A Multivariate Homogeneously Weighted Moving Average Control Chart

This paper presents a multivariate homogeneously weighted moving average (MHWMA) control chart for monitoring a process mean vector. The MHWMA control chart statistic gives a specific weight to the current observation, and the remaining weight is evenly distributed among the previous observations. We present the design procedure and compare the average run length (ARL) performance of the proposed chart with multivariate Chi-square, multivariate EWMA, and multivariate cumulative sum control charts. The ARL comparison indicates superior performance of the MHWMA chart over its competitors, particularly for the detection of small shifts in the process mean vector. Examples are also provided to show the application of the proposed chart. - 2013 IEEE.Scopu

An Expected Average Run Length (EARL) Performance Comparison of the SSGR and EWMA Control Charts

The acceleration use of control charts in industrial processes has led to the effectiveness in their evaluation by quality practitioners. This is crucial, as it influences their decisions on the choice of which control charts to employ. This study aims to explore and compare the performance of the side sensitive group runs (SSGR) and exponentially weighted moving average (EWMA) control charts. In general, the average run length (ARL) characteristics were used to evaluate the performance of these control charts. The ARL, which considers the exact shift size in the process, is restricted in the case when the practitioner cannot identify the process shift size (unknown shift size). In this situation, the expected average run length (EARL) is an alternative performance criterion. Upon comparison of the findings obtained, the EWMA chart has superior performance when (δmin, δmax) = (0.1, 0.4). In contrast, the SSGR chart overtakes the EWMA chart when (δmin, δmax) = (0.5, 0.8) and (δmin, δmax) = (0.9, 1.2), except when the sample size n = 3 for (δmin, δmax) = (0.5, 0.8). For this particular combination, the EWMA chart performs slightly better than the SSGR chart. The outcome of this study is expected to contribute to practitioners in identifying suitable control charts in process monitoring and implementation

On Phase-I monitoring of process location parameter with auxiliary information-based median control charts

A control chart is often used to monitor the industrial or services processes to improve the quality of the products. Mostly, the monitoring of location parameters, both in Phase I and Phase II, is done using a mean control chart with the assumption that the process is free from outliers or the estimators are correctly estimated from in-control samples. Generally, there are question marks about such kind of narratives. The performance of the mean chart is highly affected in the presence of outliers. Therefore, the median chart is an attractive alternative to the mean chart in this situation. The control charts are usually implemented in two phases: Phase I (retrospective) and Phase II (prospective/monitoring). The efficiency of any control chart in Phase II depends on the accuracy of control limits obtained from Phase I. The current study focuses on the Phase I analysis of location parameters using median control charts. We examined the performance of different auxiliary information-based median control charts and compared the results with the usual median chart. Standardized variance and relative efficacy are used as performance measures to evaluate the efficiency of median estimators. Moreover, the probability to signal measure is used to evaluate the performance of proposed control charts to detect any potential changes in the process. The results revealed that the proposed auxiliary information based median control charts perform better in Phase I analysis. In addition, a practical illustration of an industrial scenario demonstrated the significance of the proposed control charts, in which the monitoring of concrete compressive strength is emphasized.This research fund was supported by the National Science Foundation of China (No. 71774070).Scopu

An Expected Average Run Length (EARL) Performance Comparison of the SSGR and EWMA Control Charts

The acceleration use of control charts in industrial processes has led to the effectiveness in their evaluation by quality practitioners. This is crucial, as it influences their decisions on the choice of which control charts to employ. This study aims to explore and compare the performance of the side sensitive group runs (SSGR) and exponentially weighted moving average (EWMA) control charts. In general, the average run length (ARL) characteristics were used to evaluate the performance of these control charts. The ARL, which considers the exact shift size in the process, is restricted in the case when the practitioner cannot identify the process shift size (unknown shift size). In this situation, the expected average run length (EARL) is an alternative performance criterion. Upon comparison of the findings obtained, the EWMA chart has superior performance when (δmin, δmax) = (0.1, 0.4). In contrast, the SSGR chart overtakes the EWMA chart when (δmin, δmax) = (0.5, 0.8) and (δmin, δmax) = (0.9, 1.2), except when the sample size n = 3 for (δmin, δmax) = (0.5, 0.8). For this particular combination, the EWMA chart performs slightly better than the SSGR chart. The outcome of this study is expected to contribute to practitioners in identifying suitable control charts in process monitoring and implementation

Unit Interval Time and Magnitude Monitoring Using Beta and Unit Gamma Distributions

Quick detection of an assignable cause is necessary for process accuracy with respect to the specifications. The aim of this study is to monitor the time and magnitude processes based on unit-interval data. To this end, maximum exponentially weighted moving average (Max-EWMA) control chart for simultaneous monitoring time and magnitude of an event is proposed. To be precise, beta and unit gamma distributions are considered to develop the Max-EWMA chart. The chart’s performance is accessed using average run length (ARL), the standard deviation of run length (SDRL), and different quantiles of the run length distribution through extensive Monte Carlo simulations. Besides a comprehensive simulation study, the proposed charting methodology is applied to a real data set. The results show that the proposed chart is more efficient in detecting small to medium-sized shifts. The results also indicate that simultaneous shifts are detected more quickly as compared to the pure shift

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

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

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)

Double Sampling Auxiliary Information Chart And Exponentially Weighted Moving Average Auxiliary Information Chart, Both Based On Variable Sampling Interval, And Measurement Errors Based Triple Sampling Chart

The concept of using auxiliary information (AI) in control charts is growing in popularity among researchers. Control charts using the AI technique have been found to be more effective than control charts without the AI technique. The first objective of this thesis is to develop a variable sampling interval (VSI) double sampling (DS) chart using the AI technique (called VSI DS-AI chart) for monitoring the process mean. The charting statistics, optimal designs and implementation of the VSI DS-AI chart are discussed. The steady-state average time to signal (ssATS) and steady-state expected average time to signal (ssEATS) criteria are used as the performance measures of the proposed VSI DS-AI chart. The ssATS and ssEATS results of the VSI DS-AI chart are compared with those of the double sampling AI, variable sample size and sampling interval AI, exponentially weighted moving average AI (EWMA-AI) and run sum AI (RS-AI) charts. The comparison reveals that the VSI DS-AI chart performs better than the competing charts for all shift sizes, except the EWMA-AI and RS-AI charts for small shifts