Effect of Measurement Error on the Multivariate CUSUM Control Chart for燙ompositional Data

The monitoring of processes is a vital mechanism for ensuring that such processes remain safe and under control. The present research aims to solve problems associated with correlated data by applying the Box-Jenkins method integrated with statistical process control (SPC) tools, namely the Shewhart chart, the moving average chart, the cumulative sum (CUSUM) chart, and the exponentially weighted moving-average (EWMA) chart. The efficiency of the four SPC tools was also compared in terms of the false alarm rate (FAR) and the missed detection rate (MDR). The findings indicated that the EWMA chart was the most effective in detecting anomaly, the Shewhart chart and the moving average chart produced high MDR, and the CUSUM chart suffered the highest FAR.

Statistical process control (SPC) is the method that monitors process quality characteristics. Through control charts, one can detect whether the present process malfunction. However, some annoyances may arise while the engineers need to choose appropriately control chart under different levels of process variation. The Shewhart, cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts have been widely used for monitoring semiconductor manufacturing processes. Generally weighted moving average (GWMA) control chart is a new method of SPC, which was proposed by Sheu and Lin (2003). The main objective of this research is using step-by-step procedures to present a comparative study of the monitoring performance for Shewhart, CUSUM, EWMA and GWMA control charts. According to a specified in-control average run length (ARL), we determine the parameters of each control chart based on the Monte Carlo numerical simulation. The setting parameters in each control chart sre displayed and tabulated. While the process means or the process standard deviations are changing in different levels, the performance of each weighted control chart can be then compared by using the ARL. A rule of thumb for selecting better control schemes is provided as a truthfully reference to help engineers in choosing the more appropriate control charts immediately when the assignable causes occurred.

Part 1 Statistical process control: development of SPC what SPC is and is not online SPC methods off-line process control SPC methodolgy other factors affecting the success of SPC. Part 2 Some basic distributions: attribute data countable data geometric distribution the Normal distribution distributions derived from the Normal distribution application of results testing for normality the Normal approximation to the binomial distribution Normal approximation to the Poisson distribution. Part 3 Process variation: reasons for process variation types of process variation some models for process variation sampling error and measurement error. Part 5 Basic Shewhart control charts for continuous variables: control charts for average level charts for control of (within group) process spread the average run length (ARL) special problems some theoretical results for Shewhart charts charts for control of process spread. Part 6 Extensions to Shewhart charts for one-at-a-time data: one-at-a-time sampling estimation of sigma for one-at-a-time data details of further control charts for control of process average level control of process spread choice of charting method practical use of Shewhart and moving average charts properties of EWMA and MA charts. Part 7 Cumulative sum techniques for continuous variables: CuSum charts - for control of average level, for control of process spread nomogram for CuSums. Part 8 Further theoretical results on control charts for continuous variables: the effect of departures from assumption on moments of x and s(2) Shewhart charts - Markov chain approach cumulative Sum charts charts for control of process spread. Part 9 The design of control charts for specification limits: single specification limits - chart for means double specification limits - high capability processes, an alternative approach. Part 10 Control of discrete data processes: Shewhart charts - for countable data (c and u), for attribute data (np and p) CuSum charts for countable data, for attribute data comparison of Shewhart and CuSum schemes. Part 11 Sampling inspection: classification of inspection plans some properties of sampling plans methods of using sampling plans for attributes. Part 12 Inspection by variables: single specification limit - sigma known, sigma unknown estimation of fraction non-conforming, single specification limit double specification limit - sigma known, sigma unknown multivariate sampling plans. Part 13 Standard sampling systems: statement of method for inspection by attributes inspection by variables International Standards for process and quality control. Part 14 Adaptive sampling plans: CSP-1 and the AOQL criterion theory of CSP-1 the AEDL criterion. (Part contents).

Statistical process control is extensively applied for monitoring the production process. One of the important tools of statistical process control for detecting the unusual changes in the manufacturing process is the control chart. In the use of a control chart, samples or subgroups are selected in a manner that if unusual changes are present, the chance for differences between subgroups will be maximized, while the chance for differences within a subgroup will be minimized. However, there are different practical engineering processes where this assumption would not be applicable. In this paper, we considered a Wind Energy process where differences within a subgroup are significant and proposed a new control chart namely Ladder Ascending Control Chart under this situation. The Ladder Ascending Control Chart is based on order statistics by using order statistic distribution as the underlying distribution. Shewhart type control limits formulae for the order statistic mean have been built. It is applied to wind energy for monitoring the wind speed using the Weibull distribution as the underlying distribution of wind speed. The average run length is provided as a performance measure for the Ladder Ascending Control Chart. A real-life example is provided for its application and interpretation.

Quality control of products and services is essential across various industries and sectors, including manufacturing, engineering, public health, economics, finance, and medicine. It is critical to ensure that product characteristics align with customer requirements while maintaining consistent quality and standards. Control charts are essential tools in Statistical Process Control (SPC), used to detect changes in process means or variability, and play a critical role in monitoring, controlling, and enhancing quality within production processes. This study evaluates the Average Run Length (ARL) of the Double Homogeneously Weighted Moving Average (DHWMA) control chart for Moving Average processes (MA(q)) with exponential white noise, using Numerical Integral Equation (NIE) methods. These methods include Simpson’s Rule, the Midpoint Rule, the Trapezoidal Rule, and the Gauss–Legendre Quadrature. Additionally, the study compares the performance of the DHWMA and HWMA control charts. The results indicate that all four NIE methods yield similar ARL values. However, CPU time analysis shows that the Midpoint Rule generally requires less computation time than the other methods. Furthermore, when evaluating change-point detection effectiveness, the DHWMA control chart consistently outperforms the HWMA chart across all shift sizes, as demonstrated by its lower Expected Average Run Length (EARL).

Three statistical control chart methods were investigated to determine the one with the highest detection probability and the best average run length (ARL). The three control charts include the Shewhart control chart of count data, cumulative sum (CUSUM) analysis of count data (Poisson CUSUM), and CUSUM analysis of time-interval (time difference between two consecutive radiation pulses) data (time-interval CUSUM). The time-interval CUSUM (CUSUMti) control chart was compared with the Poisson CUSUM (CUSUMcnt) and the Shewhart control charts with experimental and simulated data. The experimental data were acquired with a DGF-4C (XIA, Inc.) system in list mode. Simulated data were obtained by using Monte Carlo techniques to obtain a random sampling of a Poisson process. All statistical algorithms were developed using R (R Development Core Team). Detection probabilities and ARLs for the three methods were compared. The time-interval CUSUM control chart resulted in a similar detection probability as that of the Poisson CUSUM control chart but had the shortest ARL at relatively higher radiation levels; e.g., about 40% shorter than the Poisson CUSUM at 10.0 counts per second (cps) (five times above the background count rate). Both CUSUM control charts resulted in a higher detection probability than that of the Shewhart control chart; e.g., 100% greater than the Shewhart control method at 4.0 cps (two times above the background count rate). In addition, when time-interval information was used, the CUSUM control chart coupled with a modified runs rule (mrCUSUMti) showed the ability to further reduce the time needed to respond to changes in radiation levels and keep the false positive rate at a required level.

A statistical weld process monitoring system is described. Using data collected while welding, the welding statistical process control (SPC) tool provides weld process quality control by implementing techniques of data trending analysis, tolerance analysis, and sequential analysis. The SPC system computes the mean, standard deviation, and range of each of the parameters sampled by the data collection system. Changes in the mean, standard deviation, and range are displayed using control (or trend) charts. The control chart displays a function of a parameter with respect to the ordering of the weld records (for a single weld) or weld number (for multiple welds). The SPC tool also permits plotting tolerance charts of the mean, standard deviation, and range for each of the sampled parameters. The tolerance chart is plotted versus the record number (or weld number) and consists of a vertical line for each record (or weld number) showing the minimum and maximum value of that parameter for that record (or weld number). The upper control limit (UCL), lower control limit (LCL), and nominal value may also be displayed on the tolerance chart printout. The SPC also performs sequential analysis, which allows the user to examine the process as it goes along, which in turn may permit the user to locate a possible change in the process before it goes out of control. Work directed toward developing an expert interpreter of the voluminous statistical output generated by the SPC is also described.

The implementation of Statistical Quality Control (SQC) has been tracked in various areas, such as agriculture, environment, industry, and health services. The employment of SQC methodologies is frequently employed for monitoring and identification of process irregularities across various fields. This research proposes and implements a novel SQC methodology in agricultural areas. A control chart is one of the SQC tools that facilitates real-time monitoring of multiple activities, including agricultural yield, industrial yield, and hospital outcomes. Advanced control charts with symmetrical data are being subjected to the new SQC method, which is suitable for this purpose. This research aims to develop a novel hybrid exponentially weighted moving average control chart for detecting the coefficient of variation (CV) using a repetitive sampling method called the HEWMARS-CV control chart. It is an effective tool for monitoring the mean and variance of a process simultaneously. The HEWMARS-CV control chart used the repetitive sampling scheme to generate two pairs of control limits to enhance the performance of the control chart. The proposed control chart is compared with the classical HEWMA and Shewhart control charts regarding the average run length (ARL) when the data has a normal distribution. The Monte Carlo simulation method is utilized to approximate the ARL values of the proposed control charts to determine their performance. The proposed control chart detects small shifts in CV values more effectively than the existing control chart. An illustrative application related to monitor the wheat yield at Rothamsted Experimental Station in Great Britain is also incorporated to demonstrate the efficiency of the proposed control chart. The efficiency of the proposed HEWMARS-CV control chart on the real data shows that the proposed control chart can detect a shift in the CV of the process, and it is superior to the existing control chart in terms of the average run length.

Abstract: Multivariate control charts are essential tools in multivariate statistical process control (MSPC). “Shewhart-type” charts are control charts using rational subgroupings which are effective in the detection of large shifts. Recently, the one-class classification problem has attracted a lot of interest. Three methods are typically used to solve this type of classification problem. These methods include the k−center method, the nearest neighbor method, one-class support vector machine (OCSVM), and the support vector data description (SVDD). In industrial applications, like statistical process control (SPC), practitioners successfully used SVDD to detect anomalies or outliers in the process. In this paper, we reformulate the standard support vector data description and derive a least squares version of the method. This least-squares support vector data description (LS-SVDD) is used to design a control chart for monitoring the mean vector of processes. We compare the performance of the LS-SVDD chart with the SVDD and T2 chart using out-of-control Average Run Length (ARL) as the performance metric. The experimental results indicate that the proposed control chart has very good performance.

Monitoring the quality of new or ongoing surgical activities is a necessity. Several Statistical Process Control (SPC) tools are available to professionals. Among them, Shewhart charts and cumulative sum charts (CUSUM charts) are useful methods to provide visual feedback before significant quality issues arise. In this paper, we discuss both methods based on our current approach. On Shewhart charts, one variable value is plotted on a time-series line. This method provides information about every single determination. Random variations of the values appear and by adjusting the adequate control limits it is possible to know whether those variations are random or out-of-control. Although large variations are easily detected, small but relevant changes are not. On the contrary, CUSUM charts have the capability of detecting small changes quickly. CUSUM is defined as a statistical tool that graphically represents the sequential monitoring of cumulative performance of any dichotomized or continuous variable under assessment. It emphasizes failures penalizing them against the correct performance when individual risk is adjusted. This makes CUSUM especially sensitive to negative changes. CUSUM can be created without the need of a specific sample size and grow with every new case included. Besides the variable under control (with specific definitions of acceptable and unacceptable outcomes), the type I and II errors for the defined parameter and the individual risk of acceptable or unacceptable outcomes must be included in the chart. Graphical representation of these three parameters is easy and intuitive to read making CUSUM graphs a reliable tool to understand the trending of the parameter under control. If performance is considered inadequate: analysis, discussion and implementation of agreed measures should be taken. Despite its limitations, CUSUM analysis is considered the best tool for quality control in health care domain.

Nowadays, statistical process control (SPC) is extensively utilized in manufacturing companies. Control charts are the foremost tool in SPC because they can timely detect assignable causes that influence the quality of the production process. Mostly, the control charts are used to monitor the process variability and the process mean. However, when the mean changes but is appraised as in-control and the standard deviation is linear to the mean, the Coefficient of Variation (CV) chart is suitable for evaluating process variability. In this study, we suggest a Generally Weighted Moving Coefficient of Variation (GWMCV) control chart using three-parameter logarithmic transformations which parameter weight for each time (ω) is more flexible than the Exponentially Weighted Moving Coefficient of Variation (EWMCV) control chart that has ω = 1. The Simulation studies show that when parameter weight 0.6≤ω≤0.9,GWMCV chart is more sensitive than EWMCV chart. As a result, the flexible parameter weights increase the diagnosis ability of the control chart. The chart is also applied to monitor the process production of NPK fertilizer. The result shows that proposed chart detect out-of-control signal rapidly than the EWMCV.

A control chart is a tool for statistical process control (SPC) used to determine variations in manufacturing processes resulting from common or assignable causes. The presence of unnatural patterns in control charts is an indication that the process has been influenced by assignable causes, and corrective actions must be taken. However, the assumption of uncorrelated or independent observations is not suitable for all of the characteristics pertaining to a product. This study presents a method with which to improve the accuracy of pattern recognition in control charts, through the autocorrelation of product characteristics. Particularly, we developed an artificial algorithm-based machine learning model to recognize unnatural patterns and processes in AR(1) simultaneously. The proposed method integrates an artificial immune system and support vector machine within a recognition system. This study evaluated the accuracy with which four patterns could be recognized. The four patterns include trends, sudden shifts, cyclic patterns, and normal patterns. Identifying unnatural patterns can greatly narrow the range of possible causes that must be investigated, thereby speeding up the diagnostic processes. Key words: Pattern recognition, artificial immune algorithm, support vector machine, autocorrelation.

Control charts are designed to detect assignable causes of variation that may occur in production processes. When traditional control charts are used there is the implicit assumption that observations are independently and identically distributed over time. It is also assumed that the probability distribution representing the observations has a known functional form and is constant over time. However, in practice, observations generated by continuous as well as discrete production processes are often serially correlated. Autocorrelation not only violates the independence assumption of traditional control charts but also can affect the performance of control charts adversely. This point has received considerable attention in the past few decades. In this paper, we investigate the performance of the multivariate cumulative sum (MCUSUM) control chart in the presence of autocorrelation. Using an average run length (ARL) criterion, it is shown that autocorrelation can deteriorate the performance of MCUSUM control charts. A solution based on a time series model is presented that improves ARL properties of MCUSUM control charts. Copyright © 2005 John Wiley & Sons, Ltd.

Detection of changes in time-series of indicators using CUSUM control charts

Moving towards process-based radiotherapy quality assurance using statistical process control