Multivariate Process Capability Research Articles

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.

Novel Heuristic Algorithm for Flexible Job Shop Scheduling based on the Longest Processing Time Rules to Minimize Makespan

This research examined the scheduling of jobs with multiple stages unto identical parallel machines to minimize the makespan. The work is motivated by a Flexible Manufacturing System case that produces various parts and has multiple machining centers. Early research towards this system proposed a stage-by-stage independent scheduling, resulting in a non-optimal solution. This study aimed to create a better solution for the system by developing a novel heuristic algorithm based on the classical longest processing time algorithm and simultaneously considering processing time for all stages when deciding the job sequencing and job-machine allocation. The algorithm is defined as Modified LPT for Multiple Identical Machine with Multi-process Capability (M-LPT MIMMPC). We performed a numerical experiment to assess the algorithm's performance by incorporating various cases. We concluded that the resulting makespans are always better than LPT's theoretical bound for parallel machine scheduling. In some cases, it successfully gave an optimal value. Although the experiment scope was still limited, the algorithm showed promising performance results.

PENERAPAN DIAGRAM KONTROL MEWMA DALAM PENGENDALIAN KUALITAS PRODUKSI KERIPIK SINGKONG PADA UMKM DI KOTA SEMARANG

Quality is the main thing that needs to be considered by every company. Ceriping Bintang Putra Bu Slamet is an UMKM (Usaha Mikro, Kecil dan Menengah) that produces cassava chips. During production, there are three quality characteristics, namely large crumbs defects, small crumbs, and chips sticking together. It is important to control these defects to produce quality products according to customer needs. This research was conducted from July to August 2021. The purpose of this study was to control the production quality of cassava chips using the Multivariate Exponentially Weighted Moving Average (MEWMA) control chart and multivariate process capability analysis. The MEWMA control chart is used to detect the shift in the process average which is more sensitive using weights (λ), while the process capability analysis is used to determine the process performance. The implementation of the MEWMA control chart is carried out in two stages, namely phase I control to obtain the optimal weighting and control limits so that it can be used in phase II control to monitor the average process for the next period. Based on the results of the analysis, the optimal weighting is λ =0,4 with BKA=201,7434, GT=113,538, and BKB=0 in phase I control. Then, the results of phase II control show a shift in the average process in a better direction. In addition, the results of the process capability analysis show an improvement in the performance of the production process from July 2021 to August 2021 with MCpm values of 0,535 and 1,147

PENERAPAN PETA KENDALI T^2 HOTELLING ALGORITMA FAST MINIMUM COVARIANCE DETERMINANT PADA PENGENDALIAN KUALITAS BAWANG MERAH VARIETAS LEMBAH PALU

The physical condition of the Palu Valley shallots variety greatly affects the quality of the fried onions that are obtained. The poor quality of shallots will affect the product that will sale by the farmers. Therefore, it is necessary to monitor by conducting the quality control analysis of the physical condition of shallots. In this study we use the quality control method of the Hotelling control map with the fast-MCD algorithm. This method is used because the outlier in the data to be analyzed. The purpose of this study is to produce average vector estimates and variance-covariance matrix estimates in the formation of the Hotelling control map. From the calculation by using the mean vector and the variant-covariant matrix with fast-MCD estimation, 93 data were obtained that experienced out of control on the Hotelling control map with the fast-MCD algorithm where the observations that experienced out of control were more than the usual of Hotelling control map. This shows that the Hotelling control map with the fast-MCD algorithm is more effective in detecting observations which contain outliers. The value of the multivariate process capability analysis is less than one showing the process is uncapable.

Improvement in Injection Molding Quality Performance with Innovative Cyclone Mixers Used in Polypropylene with Spherical Silicon Dioxide Composites.

This research proposes an innovative design of a new cyclone mixer for the quality of polymer materials, and it presents a systematic optimization model of process parameters for plastic injection molding. Thermo gravimetric analysis (TGA) and differential scanning calorimetry (DSC) were used to determine the appropriate thermal properties of processing in order to select appropriate control factors and level values for a Taguchi orthogonal array. The injection molding machine was used to make sample test pieces for tensile strength, hardness and impact strength. Significant factors were found by the signal-to-noise (S/N) ratio with an analysis of variation (ANOVA), and the single-quality optimal parameter combination was obtained. The reproducibility of the experiment was evaluated, and various quality weights were evaluated by principal components analysis (PCA). The multi-quality optimal parameter combination was found, and the comprehensive scores were compared. Finally, the process capability indices were combined with a multi-process capability analysis chart (MPCAC) to compare the process yields of cyclone mixing and screw mixing. The mechanical properties of products were evaluated to verify the performance of cyclone mixing and to provide perfect information for the injection molding quality performance of cyclone mixing and screw mixing. It was concluded that the overall quality of the cyclone mixing products is 42.72, and the total quality of the screw mixing products is 41.85. The total number of defects for the cyclone mixing is 9659 ppm, and that of the screw mixing is 10688 ppm. It can be seen that, for the overall product quality performance, cyclone mixing can be applied in the plastic injection molding process instead of screw mixing.

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.

Un índice de capacidad de procesos para distribuciones multivariadas normales y no normales, de variables correlacionadas y no correlacionadas

DOI: https://doi.org/10.26439/ing.ind2020.n038.4814 The multivariate process capability analysis includes many indices that are only used when the data is normal and others, when the data is not normal. The same occurs with correlated and uncorrelated quality variables. In this research work, a CPME multivariate capability index was developed by initially using a univariate index—depending on whether the data was o not normal—and any correlation between variables, and then through a characteristic function for the multivariate data. This index may be used in all the aforementioned cases. Some examples of this alternative are presented on a set of real and simulated data, where a broad performance of our proposed index was found against other similar capability indices.

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.

Multiple Process Capability Improvement Method based on Principal Component Analysis

For the traditional multi-process capability construction method based on principal component analysis, the process variables are mainly considered, but not the process capability, which leads to the deviation of the contribution rate of principal component. In response to the question, this paper first clarifies the problem from two aspects: theoretical analysis and example proof. Secondly, aiming at the rationality of principal components degree, an evaluation method for pre-processing data before constructing MPCI using PCA is proposed. The pre-processing of data is mainly to standardize the specification interval of quality characteristics making the principal components degree more reasonable and optimizes the process capability evaluation method. Finally, the effectiveness and feasibility of the method are proved by an application example.

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.