —the celebrated superstructure of univariate process capability indices . Some statistical properties of are studied, particularly of , a member MPCI of the superstructure, which measures potential capability of a multivariate process. A threshold value of is computed, and this can be considered as a logical cut‐off for other member indices of as well. The expression for the upper limit of the proportion of nonconformance is derived as a function of . Density plots of asymptotic distributions of four major member indices of , namely, , , , and , are made. Finally, a numerical example is discussed to supplement the theory developed in this paper.

On properties of probability‐based multivariate process capability indices

AbstractMultivariate process capability indices (MPCIs) have been proposed to measure multivariate process capability in real‐world application over the past three decades. For the practitioner's point of view, the intention of this paper is to examine the performances and distributional properties of probability‐based MPCIs. Considering issues of construction of capability indices in multivariate setup and computation with performance, we found that probability‐based MPCIs are a proper generalization of univariate basic process capability indices (PCIs). In the beginning of this decade, computation of probability‐based indices was a difficult and time‐consuming task, but in the computer age statistics, computation of probability‐based MPCIs is simple and quick. Recent work on the performance of MPCI NMCpm and distributional properties of its estimator reasonably recommended this index, for use in practical situations. To study distributional properties of natural estimators of probability‐based MPCIs and recommended index estimator, we conducted simulation study. Though natural estimators of probability‐based indices are negatively biased, they are better with respect to mean, relative bias, mean square error. Probability‐based MPCI MCpm is better as compared with NMCpm with respect to performance and as its estimator quality. Hence, in real‐world practice, we recommend probability‐based MPCIs as a multivariate analogue of basic PCIs.

Multivariate Process Incapability Index Considering Measurement Error in Fuzzy Environment

Process Capability Indices (PCI) show that the process conforms to the specification limits; when the product quality depends on more than one characteristic, Multivariate Process Capability Indices (MCPI) are used. By modifying in the process capability indices, the process incapability indices are created; these indices then provide information about the accuracy and precision of the process separately. In the real world, in most cases, the parameters cannot be specified precisely; therefore, the use of fuzzy sets can solve this problem in statistical quality control. The purpose of this paper is to present, for the first time, a Multivariate Process Incapability Index by considering the measurement error in a fuzzy environment. The presented index is shown for practical examples solved by considering Triangular Fuzzy Numbers; then the capability of the model is compared to the time when fuzzy logic is not used. The obtained results emphasize that ignoring the measurement error also leads to the incorrect calculation of process capability, causing a lot of damage to manufacturing industries, especially high-tech ones.

Quality Control of HDPE Bottles Production Processes based on Multivariate Attribute Data using T2 Hotelling Control Chart as A Responds of Environment and Sustainability Issues

This research was conducted to determine the current process capability in producing the M500 bottle, where the process capability index can be calculated from the results of a control chart whose data is considered to be statistically controlled. Multivariate control charts can be used in controlling the quality of the process at CV X because the quality characteristics of the products are more than one, and the controls must be carried out together. Correlated variables used in making multivariate control charts are different thicknesses, leaks, and dents. The results of the hotelling’s T2 control chart show that the process has not been controlled because four observations are out of control. MYT decomposition results show that variables that cause observations to become uncontrolled are different thicknesses and dents. After revising the control chart, it is known that the current multivariate process capability index is 0.79, which means the process is said to be incapable and needs to be improved. The suggested improvement given to overcome the problem of different thicknesses is to position the die right in the middle so that the thickness on all sides is the same and for dented conditions can be reduced by adjusting the blowing temperature and pressure according to the standard.

Impact of multivariate normality assumption on multivariate process capability indices

Process Capability Index (PCI) is a very popular tool for assessing performance of processes (often involving a single quality characteristic). Multivariate process capability indices (MPCI) are comparatively new to the literature and hence often involve some difficulties in practical applications. One such hurdle is multivariate normality assumption of the underlying distribution of the quality characteristics. While such assumption gives some computational as well as theoretical advantage in formulating MPCIs, often data encountered in practice do not follow multivariate normal distribution due to several reasons. Consequently, the computed values of the MPCIs may give misleading results. In the present article, we have made performance analysis of some MPCIs in the light of a dataset which has been widely used in the literature, particularly in the context of MPCIs. Most of these MPCIs were already applied to the said data in the literature and our objective is to make their comparative performance analysis. In this context, the data, though actually non-normal, is often concluded as multivariate normal by several researchers. Therefore, while making the performance analysis of the MPCIs, this aspect has also been incorporated to put emphasis on the importance of distributional assumption in a multivariate process capability analysis.

Analysis of Multivariate Process Capability Using Box-Cox Transformation

The process control methods based on the statistical analysis apply the analysis method or mathematical model under the assumption that the process characteristic is normally distributed. However, the distribution of data collected by the automatic measurement system in real time is often not followed by normal distribution. As the statistical analysis tools, the process capability index (PCI) has been used a lot as a measure of process capability analysis in the production site. However, PCI has been usually used without checking the normality test for the process data. Even though the normality assumption is violated, if the analysis method under the assumption of the normal distribution is performed, this will be an incorrect result and take a wrong action. When the normality assumption is violated, we can transform the non-normal data into the normal data by using an appropriate normal transformation method. There are various methods of the normal transformation. In this paper, we consider the Box-Cox transformation among them. Hence, the purpose of the study is to expand the analysis method for the multivariate process capability index using Box-Cox transformation. This study proposes the multivariate process capability index to be able to use according to both methodologies whether data is normally distributed or not. Through the computational examples, we compare and discuss the multivariate process capability index between before and after Box-Cox transformation when the process data is not normally distributed.

Comparison Analysis of Multivariate Process Capability Indices

Recently, the manufacturing process system in the industrial field has become more and more complex and has been influenced by many and various...

Multivariate statistical control chart and process capability indices for simultaneous monitoring of project duration and cost

Statistical process control (SPC) techniques have been implemented in a few studies in order to determine action limits on the earned value management (EVM) indices to assist project managers in monitoring project performance. Nevertheless, these indices are correlated, reliance on univariate control charts when more than one variable are involved and they are correlated may lead to unsatisfactory results such as increasing the rate of false alarms. This study presented an approach to overcome this limitation by applying multivariate Hotelling's T2 control chart to take into account possible correlations between EVM indicators and describe the entire capability of the project performance more accurately. Furthermore, in order to quantify how well a project can meet its requirements, some practical multivariate process capability indices (PCIs) are introduced. This approach provides management with more reliable information about the deviations between planned and actual performance both in terms of time and cost simultaneously.

A Multivariate KPI-Based Method for Quality Assurance in Lithium-Ion-Battery Production

The development of lithium-ion batteries (LIBs) is facing challenges due to the high level of uncertainty in cause-effect-relationships (CERs) in the manufacturing process. This process is characterized as an interlinked chain of input, intermediate and quality properties, which determine the quality of LIBs. In order to reduce the ramp-up time for LIB production plants, an understanding of influencing properties must be established. Existing methods to investigate these properties are usually expert-based or assess individual process steps. Thus, this paper presents a method, which utilizes multivariate process capability indices for the identification of CERs and quality assurance in the field of LIB production. This data-driven approach was applied to and evaluated on the production data of the prototype line for prismatic LIBs at the BMW Group in Munich.

Multivariate process incapability vector

AbstractProcess capability indices evaluate the capability of the processes in satisfying customer's requirements. This paper introduces a superstructure multivariate process incapability vector for multivariate normal processes and then, compares it with four recently proposed multivariate process capability indices to show its better performance. In addition, the effects of two modification factors are investigated. Also, bootstrap confidence intervals for the first component of the proposed vector are obtained. Furthermore, real manufacturing data sets are presented to demonstrate the applicability of the proposed vector.

Multivariate Process Capability Index Using Inverted Normal Loss Function

Multivariate Process Capability Index Using Inverted Normal Loss Function