Generally weighted moving coefficient of variation (GWMCV) control chart using three parametric log-normal transformations

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.

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.

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.

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

Control charts (CCs) are one of the main tools in Statistical Process Control that have been widely adopted in manufacturing sectors as an effective strategy for malfunction detection throughout the previous decades. Measurement errors (M.E's) are involved in the quality characteristic of interest, which can effect the CC's performance. The authors explored the impact of a linear model with additive covariate M.E on the multivariate cumulative sum (CUSUM) CC for a specific kind of data known as compositional data (CoDa). The average run length is used to assess the performance of the proposed chart. The results indicate that M.E's significantly affects the multivariate CUSUM-CoDa CCs. The authors have used the Markov chain method to study the impact of different involved parameters using six different cases for the variance-covariance matrix (VCM) (i.e., uncorrelated with equal variances, uncorrelated with unequal variances, positively correlated with equal variances, positively correlated with unequal variances, negatively correlated with equal variances and negatively correlated with unequal variances). The authors concluded that the error VCM has a negative impact on the performance of the multivariate CUSUM-CoDa CC, as the increases with an increase in the value of the error VCM. The subgroup size m and powering operator b positively impact the proposed CC, as the decreases with an increase in m or b. The number of variables p also has a negative impact on the performance of the proposed CC, as the values of increase with an increase in p. For the implementation of the proposal, two illustrated examples have been reported for multivariate CUSUM-CoDa CCs in the presence of M.E's. One deals with the manufacturing process of uncoated aspirin tablets, and the other is based on monitoring the machines involved in the muesli manufacturing process.

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.

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.

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).

Consider a mass production line for a single “part” and let us center our interest on a single “dimension” of the part. There will always be some variability in the dimension because of the sum of several variables whose causes are not usually understood and whose effects might not be controllable if they were. The dimension of the part is thus a random variable, but one whose mean and variance can change with time as something goes wrong with the “machinery” producing the part. If the process is stable and only the “usual” system of chance causes is operating (which implies that the mean θ and variance σ2 of the process are constant), we say that the process is in statistical control and that it has an inherent variability σ2. If the mean or variance wanders from those stable values, we say that an assignable cause is operating, meaning that it can be understood/controlled. The term quality control refers to control of quality by any means, but statistical quality control refers to the control of quality through the use of certain statistical tools to be described shortly. The best known of those tools is the Shewhart Control Chart, which is used to demonstrate statistical control and to detect the presence of assignable causes. There are control charts for the mean, range, standard deviation, fraction defective, and number of defects per unit. Three horizontal lines plus the data make up the control charts. The 3 lines are a centerline, an upper control limit, and a lower control limit. (One of the control limits may be omitted if there is no interest in it.) The centerline is an “average” of the statistic being plotted, and the control limits are at distances of 3 standard deviations (of the statistic) above and below the centerline.

A hybrid fuzzy-statistical clustering approach for estimating the time of changes in fixed and variable sampling control charts

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 the application of statistical methods to the measurement and analysis of variation process. Various regulatory authorities such as Validation Guidance for Industry (2011), International Conference on Harmonisation ICH Q10 (2009), the Health Canada guidelines (2009), Health Science Authority, Singapore: Guidance for Product Quality Review (2008), and International Organization for Standardization ISO-9000:2005 provide regulatory support for the application of statistical process control for better process control and understanding. In this study risk assessments, normal probability distributions, control charts, and capability charts are employed for selection of critical quality attributes, determination of normal probability distribution, statistical stability, and capability of production processes, respectively. The objective of this study is to determine tablet production process quality in the form of sigma process capability. By interpreting data and graph trends, forecasting of critical quality attributes, sigma process capability, and stability of process were studied. The overall study contributes to an assessment of process at the sigma level with respect to out-of-specification attributes produced. Finally, the study will point to an area where the application of quality improvement and quality risk assessment principles for achievement of six sigma-capable processes is possible. Statistical process control is the most advantageous tool for determination of the quality of any production process. This tool is new for the pharmaceutical tablet production process. In the case of pharmaceutical tablet production processes, the quality control parameters act as quality assessment parameters. Application of risk assessment provides selection of critical quality attributes among quality control parameters. Sequential application of normality distributions, control charts, and capability analyses provides a valid statistical process control study on process. Interpretation of such a study provides information about stability, process variability, changing of trends, and quantification of process ability against defective production. Comparative evaluation of critical quality attributes by Pareto charts provides the least capable and most variable process that is liable for improvement. Statistical process control thus proves to be an important tool for six sigma-capable process development and continuous quality improvement.

Nonparametric control charts are more practical tools for statistical process control (SPC), as they are robust in situations in which the underlying distribution is unknown. Comprehensibility and simplicity of exceedance statistics provide great convenience to analysts in multivariate SPC applications. By using the exceedance statistics, analysts save time and avoid complex calculations. Therefore, in this study, a bivariate nonparametric exponentially weighted moving average (BEWMA-EX) control chart is proposed based on the exceedance statistics to detect the shifts in the location parameter. The performance of the proposed BEWMA-EX chart is compared with the multivariate sign EWMA (MSEWMA) control chart under some well-known bivariate distributions, such as bivariate normal, t, and gamma distributions. The BEWMA-EX chart outperforms the MSEWMA control chart in terms of run-length properties. To highlight the importance of the stated study, the BEWMA-EX chart is implemented on industrial engineering datasets related to coal power plant and aluminum electrolytic capacitor manufacturing processes. The findings are promising and support the simulated results.

A control chart is a crucially important tool in statistical process control that is essentially used to determine when a process remains in-control vis-a-vis when a process does not remain in-control. A process is said to be in-control if it is under the influence of chance or common causes of variation alone. Otherwise, when some assignable or special causes of variation remain present, the process is said to be out-of-control. The sample size, sampling interval, and control limits’ multiplier are the important parameters required to design a control chart. In this paper, we have proposed an economic statistical design of the p-chart to optimize the expected cost per cycle ([Formula: see text]). Genetic Algorithm (GA) has been used to solve the proposed economic statistical design of the [Formula: see text]-chart. The proposed approach is demonstrated with the help of two numerical examples and the corresponding results are found to be quite encouraging for minimizing [Formula: see text] when compared to another pertinent model given in the literature. The utilitarian value of this article can be found while implementing the “control phase” in Six Sigma under the broader gamut of industrial engineering. The sensitivity analysis has also been carried out to investigate the influence of changes in input parameters on the output parameters for the proposed model.

Statistical Process Control (SPC) charts are frequently used in the semiconductor manufacturing environment to monitor process quality and detect special-cause variations, hence, to take corrective actions when necessary. The important aspects of control charts to consider on production floors are identifying the primary objective of implementing control charts, the type of data to monitor and the most appropriate control limits to establish. When the quality data is a type of attribute data like the proportion of defectives from a production lot, a p-chart approach is most suitable. In p-chart applications, although the assumption of normally distributed process data is not mandatory, the widespread practice is to assume the normal distribution of process data when establishing the control limits. Yet again, the reality of industrial settings is that process data are most likely influenced by outliers, resulting in highly skewed distributions. This paper addresses these issues by proposing robust SPC charting techniques to detect special-cause variations in the semiconductor manufacturing processes. Here, we present a case study of a semiconductor company in Malaysia, Dominant Opto Technologies Sdn. Bhd. to propose three robust statistical approaches for monitoring the proportion of defectives in production lots. We apply M-estimates, median, and interquartile range to calculate the upper control limits (UCL) and found that robust estimators are more effective in detecting early process deterioration and capturing the out-of-control (OOC) conditions better than traditional control charts. By proposing robust methods, this study enlightens the practical aspects of process quality improvement for real-life manufacturing setups. Because a high OOC rate may impact manufacturing productivity, we recommend the decision-makers choose the types of control charts based on the implications of each robust approach toward quality and productivity. The significance of this study includes providing insights into setting up the appropriate attribute control charts for detecting defective proportions for professionals and SPC researchers working in these areas.