Development Of Two New Auxiliary Information Control Charts, And Economic And Economic-Statistical Designs Of Several Auxiliary Information Control Charts

The use of auxiliary information (AI) concept in control charts is receiving increasing attention among researchers. Control charts with auxiliary characteristics have been shown to be more efficient than control charts without such characteristics. The salient feature of the AI concept has motivated us to develop two new AI charts. The first objective of this thesis is to develop the run sum X - AI (RS X - AI) chart for monitoring the process mean. Optimal parameters computed using the optimization algorithms developed and the step-by-step approach for constructing the optimal RS - AI chart are provided in this thesis. The average run length (ARL) and expected average run length (EARL) performance criteria are used to evaluate the performance of the RS X - AI chart. Results show that the RS X - AI chart generally surpasses the existing X - AI, synthetic X - AI and EWMA X - AI charts in the detection of outof- control signals. The second objective of this thesis is to develop the variable sampling interval exponentially weighted moving average t AI (VSI EWMA t - AI) chart for monitoring the process mean when errors in estimating the process standard deviation exist. The VSI EWMA t - AI chart allows either the short or long sampling interval to be adopted, based on information from the process quality given by the current plotting statistic of the chart

A Nonparametric HEWMA-p Control Chart for Variance in Monitoring Processes

Control charts are considered as powerful tools in detecting any shift in a process. Usually, the Shewhart control chart is used when data follows the symmetrical property of a normal distribution. In practice, the data from the industry may follow a non-symmetrical distribution or an unknown distribution. The average run length (ARL) is a significant measure to assess the performance of the control chart. The ARL may mislead when the statistic is computed from an asymmetric distribution. To handle this issue, in this paper, an ARL-unbiased hybrid exponentially weighted moving average proportion (HEWMA-p) chart is proposed for monitoring the process variance for a non-normal distribution or an unknown distribution. The efficiency of the proposed chart is compared with the existing chart in terms of ARLs. The proposed chart is more efficient than the existing chart in terms of ARLs. A real example is given for the illustration of the proposed chart in the industry.11Ysciescopu

Efficient Auxiliary Information Based Exponentially Weighted Moving Coefficient of Variation Control Chart using Hybrid Estimator : An Application to Monitor NPK Fertilizer

In this era, manufacturing sectors should ensure the quality of their production process and products. They must reduce the variability that occurs in their operation. Coefficient variation control charts have become important statistical Process Control (SPC) tools for monitoring processes when the process mean linear function with the standard deviation. In recent years, auxiliary information-based-CV control charts using memory type structure have been investigated to enhance the sensitivity of control charts. Auxiliary information is selected when the variable remains stable during the monitoring period. Nevertheless, the AIB statistic is constructed based on lognormal transformation, and no research investigated the memory type CV chart using estimator of AIB-CV from the combination of ratio and regression form called hybrid form. This research proposes a hybrid auxiliary information-based exponentially weighted moving coefficient of variation (Hybrid AIB-EWMCV) control chart for detecting small to moderate shifts in the CV process. The Average Run Length (ARL) simulation shows that increasing the level of correlation and sample sizes enhances the detection ability of the control chart. Also, the proposed chart performs well than existing chart. A real dataset from fertilizer manufacturing is implemented to explain the condition of the process by using a Hybrid AIB-EWMCV control chart

New Variable Parameters Chart Based On Auxiliary Information And Multivariate Charts For Short Production Runs

Contemporarily, enterprises strive to continuously enhance quality which is a basis of customer satisfaction. Numerous advancements to the control charting scheme have been made to enhance process monitoring. In this thesis, the variable parameters chart with auxiliary information (abbreviated as VP-AI) is proposed. The VP-AI chart is designed with a regression estimator that has an improved precision due to the use of auxiliary variable to estimate the population mean. By adopting the Markov chain method, the average time to signal (ATS) and expected ATS (EATS) formulae are derived for known and unknown shift sizes. The findings show that the VP-AI chart prevails over the basic VP chart and justifies the integration of auxiliary information to improve the sensitivity of the VP chart. A comparison of the VP-AI chart with its competing charts shows that, for all shifts, the performance of the VP-AI chart surpasses the Shewhart AI (SH-AI), synthetic AI (SYN-AI) and variable sample size and sampling interval AI (VSSI-AI) charts considerably. Additionally, for most shifts, the VP-AI chart has a superior performance in comparison with the exponentially weighted moving average AI (EWMA-AI) and run sum AI (RS-AI) charts. The application of the VP-AI chart is shown using an illustrative example based on a real dataset. In many situations, the process is multivariate in nature, where more than one quality characteristic has to be monitored simultaneously. Furthermore, many companies have adopted the short production runs technique to be more flexible and specialized. Hence, in this thesis, the fixed sample size (FSS) 2 T short-run chart is develope

New Variable Parameters Chart Based On Auxiliary Information And Multivariate Charts For Short Production Runs

Contemporarily, enterprises strive to continuously enhance quality which is a basis of customer satisfaction. Numerous advancements to the control charting scheme have been made to enhance process monitoring. In this thesis, the variable parameters chart with auxiliary information (abbreviated as VP-AI) is proposed. The VP-AI chart is designed with a regression estimator that has an improved precision due to the use of auxiliary variable to estimate the population mean. By adopting the Markov chain method, the average time to signal (ATS) and expected ATS (EATS) formulae are derived for known and unknown shift sizes. The findings show that the VP-AI chart prevails over the basic VP chart and justifies the integration of auxiliary information to improve the sensitivity of the VP chart. A comparison of the VP-AI chart with its competing charts shows that, for all shifts, the performance of the VP-AI chart surpasses the Shewhart AI (SH-AI), synthetic AI (SYN-AI) and variable sample size and sampling interval AI (VSSI-AI) charts considerably. Additionally, for most shifts, the VP-AI chart has a superior performance in comparison with the exponentially weighted moving average AI (EWMA-AI) and run sum AI (RS-AI) charts. The application of the VP-AI chart is shown using an illustrative example based on a real dataset. In many situations, the process is multivariate in nature, where more than one quality characteristic has to be monitored simultaneously. Furthermore, many companies have adopted the short production runs technique to be more flexible and specialized

Design of side-sensitive double sampling control schemes for monitoring the location parameter

Double sampling procedure is adapted from a statistical branch called acceptance sampling. The first Shewhart-type double sampling monitoring scheme was introduced in the statistical process monitoring (SPM) field in 1974. The double sampling monitoring scheme has been proven to effectively decrease the sampling effort and, at the same time, to decrease the time to detect potential out-of-control situations when monitoring the location, variability, joint location and variability using univariate or multivariate techniques. Consequently, an overview is conducted to give a full account of all 76 publications on double sampling monitoring schemes that exist in the SPM literature. Moreover, in the review conducted here, these are categorized and summarized so that any research gaps in the SPM literature can easily be identified. Next, based on the knowledge gained from the literature review about the existing designs for monitoring the process mean, a new type of double sampling design is proposed. The new charting region design lead to a class of a control charts called a side-sensitive double sampling (SSDS) monitoring schemes. In this study, the SSDS scheme is implemented to monitor the process mean when the underlying process parameters are known as well as when they are unknown. A variety of run-length properties (i.e., the 5th, 25th, 50th, 75th, 95th percentiles, the average run-length (), standard deviation of the run-length (), the average sample size () and the average extra quadratic loss () metrics) are used to design and implement the new SSDS scheme. Comparisons with other established monitoring schemes (when parameters are known and unknown) indicate that the proposed SSDS scheme has a better overall performance. Illustrative examples are also given to facilitate the real-life implementation of the proposed SSDS schemes. Finally, a list of possible future research ideas is given with hope that this will stimulate more future research on simple as well as complex double sampling schemes (especially using the newly proposed SSDS design) for monitoring a variety of quality characteristics in the future.StatisticsM. Sc. (Statistics

Some theoretical comments regarding the run-length properties of the synthetic and runs-rules monitoring schemes – Part 1: zero-state

Please read abstract in the article.The SARChI Chair at the University of Pretoria, the National Research Foundation (NRF) and Department of Science and Technology’s Innovation Doctoral scholarship, and the Department of Statistics’ STATOMET.hj2020Science, Mathematics and Technology EducationStatistic

New Variable Sampling Interval Run Sum Standard Deviation And Run Sum Multivariate Coefficient Of Variation Charts

In Statistical Process Control (SPC), the control charting technique is an effective method to solve quality issues in manufacturing and service industries. The R and S charts are commonly used to monitor the process variance in industries due to the charts’ simplicity and high sensitivity toward large shifts. However, these charts are not sensitive toward small and moderate shifts in the process variance. On the other hand, the more sophisticated charts, such as the exponentially weighted moving average (EWMA) S chart and the cumulative sum (CUSUM) S chart are very effective in detecting small changes in the process variance. However, most quality practitioners do not adopt these charts in real applications due to their design complexity. In view of this setback, the variable sampling interval (VSI) approach is incorporated into the run sum (RS) S chart, in order to suggest an effective, yet a simple chart, for detecting small, moderate and large shifts in the process variance. Apart from that, the coefficient of variation (CV) is an important quality characteristic to take into account when the process mean and standard deviation are not constant, even though the process is in-control

Contributions to improve the power, efficiency and scope of control-chart methods : a thesis submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Statistics at Massey University, Albany, New Zealand

Listed in 2019 Dean's List of Exceptional ThesesDetection of outliers and other anomalies in multivariate datasets is a particularly difficult problem which spans across a range of systems, such as quality control in factories, microarrays or proteomic analyses, identification of features in image analysis, identifying unauthorized access in network traffic patterns, and detection of changes in ecosystems. Multivariate control charts (MCC) are popular and sophisticated statistical process control (SPC) methods for monitoring characteristics of interest and detecting changes in a multivariate process. These methods are divided into memory-less and memory-type charts which are used to monitor large and small-to-moderate shifts in the process, respectively. For example, the multivariate χ2 is a memory-less control chart that uses only the most current process information and disregards any previous observations; it is typically used where any shifts in the process mean are expected to be relatively large. To increase the sensitivity of the multivariate process control tool for the detection of small-to-moderate shifts in the process mean vector, different multivariate memory-type tools that use information from both the current and previous process observations have been proposed. These tools have proven very useful for multivariate independent normal or "nearly" normal distributed processes. Like most univariate control-chart methods, when the process parameters (i.e., the process mean vector or covariance parameters, or both) are unknown, then MCC methods are based on estimated parameters, and their implementation occurs in two phases. In Phase I (retrospective phase), a historical reference sample is studied to establish the characteristics of the in-control state and evaluate the stability of the process. Once the in-control reference sample has been deemed to be stable, the process parameters are estimated from Phase I, and control chart limits are obtained for use in Phase II. The Phase II aspect initiates ongoing regular monitoring of the process. If successive observed values obtained at the beginning of Phase II fall within specified desired in-control limits, the process is considered to be in control. In contrast, any observed values during Phase II which fall outside the specified control limits indicate that the process may be out of control, and remedial responses are then required. Although conventional MCC are well developed from a statistical point of view, they can be difficult to apply in modern, data-rich contexts. This serious drawback comes from the fact that classical MCC plotting statistics requires the inversion of the covariance matrix, which is typically assumed to be known. In practice, the covariance matrix is seldom known and often empirically estimated, using a sample covariance matrix from historical data. While the empirical estimate of the covariance matrix may be an unbiased and consistent estimator for a low-dimensional data matrix with an adequate prior sample size, it performs inconsistently in high-dimensional settings. In particular, the empirical estimate of the covariance matrix can lead to in ated false-alarm rates and decreased sensitivity of the chart to detect changes in the process. Also, the statistical properties of traditional MCC tools are accurate only if the assumption of multivariate normality is satisfied. However, in many cases, the underlying system is not multivariate normal, and as a result, the traditional charts can be adversely affected. The necessity of this assumption generally restricts the application of traditional control charts to monitoring industrial processes. Most MCC applications also typically focus on monitoring either the process mean vector or the process variability, and they require that the process mean vector be stable, and that the process variability be independent of the process mean. However, in many real-life processes, the process variability is dependent on the mean, and the mean is not necessarily constant. In such cases, it is more appropriate to monitor the coefficient of variation (CV). The univariate CV is the ratio of the standard deviation to the mean of a random variable. As a relative dispersion measure to the mean, it is useful for comparing the variability of populations having very different process means. More recently, MCC methods have been adapted for monitoring the multivariate coefficient of variation (CV). However, to date, studies of multivariate CV control charts have focused on power - the detection of out-of-control parameters in Phase II, while no study has investigated their in-control performance in Phase I. The Phase I data set can contain unusual observations, which are problematic as they can in uence the parameter estimates, resulting in Phase II control charts with reduced power. Relevant Phase I analysis will guide practitioners with the choice of appropriate multivariate CV estimation procedures when the Phase I data contain contaminated samples. In this thesis, we investigated the performance of the most widely adopted memory-type MCC methods: the multivariate cumulative sum (MCUSUM) and the multivariate exponentially weighted moving average (MEWMA) charts, for monitoring shifts in a process mean vector when the process parameters are unknown and estimated from Phase I (chapters 2 and 3). We demonstrate that using a shrinkage estimate of the covariance matrix improves the run-length performance of these methods, particularly when only a small Phase I sample size is available. In chapter 4, we investigate the Phase I performance of a variety of multivariate CV charts, considering both diffuse symmetric and localized CV disturbance scenarios, and using probability to signal (PTS) as a performance measure. We present a new memory-type control chart for monitoring the mean vector of a multivariate normally distributed process, namely, the multivariate homogeneously weighted moving average (MHWMA) control chart (chapter 5). We present the design procedure and compare the run length performance of the proposed MHWMA chart for the detection of small shifts in the process mean vector with a variety of other existing MCC methods. We also present a dissimilarity-based distribution-free control chart for monitoring changes in the centroid of a multivariate ecological community (chapter 6). The proposed chart may be used, for example, to discover when an impact may have occurred in a monitored ecosystem, and is based on a change-point method that does not require prior knowledge of the ecosystem's behaviour before the monitoring begins. A novel permutation procedure is employed to obtain the control-chart limits of the proposed charting test-statistic to obtain a suitable distance-based model of the target ecological community through time. Finally, we propose enhancements to some classical univariate control chart tools for monitoring small shifts in the process mean, for those scenarios where the process variable is observed along with a correlated auxiliary variable (chapters 7 through 9). We provide the design structure of the charts and examine their performance in terms of their run length properties. We compare the run length performance of the proposed charts with several existing charts for detecting a small shift in the process mean. We offer suggestions on the applications of the proposed charts (in chapters 7 and 8), for cases where the exact measurement of the process variable of interest or the auxiliary variable is diffcult or expensive to obtain, but where the rank ordering of its units can be obtained at a negligible cost. Thus, this thesis, in general, will aid practitioners in applying a wider variety of enhanced and novel control chart tools for more powerful and effcient monitoring of multivariate process. In particular, we develop and test alternative methods for estimating covariance matrices of some useful control-charts' tools (chapters 2 and 3), give recommendations on the choice of an appropriate multivariate CV chart in Phase I (chapter 4), present an efficient method for monitoring small shifts in the process mean vector (chapter 5), expand MCC analyses to cope with non-normally distributed datasets (chapter 6) and contribute to methods that allow efficient use of an auxiliary variable that is observed and correlated with the process variable of interest (chapters 7 through 9)