Process capability assessment for univariate and multivariate non-normal correlated quality characteristics

In today's competitive business and industrial environment, it is becoming more crucial than ever to assess precisely process losses due to non-compliance to customer specifications. To assess these losses, industry is extensively using Process Capability Indices for performance evaluation of their processes. Determination of the performance capability of a stable process using the standard process capability indices such as and requires that the underlying quality characteristics data follow a normal distribution. However it is an undisputed fact that real processes very often produce non-normal quality characteristics data and also these quality characteristics are very often correlated with each other. For such non-normal and correlated multivariate quality characteristics, application of standard capability measures using conventional methods can lead to erroneous results. The research undertaken in this PhD thesis presents several capability assessment methods to estimate more precisely and accurately process performances based on univariate as well as multivariate quality characteristics. The proposed capability assessment methods also take into account the correlation, variance and covariance as well as non-normality issues of the quality characteristics data. A comprehensive review of the existing univariate and multivariate PCI estimations have been provided. We have proposed fitting Burr XII distributions to continuous positively skewed data. The proportion of nonconformance (PNC) for process measurements is then obtained by using Burr XII distribution, rather than through the traditional practice of fitting different distributions to real data. Maximum likelihood method is deployed to improve the accuracy of PCI based on Burr XII distribution. Different numerical methods such as Evolutionary and Simulated Annealing algorithms are deployed to estimate parameters of the fitted Burr XII distribution. We have also introduced new transformation method called Best Root Transformation approach to transform non-normal data to normal data and then apply the traditional PCI method to estimate the proportion of non-conforming data. Another approach which has been introduced in this thesis is to deploy Burr XII cumulative density function for PCI estimation using Cumulative Density Function technique. The proposed approach is in contrast to the approach adopted in the research literature i.e. use of best-fitting density function from known distributions to non-normal data for PCI estimation. The proposed CDF technique has also been extended to estimate process capability for bivariate non-normal quality characteristics data. A new multivariate capability index based on the Generalized Covariance Distance (GCD) is proposed. This novel approach reduces the dimension of multivariate data by transforming correlated variables into univariate ones through a metric function. This approach evaluates process capability for correlated non-normal multivariate quality characteristics. Unlike the Geometric Distance approach, GCD approach takes into account the scaling effect of the variance-covariance matrix and produces a Covariance Distance variable that is based on the Mahanalobis distance. Another novelty introduced in this research is to approximate the distribution of these distances by a Burr XII distribution and then estimate its parameters using numerical search algorithm. It is demonstrates that the proportion of nonconformance (PNC) using proposed method is very close to the actual PNC value

Development and application of process capability indices

In order to measure the performance of manufacturing processes, several process capability indices have been proposed. A process capability index (PCI) is a unitless number used to measure the ability of a process to continuously produce products that meet customer specifications. These indices have since helped practitioners understand and improve their production systems, but no single index can fully measure the performance of any observed process. Each index has its own drawbacks which can be complemented by using others. Advantages of commonly used indices in assessing different aspects of process performance have been highlighted. Quality cost is also a function of shift in mean, shift in variance and shift in yield. A hybrid is developed that complements the strengths of these individual indices and provides the set containing the smallest number of indices that gives the practitioner detailed information on the shift in mean or variance, the location of mean, yield and potential capability. It is validated that while no single index can fully assess and measure the performance of a univariate normal process, the optimal set of indices selected by the proposed hybrid can simultaneously provide precise information on the shift in mean or variance, the location of mean, yield and potential capability. A simulation study increased the process variability by 100% and then reduced by 50%. The optimal set managed to pick such a shift. The asymmetric ratio was able to detect both the 10% decrease and 20% increase in µ but did not alter significantly with a 50% decrease or a 100% increase in σ, which meant it was not sensitive to any shift in σ. The implementation of the hybrid provides the quality practitioner, or computer-aided manufacturing system, with a guideline on prioritised tasks needed to improve the process capability and reduce the cost of poor quality. The author extended the proposed hybrids to fully measure the performance of a process with multiple quality characteristics, which follow normal distribution and are correlated. Furthermore, for multivariate normal processes with correlated quality characteristics, process capability analysis is not complete without fault diagnostics. Fault diagnostics is the identification and ranking of quality characteristics responsible for multivariate process poor performance. Quality practitioners desire to identify and rank quality characteristics, responsible for poor performance, in order to prioritise resources for process quality improvement tasks thereby speeding up the process and minimising quality costs. To date, none of the existing commonly used source identification approaches can classify whether the process behaviour is caused by the shift in mean or change in variance. The author has proposed a source identification algorithm based on mean and variance impact factors to address this shortcoming. Furthermore, the author developed a novel fault diagnostic hybrid based on the proposed optimal set selection algorithm, principal component analysis, machine learning, and the proposed impact-factor. The novelty of this hybrid is that it can carry out a full multivariate process capability analysis and provides a robust tool to precisely identify and rank quality characteristics responsible for the shifts in mean, variance and yield. The fault diagnostic hybrid can guide the practitioners to identify and prioritise quality characteristics responsible for the poor process performance, thereby reducing the quality cost by effectively speeding up the multivariate process improvement tasks. Simulated scenarios have been generated to increase/decrease some components of the mean vector (µ2/µ4) and in increase/reduce the variability of some components (σ1 reduced to close to zero/σ6 multiplied by 100%). The hybrid ranked X2 and X6 as the most contributing variables to the process poor performance and X1 and X4 as the major contributors to process yield. There is a great challenge in carrying out process capability analysis and fault diagnostics on a high dimensional multivariate non-normal process, with multiple correlated quality characteristics, in a timely manner. The author has developed a multivariate non-normal fault diagnostic hybrid capable of assessing performance and perform fault diagnostics on multivariate non-normal processes. The proposed hybrid first utilizes the Geometric Distance (GD) approach, to reduce dimensionality of the correlated data into fewer number of independent GD variables which can be assessed using univariate process capability indices. This is followed by fitting Burr XII distribution to independent GD variables. The independent fitted distributions are used to estimate both yield and multivariate process capability in a time efficient way. Finally, machine learning approach, is deployed to carry out the task of fault diagnostic by identifying and ranking the correlated quality characteristics responsible for the poor performance of the least performing GD variable. The results show that the proposed hybrid is robust in estimating both yield and multivariate process capability, carrying out fault diagnostics beyond GD variables, and identifying the original characteristic responsible for poor performance. The novelty of the proposed non-normal fault diagnostic hybrid is that it considers quality characteristics related to the least performing GD variable, instead of investigating all the quality characteristics of the multivariate non-normal process. The efficacy of the proposed hybrid is assessed through a real manufacturing examples and simulated scenarios. Variables X1,, X2 and X3 shifted away from the target by 25%, 15% and 35%, respectively, and the hybrid was able to select variables X3 to be contributing the most to the corresponding geometric distance variable's poor performance

Monitoring and performance analysis of regression profiles

There are many cases in industrial and non-industrial sections where the quality characteristics are in the form of profiles. Profile monitoring is a relatively new set of techniques in statistical quality control that is used in situations where the state of product or process is presented by regression models. In the past few years, most research in the field of profile monitoring has mainly focused on the use of effective statistical charting methods, study of more general shapes of profiles, and the effects of violations of assumptions in profile monitoring. Despite several research on the application of artificial neural networks to statistical quality control, no research has investigated the application of neural networks in monitoring profiles. Likewise, there is no research in the literature on the process capability analysis in profile processes. The process capability analysis is to evaluate the ability of a process to meet the customer/engineering specifications and must be done in Phase I of profile monitoring. In a review study on profile monitoring, Woodall (2007) pointed out the importance of process capability analysis in profiles. In this research, we use artificial neural networks (ANN) to detect and classify shifts in linear profiles. Three monitoring methods based on ANN are developed to monitor linear profiles in Phase II. We compare the results for different shift scenarios with existing methods in linear profile monitoring and discuss the results. Furthermore, in this thesis, we evaluate the estimation of process capability indices (PCIs) in linear profiles. We propose a method based on the relationship between proportions of non-conformance and the process capability indices in the profile process. In most existing profile monitoring methods in the literature, it is assumed that the profile design points are deterministic (fixed) so they are unchanged from one profile to another one. In this research, we investigate the estimation of the PCI in normal linear profiles for different scenarios of deterministic and arbitrary (random) data acquisition schemes as well as fixed or linear functional specification limits. We apply the proposed method in estimating the PCI in a yogurt production process. This thesis also focuses on the investigation of the process capability analysis in profiles with non-normal error terms. In this study, we review the methods for estimating PCI in non-normal data and carry out a comprehensive comparison study to evaluate the performance of these methods. Then these methods are applied in the leukocyte filtering process to evaluate the PCI with effect of non-normality in a blood service section. In addition, we develop a new method based on neural networks to estimate the parameters of the Burr XII distribution, which is required in some of the PCI estimation methods with non-normal environments. Finally, in this research we propose five methods to estimate process capability index in profiles where residuals follow non-normal distributions. In a comparison study using Monte Carlo simulations we evaluate the performance of the proposed methods in terms of their precision and accuracy. We provide conclusions and recommendation for the future research at the end

Control Chart of T² Hotelling on Quality Control Activities of Crude Palm Oil (CPO) at PT Cipta Graha Garwita, Seluma Regency, Bengkulu Province

PT Cipta Graha Garwita (CGG) is a palm oil producer focused on product quality, especially crude palm oil (CPO) for both food and non-food applications. Despite CGG's good reputation, variability in quality characteristics such as Free Fatty Acid (FFA) and moisture can affect the final quality of CPO. This study aims to apply a statistical quality control system to monitor and improve the consistency of CPO quality using T² Hotelling control charts. Statistical quality control methods ensure that products meet standards by reducing variability. One such tool is the T² Hotelling control chart, effective for monitoring multivariate variables using mean vectors and variance-covariance matrices. This study involves steps from data collection, testing multivariate normality assumptions, calculating T² Hotelling control charts, to determining control limits. Testing for multivariate normality assumptions showed the data met normal distribution criteria. The first and second stage T² Hotelling control charts identified several out-of-control observations. These out-of-control observations were excluded, and further analysis showed that after their removal, all data were within statistical control limits. This study recommends further analysis to determine the causes of out-of-control observations using Ishikawa diagrams and process capability evaluation to ensure consistent product quality

Possibilities of using graphical and numerical tools in the exposition of process capability assessment techniques

Purpose: The paper focuses on how the problem of process capability assessment can be handled when taught, using convenient numerical and graphical means. The contents of the paper results from the authors' own academic and practical experience, which suggested that many important steps are overlooked in the process of selecting and using capability indices. Methodology/Approach: Selected problems in capability assessment are illustrated with suitable examples and graphs. Findings: The authors' experience is reflected in the paper, aiming to emphasize what matters and how, and what does not. Also, a new capability index is introduced. Research Limitation/implication: The style in which the problems are analysed may serve as a guide for further studies in the field and capability index applications. Originality/Value of paper: The paper also contains, aside from specific examples, some more advanced techniques, and is therefore accompanied by software readouts, since computer support is required in such cases. Category: Conceptual paperWeb of Science232331

A New SVDD-Based Multivariate Non-parametric Process Capability Index

Process capability index (PCI) is a commonly used statistic to measure ability of a process to operate within the given specifications or to produce products which meet the required quality specifications. PCI can be univariate or multivariate depending upon the number of process specifications or quality characteristics of interest. Most PCIs make distributional assumptions which are often unrealistic in practice. This paper proposes a new multivariate non-parametric process capability index. This index can be used when distribution of the process or quality parameters is either unknown or does not follow commonly used distributions such as multivariate normal

Acceptance sampling plan for multiple manufacturing lines using EWMA process capability index

The problem of developing a product acceptance determination procedure for multiple characteristics has attracted the quality assurance practitioners. Due to sufficient demands of consumers, it may not be possible to deliver the quantity ordered on time using the process based on one manufacturing line. So, in factories, product is manufactured using multiple manufacturing lines and combine it. In this manuscript, we present the designing of an acceptance sampling plan for products from multiple independent manufacturing lines using exponentially weighted moving average (EWMA) statistic of the process capability index. The plan parameters such as the sample size and the acceptance number will be determined by satisfying both the producer's and the consumer's risks. The efficiency of the proposed plan will be discussed over the existing sampling plan. The tables are given for industrial use and explained with the help of industrial examples. We conclude that the use of the proposed plan in these industries minimizes the cost and time of inspection. Smaller the sample size means low inspection cost. The proposed plan for some non-normal distributions can be extended as a future research. The determination of sampling plan using cost model is also interested area for the future research. ? 2017 The Japan Society of Mechanical Engineers.11Ysciescopu