Multivariate Process Capability Indices Research Articles

MULTIVARIATE PROCESS CAPABILITY ASSESSMENT AND IMPROVEMENT: A CASE STUDY

ABSTRACTIn today’s competitive manufacturing environment, the challenge is to responsivelyproduce products with minimum cost and high quality. Achieving and controlling thetargeted quality level in manufacturing processes does not only increase customersatisfaction, but it can also result in significant cost and time savings. Further,measuring the process performance is a critical issue in process improvementinitiatives. The common practice in several industries is using the Univariate ProcessCapability Indices (UPCIs) to measure the process performance, which are based ononly a single quality characteristic. In most of the applications, it is not acceptable tojudge the performance based on a single quality characteristic as it actually relies onmore than one characteristic. In this paper, univariate and multivariate PCIs are usedto measure the performance of the flare making process. This process is a criticalstep in the straight fluorescent light bulb production line. In addition, multivariatecontrol charts such as the Hotelling
 as well as the Multivariate ExponentiallyWeighted Moving Average (MEWMA) are constructed for the collected data to verifythat the process is in control before assessing its capability. Besides, PrincipalComponent Analysis (PCA) and Joint Normal Distribution (JND) techniques areapplied in the multivariate process capability assessment. In this paper, MultivariateProcess Capability Indices (MPCIs) have been evaluated to compare the processperformance before and after improvement efforts. In the considered case study,MPCIs provide the user with an overall assessment of process capability regardlessof the fluctuations in the individual variables capabilities.

Study on the Robust Tolerance Design with Multiple Resource Suppliers on Cloud Manufacturing Platform

The robust tolerance design in the scenario with multiple resource suppliers is faced with greater uncertainty in the new manufacturing era. This paper studies the robust tolerance design on cloud manufacturing platform, in which a two-level game is put forward to reveal the relationship and behavior between the products and resource suppliers. According to the scenario with multiple resource suppliers, the multivariate process capability index has been introduced to solve the problem of robust tolerance design faced up with cloud manufacturing environment. A case study is used to illustrate the proposed model.

Multivariate process capability analysis applied to AISI 52100 hardened steel turning

Hard turning operations have been extensively investigated owing to their ability to reduce process cycle time, increase process flexibility, ensure high-dimensional accuracy, and enable machining without a cutting fluid. These processes are rather common for dealing with multiple quality characteristics. To evaluate the process ability and meet customer needs, multivariate statistical techniques are recommended for estimating the capability indices. Principal component analysis can be applied to reducing the problem dimension and estimate process capability indices. The aim of this study was to assess the capability of AISI 52100 hardened steel turning operations and achieve process specifications. Multivariate process capability indices were calculated to assess five roughness parameters of surface finishing. By using a weighted approach of principal component analysis, a new method is proposed for estimating the process capability indices. The results highlight not only the relevance of conducting a multivariate capability analysis in the case of actual machining but also how successfully the proposed method was performed.

Unification of some multivariate process capability indices for asymmetric specification region

In manufacturing industries, it is often seen that the bilateral specification limits corresponding to a particular quality characteristic are not symmetric with respect to the stipulated target. A unified superstructureof univariate process capability indices was specially designed for processes with asymmetric specification limits. However, as in most of the practical situations a process consists of a number of inter‐related quality characteristics, subsequently, a multivariate analogue of, which is calledCM(u,v), was developed. In the present paper, we study some properties ofCM(u,v) like threshold value and compatibility with the asymmetry in loss function. We also discuss estimation procedures for plug‐in estimators of some of the member indices ofCM(u,v). Finally, the superstructure is applied to a numerical example to supplement the theory developed in this article.

A new multivariate process capability index

Multivariate process capability indices are applied to account the capability of the processes which the quality of the products depends on two or more related characteristics. We call a tolerance region asymmetric, when the target value of at least one characteristic is not the mid-point of the tolerance interval. This paper introduces a superstructure index to measure the capability of multivariate normal process in asymmetric tolerance regions, which could be applied for symmetric cases, too. In addition, the effects of two modification factors in the index which weigh the mean departure from target and process variability are investigated. Furthermore, some examples are presented to demonstrate the applicability and effectiveness of the proposed index.

A review of univariate and multivariate process capability indices

This paper offers a review of univariate and multivariate process capability indices (PCIs). PCIs are statistic indicators widely used in the industry to quantify the capability of production processes by relating the variability of the measures of the product characteristics with the admissible one. Univariate PCIs involve single-product characteristics while multivariate PCIs deal with the multivariate case. When analyzing the capability of processes, decision makers of the industry may choose one PCI among all the PCIs existing in the literature depending on different criteria. In this article, we describe, cluster, and discuss univariate and multivariate PCIs. To cluster the PCIs, we identify three classes of characteristics: in the first class, the characteristics related to the information of the process data input are included; the second class includes characteristics related to the approach used to calculate the PCIs; and in the third class, we find characteristics related to the information that the PCIs give. We discuss the strengths and weaknesses of each PCI using four criteria: calculation complexity, globality of the index, relation to proportion of nonconforming parts, and robustness of the index. Finally, we propose a framework that may help practitioners and decision makers of the industry to select PCIs.

Robustness Indices in Multistage Problems

The study of robustness in single‐stage manufacturing has been surveyed by many researchers, while modeling of robustness in multistage manufacturing using multivariate data is seldom explored. The aim of this paper is to develop a methodology to model process robustness in a multistage manufacturing system. This paper proposes a methodology to study the robustness of a multistage process that creates a component and process capability that acts as a surrogate measure of robustness. A powerful technique to facilitate the analysis of the mentioned problem, response surfaces express the behavior of responses considering the above controllable factors (quality characteristics). A common approach to estimating response surfaces using experimental data is the ordinary least squares method. Because this method is very sensitive to outliers and correlated responses, in this paper, a robust coefficient estimation method is proposed for multiresponse surfaces in multistage processes based on M‐estimators. The results show that considering the proposed robustness criteria based on a multivariate process capability index, the robust multistage process would perform better than the individual stage process. This paper adds to the body of knowledge on the robustness of multistage manufacturing processes, and also the relationship between robustness and capability is to be explored as surrogate robustness indices in the multistage process. The efficiency of the proposed approach is assessed by a small simulation study besides a real manufacturing case study. Copyright © 2017 John Wiley & Sons, Ltd.

Development of multivariate process monitoring strategy for a typical process industry

The study demonstrated the application of partial least square regression technique in the development of a monitoring strategy for a process industry. The process industry under consideration is an integrated steel plant engaged in the production of steel billets. The steel making shop which has been the focus of the study is a complex process replete with numerous and inter-related process, feedstock and quality characteristics. The main challenge addressed in this paper is the development of a monitoring strategy for the concerned steel making shop taking into account all the characteristics (process, feedstock and quality) simultaneously. The strategy thus devised seems to bode well, as it was correctly able to ascertain the status (in state of statistical control or out-of-control) of the process. Further capability studies via the employment of a multivariate process capability index were carried out to determine the efficacy of the process in producing end products. The capability study highlighted the fact that the process needs readjustment as a substantial amount of end products produced were out of specifications.

ON THE MULTIVARIATE PROCESS CAPABILITY VECTOR IN FUZZY ENVIRONMENT

The production of a process is expected to meet customer demands, specifications or engineering tolerances. The ability of a process to meet these expectations is expresed as a single number using a process capability index. When the quality of the products relates to more than one characteristic, multivariate process capability indices are applied. As it is known, in some circumstances we are faced with imprecise data. So, fuzzy logic is engaged to deal with them. In this article, the specification limits and the target value of each characteristic and also, the data gathered from the process are assumed to be imprecise and a new fuzzy multivariate capability vector is introduced. As a whole, the present article provides a research of the application of fuzzy logic in multivariate capability vector.

Distributional Properties of Multivariate Process Capability Indices under Normal and Non-normal Distributions

Multivariate capability analysis has been the focus of study in recent years, during which many authors have proposed different multivariate capability indices. In the operative context, capability indices are used as measures of the ability of the process to operate according to specifications. Because the numerical value of the index is used to conclude about the capability of the process, it is essential to bear in mind that almost always that value is obtained from a sample of process units. Therefore, it is really necessary to know the properties that the indices have when they are calculated on sampling information, in order to assess the goodness of the inferences made from them. In this work, we conduct a simulation study to investigate distributional properties of two existing indices: NMCpm index based on ratio of volumes and Mp2 index based on principal component analysis. We analyze the relative bias and the mean square error of the estimators of the indices, and we also obtain their empirical distributions that are used to estimate the probability that the indices classify correctly a process as capable or as incapable. The results allow us to recommend the use of one of these indices, as it has shown better properties. Copyright © 2016 John Wiley & Sons, Ltd.

Fuzzy multivariate process capability vector

Process capability indices are numerical measures used to determine whether the process products meet the quality requirement dedicated by the customers and producers or not. When the products' quality counts on two or more correlated characteristics, multivariate process capability indices are applied. In this paper, we focus on two indices proposed by Shahriari and Abdollahzadeh (2009) and Taam et al. (1993). The traditional multivariate capability indices can't be applied if the specification limits and target value of each characteristic are presented in a linguistic form. Instead, the fuzzy set theory is used to deal with these circumstances. Here, the fuzzy formulations of the indices are developed. Furthermore, numerical examples are presented to illustrate the applicability of the proposed methods and we make a comparison between them.

Modelling process robustness: a case study of centrifugal casting

A robust process minimises the effect of the noise factors on the performance of a product or process. The variation of the performance of a robust process can be measured through modelling and analysis of process robustness. In this paper, a comprehensive methodology for modelling and analysis of process robustness is developed considering a number of relevant tools and techniques such as multivariate regression, control charting and simulation within the broad framework of Taguchi method. The methodology as developed considers, in specific terms, process modelling using historical data pertaining to responses, inputs variables and parameters as well as simulated noise variables data, identification of the model responses at each experimental setting of the controllable variables, estimation of multivariate process capability indices and control of their variability using control charting for determining optimal settings of the process variables using design of experiment-based Taguchi Method. The methodology is applied to a centrifugal casting process that produces worm-wheels for steam power plants in view of its critical importance of maintaining consistent performance in various under controllable situations (input conditions). The results show that the process settings as determined ensure minimum in-control variability with maximum performance of the centrifugal casting process, indicating improved level of robustness.

Multivariate Process Capability Index Based on Data Depth Concept

The purpose of this paper is to provide a multivariate process capability index, which could be used regardless on data distribution and also on data correlation. Such an index could be defined because of application of non‐parametric methodology that utilizes a data depth concept. Based on this concept, a two‐phase methodology was developed. In the first phase the modified tolerance region is estimated, while in the second one, a current process is assessed using the proposed three‐component index. Estimation of a modified tolerance region on the basis on historical data allows applying the methodology not only for bilateral quality characteristics but also for unilateral ones, where often in practice, the modified tolerance region could be defined as a closed region. The performance of the proposed index was evaluated using bilateral and unilateral examples. The obtained results showed that the proposed index performs satisfactorily for all the considered cases. Copyright © 2016 John Wiley & Sons, Ltd.

New multivariate process capability indices for measuring the performance of multivariate processes subject to non-normal distributions

Purpose – In the past few years, several capability indices have been developed for evaluating the performance of multivariate manufacturing processes under the normality assumption. However, this assumption may not be true in most practical situations. Thus, the purpose of this paper is to develop new capability indices for evaluating the performance of multivariate processes subject to non-normal distributions. Design/methodology/approach – In this paper, the authors propose three non-normal multivariate process capability indices (MPCIs) RNMC p , RNMC pm and RNMC pu by relieving the normality assumption. Using the two normal MPCIs proposed by Pan and Lee, a weighted standard deviation method (WSD) is used to modify the NMC p and NMC pm indices for the-nominal-the-best case. Then the WSD method is applied to modify the multivariate ND index established by Niverthi and Dey for the-smaller-the-better case. Findings – A simulation study compares the performance of the various multivariate indices. Simulation results show that the actual non-conforming rates can be correctly reflected by the proposed capability indices. The numerical example further demonstrates that the actual quality performance of a non-normal multivariate process can properly reflected by the proposed capability indices. Practical implications – Process capability index is an important SPC tool for measuring the process performance. If the non-normal process data are mistreated as a normal one, it will result in an improper decision and thereby lead to an unnecessary quality loss. The new indices can provide practicing managers and engineers with a better decision-making tool for correctly measuring the performance for any multivariate process or environmental system. Originality/value – Once the existing multivariate quality/environmental problems and their Key Performance Indicators are identified, one may apply the new capability indices to evaluate the performance of various multivariate processes subject to non-normal distributions.

Process capability – a surrogate measure of process robustness: a case study

Purpose– The purpose of this paper is to obtain a better understanding on robust performance of a hardening and tempering process producing component worm shaft used in the steam power plant. This research is capable to explaining the variation of process capability in terms of robustness.Design/methodology/approach– This paper proposed a methodology (a combination of simulation, regression modelling and robust design technique) to study robustness of a hardening and tempering process producing component worm shaft used in the steam power plant and process capability acts as a surrogate measure of robustness. In each experimental run, the values of responses and the corresponding multivariate process capability indices across the outer array are determined. The variation of process performance (process capability values) due to random noise variation is studied using a general purpose process control chart (R-chart).Findings– The results provide useful information in term of insensitiveness of the process against the noise (raw material and process noise) variation where the process capability acts as a surrogate measure of process robustness and explains the variation of process capability in term of robustness.Practical implications– This paper adds to the body of knowledge on robustness of a manufacturing process. This paper may be of particular interest to practicing engineers as it suggests what factors should be more emphasis to achieve robust (consistent) performance from the process.Originality/value– The originality of this paper lies within the context in which this study is to address key relationships between process robustness and process capability in a manufacturing industry.

A new process capability index for multiple quality characteristics based on principal components

This paper presents a new multivariate process capability index (MPCI) which is based on the principal component analysis (PCA) and is dependent on a parameter which can take on any real number. This MPCI generalises some existing multivariate indices based on PCA proposed by several authors when or . One of the key contributions of this paper is to show that there is a direct correspondence between this MPCI and process yield for a unique value of . This result is used to establish a relationship between the capability status of the process and to show that under some mild conditions, the estimators of this MPCI is consistent and converge to a normal distribution. This is then applied to perform tests of statistical hypotheses and in determining sample sizes. Several numerical examples are presented with the objective of illustrating the procedures and demonstrating how they can be applied to determine the viability and capacity of different manufacturing processes.

The Study of Relationship between Multivariate Capability Indices and Sampling Number

ultivariate process capability indices (MPCI), as an important means of statistical process control (SPC), can be used to ensure the high reliability of semiconductors manufacturing process. However, the reasonable sampling number is an important factor when considering MPCI values. As general, the large sample number requires much effort and time, or even cannot be achieved. In this paper, we evaluated the impact of different sample size on the calculations of multivariate process capability indices using simulation and analyses. After getting enough data and choosing disparate sample numbers, corresponding multivariate process capability indices can be obtained, which demonstrate the relationship between sampling numbers and calculation results. The conclusions have critical guiding significance for manufacturing semiconductors with high reliability requirement.

Multivariate Process Capability Indices: A Directional Approach

We propose a unified, universal, natural, and very intuitive way how to obtain new multivariate and tool wear extensions of univariate process capability indices by means of projection pursuit. We also illustrate the methodology in detail of the popular precision and accuracy indices, generalize the latter in a few different ways in the same spirit, add some personal insight, discuss the computational issues involved, and demonstrate the advantages of our approach in a small data example.

Modified multivariate process capability index using principal component analysis

The existing research of process capability indices of multiple quality characteristics mainly focuses on nonconforming of process output, the concept development of univariate process capability indices, quality loss function and various comprehensive evaluation methods. The multivariate complexity increases the computation difficulty of multivariate process capability indices(MPCI), which makes them hard to be used in practice. In this paper, a new PCA-based MPCI approach is proposed to assess the production capability of the processes that involve multiple product quality characteristics. This approach first transforms the original quality variables into standardized normal variables. MPCI measures are then provided based on the Taam index. Moreover, the statistical properties of these MPCIs, such as confidence intervals and lower confidence bound, are given to let the practitioners understand the capability indices as random variables instead of deterministic variables. A real manufacturing data set and a synthetic data set are used to demonstrate the effectiveness of the proposed method. An implementation procedure is also provided for quality engineers to apply our MPCI approach in their manufacturing processes. The case studies demonstrate the effectiveness and feasibility of this new kind of MPCI, which is easier to be used in production practice. The proposed research provides a novel approach of MPCI calculation.

Determining quality risk for correlated bivariate normal characteristics

Most multivariate process capability indices proposed by other researchers provide quality measure in losses due to variability and being off-target. Some suggested loss function models that estimate losses due to rejection and quality costs but failed to consider the correlation between the multivariate quality characteristics. In this paper, we propose a novel new approach for estimating the total expected quality cost that provides quality cost measure not only in losses due to variability and being off-target but also losses due to rejection. The proposed model also estimates the quality costs for correlated quality characteristics with nominal specifications and provides the estimated costs due to individual characteristics; it helps to identify those process quality characteristics which have high variation when compared with their specification spread. The model will also improve the estimate of the rejection cost suggested by earlier researchers as it identifies the reject region as the region outside of the modified tolerance region. We present four different correlated bivariate normal process scenarios where the proposed method can be applicable and demonstrate that our approach provides a robust tool in estimating the risk of the product being rejected and performs as well as existing methods in estimating the total quality cost.