scholarly journals On the Use of Copula for Quality Control Based on an AR(1) Model

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2211
Author(s):  
Timothy M. Young ◽  
Ampalavanar Nanthakumar ◽  
Hari Nanthakumar
Keyword(s):  
Control Charts ◽  
Average Run Length ◽  
Sensor Data ◽  
Statistical Control ◽  
Statistical Process ◽  
Clayton Copula ◽  
Process Standard Deviation ◽  
Manufacturing Applications ◽  
Using Data ◽  
Online Sensors

Manufacturing for a multitude of continuous processing applications in the era of automation and ‘Industry 4.0′ is focused on rapid throughput while producing products of acceptable quality that meet customer specifications. Monitoring the stability or statistical control of key process parameters using data acquired from online sensors is fundamental to successful automation in manufacturing applications. This study addresses the significant problem of positive autocorrelation in data collected from online sensors, which may impair assessment of statistical control. Sensor data collected at short time intervals typically have significant autocorrelation, and traditional statistical process control (SPC) techniques cannot be deployed. There is a plethora of literature on techniques for SPC in the presence of positive autocorrelation. This paper contributes to this area of study by investigating the performance of ‘Copula’ based control charts by assessing the average run length (ARL) when the subsequent observations are correlated and follow the AR(1) model. The conditional distribution of yt given yt−1 is used in deriving the control chart limits for three different categories of Copulas: Gaussian, Clayton, and Farlie-Gumbel-Morgenstern Copulas. Preliminary results suggest that the overall performance of the Clayton Copula and Farlie-Gumbel-Morgenstern Copula is better compared to other Archimedean Copulas. The Clayton Copula is the more robust with respect to changes in the process standard deviation as the correlation coefficient increases.

Time Series Control Charts in the Presence of Model Uncertainty

2002 ◽  
Vol 124 (4) ◽  
pp. 891-898 ◽  
Author(s):  
Daniel W. Apley
Keyword(s):  
Time Series ◽  
Model Uncertainty ◽  
Control Charts ◽  
Average Run Length ◽  
Moving Average ◽  
Process Data ◽  
Estimation Errors ◽  
Statistical Process ◽  
Modeling Errors ◽  
Autocorrelated Processes

Time series control charts are popular methods for statistical process control of autocorrelated processes. In order to implement these methods, however, a time series model of the process is required. Since time series models must always be estimated from process data, model estimation errors are unavoidable. In the presence of modeling errors, time series control charts that are designed under the assumption of a perfect model may have an actual in-control average run length that is substantially shorter than desired. This paper presents a method for incorporating model uncertainty information into the design of time series control charts to provide a level of robustness with respect to modeling errors. The focus is on exponentially weighted moving average charts and Shewhart individual charts applied to the time series residuals.

A MAGNITUDE-ROBUST CONTROL CHART FOR MONITORING AND ESTIMATING STEP CHANGES IN A POISSON RATE PARAMETER

2007 ◽  
Vol 14 (01) ◽  
pp. 1-19 ◽  
Author(s):  
MARCUS B. PERRY ◽  
JOSEPH J. PIGNATIELLO ◽  
JAMES R. SIMPSON
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Average Run Length ◽  
Maximum Likelihood Estimates ◽  
Cusum Chart ◽  
Rate Parameter ◽  
Statistical Process ◽  
Wide Range ◽  
Statistical Process Control Charts ◽  
Performance Results

Statistical process control charts are intended to assist operators in detecting process changes. If a process change does occur, the control chart should detect the change quickly. If the operator is provided with an estimate as to when the process changed, the search to find the special cause can be more easily facilitated. We investigate a process-monitoring tool for Poisson count data that quickly responds to process mean count rate changes regardless of the magnitude of the change, while supplying useful diagnostic information. A likelihood ratio approach was used to develop a control chart for a permanent step change in a Poisson process rate parameter. The average run length (ARL) performance of this chart is compared to that of several Poisson cumulative sum (CUSUM) control charts. Our performance results show that the proposed chart performs better than any one CUSUM chart over a wide range of potential shift magnitudes. The proposed chart also provides maximum likelihood estimates of the time and the magnitude of the process shift. These crucial change point diagnostics can greatly enhance the special cause investigation.

Defining Quality of Perioperative Care by Statistical Process Control of Adverse Outcomes 

1995 ◽  
Vol 82 (5) ◽  
pp. 1181-1188 ◽  
Author(s):  
Robert S. Lagasse ◽  
Ellen S. Steinberg ◽  
Robert I. Katz ◽  
Albert J. Saubermann
Keyword(s):  
Peer Review ◽  
Perioperative Care ◽  
Control Charts ◽  
Statistical Control ◽  
Healthcare Organizations ◽  
Statistical Process ◽  
Human Errors ◽  
Clinical Indicators ◽  
System Errors

Background Through peer review, we separated the contributions of system error and human (anesthesiologist) error to adverse perioperative outcomes. In addition, we monitored the quality of our perioperative care by statistically defining a predictable rate of adverse outcome dependent on the system in which practice occurs and respondent to any special causes for variation. Methods Traditional methods of identifying human errors using peer review were expanded to allow identification of system errors in cases involving one or more of the anesthesia clinical indicators recommended in 1992 by the Joint Commission on Accreditation of Healthcare Organizations. Outcome data also were subjected to statistical process control analysis, an industrial method that uses control charts to monitor product quality and variation. Results Of 13,389 anesthetics, 110 involved one or more clinical indicators of the Joint Commission on Accreditation of Healthcare Organizations. Peer review revealed that 6 of 110 cases involved two separate errors. Of these 116 errors, 9 (7.8%) were human errors and 107 (92.2%) were system errors. Attribute control charts demonstrated all indicators, excepting one (fulminant pulmonary edema), to be in statistical control. Conclusions The major determinant of our patient care quality is the system through which services are delivered and not the individual anesthesia care provider. Outcome of anesthesia services and perioperative care is in statistical control and therefore stable. A stable system has a measurable, communicable capability that allows description and prediction of the quality of care we provide on a monthly basis.

scholarly journals An EWMA-DiD Control Chart to Capture Small Shifts in the Process Average Using Auxiliary Information

Technologies ◽  
2018 ◽  
Vol 6 (3) ◽  
pp. 69
Author(s):  
Muhammad Mughal ◽  
Muhammad Azam ◽  
Muhammad Aslam
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Average Run Length ◽  
Auxiliary Information ◽  
Process Variations ◽  
Specific Situation ◽  
Practical Application ◽  
Statistical Process ◽  
Real Scenario ◽  
Better Than

Among the Statistical Process Control (SPC) techniques, control charts are considered to be high weight-age due to their effectiveness in process variation. As the Shewhart’s charts are not that active in monitoring small and moderate process variations, the statisticians have been making efforts to improve the performance of the control chart by introducing several techniques within the tool. These techniques consist of experimenting with different estimators, different sampling selection techniques, and mixed methodologies. The proposed chart is one of the examples of a mixed chart technique that has shown its efficiency in monitoring small variations better than any of the existing techniques in the specific situation of auxiliary information. To show and compare its performance, average run length (ARL) tables and ARL curves have been presented in the article. An industrial example has also been included to show the practical application of the proposed chart in a real scenario.

Statistical Process Control on Time Delay Feedback Adjustment Process

2011 ◽  
Vol 211-212 ◽  
pp. 305-309
Author(s):  
Hai Yu Wang
Keyword(s):  
Time Delay ◽  
Control Chart ◽  
Control Charts ◽  
Average Run Length ◽  
Adjustment Process ◽  
Statistical Process ◽  
Controlled Processes ◽  
Monitoring Process ◽  
Set Up ◽  
And Control

Control chart can be designed to quickly detect small shifts in the mean of a sequence of independent normal observations. But this chart cannot perform well for autocorrelated process. The main goal of this article is to suggest a control chart method using to monitoring process with different time delay feedback controlled processes. A quality control model based on delay feedback controlled processes is set up. And the calculating method of average run length of control charts based on process output and control action of multiple steps delay MMSE feedback controlled processes is provided to evaluate control charts performance. A simple example is used to illustrate the procedure of this approach.

scholarly journals GRAFIK PENGENDALI MIXED EXPONENTIALLY WEIGHTED MOVING AVERAGE – CUMULATIVE SUM (MEC) DALAM ANALISIS PENGAWASAN PROSES PRODUKSI (Studi Kasus : Wingko Babat Cap “Moel”)

2021 ◽  
Vol 10 (1) ◽  
pp. 114-124
Author(s):  
Aulia Resti ◽  
Tatik Widiharih ◽  
Rukun Santoso
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Average Run Length ◽  
Moving Average ◽  
Exponentially Weighted Moving Average ◽  
Cumulative Sum ◽  
Statistical Process ◽  
Cusum Charts ◽  
Weighted Moving Average ◽  
Exponentially Weighted

Quality control is an important role in industry for maintain quality stability.  Statistical process control can quickly investigate the occurrence of unforeseen causes or process shifts using control charts. Mixed Exponentially Weighted Moving Average - Cumulative Sum (MEC) control chart is a tool used to monitor and evaluate whether the production process is in control or not. The MEC control chart method is a combination of the Exponentially Weighted Moving Average (EWMA) and Cumulative Sum (CUSUM) charts. Combining the two charts aims to increase the sensitivity of the control chart in detecting out of control. To compare the sensitivity level of the EWMA, CUSUM, and MEC methods, the Average Run Length (ARL) was used. From the comparison of ARL values, the MEC chart is the most sensitive control chart in detecting out of control compared to EWMA and CUSUM charts for small shifts. Keywords: Grafik Pengendali, Exponentially Weighted Moving Average, Cumulative Sum, Mixed EWMA-CUSUM, Average Run Lenght, EWMA, CUSUM, MEC, ARL

scholarly journals Improving Process Performance of Cotton Spinning by Using Statistical Process Control Techniques

2020 ◽  
pp. 15-22
Author(s):  
Dereje Girma ◽  
Omprakash Sahu
Keyword(s):  
Process Control ◽  
Statistical Process Control ◽  
Control Charts ◽  
Shop Floor ◽  
Statistical Control ◽  
Statistical Process ◽  
Process Capability Analysis ◽  
Capability Analysis ◽  
R Process ◽  
And Control

Identifying the presence and understanding the causes of process variability are key requirements for well controlled and quality manufacturing. This pilot study demonstrates the introduction of Statistical Process Control (SPC) methods to the spinning department of a textile manufacturing company. The methods employed included X Bar and R process control charts as well as process capability analysis. Investigation for 29 machine processes identified that none were in statistical control. Recommendations have been made for a repeat of the study using validated data together with practical application of SPC and control charts on the shop floor and extension to all processes within the factory.

PACS Monitoring

2010 ◽  
pp. 244-263
Author(s):  
Carrison K.S. Tong ◽  
Eric T.T. Wong
Keyword(s):  
Process Control ◽  
Statistical Process Control ◽  
Control Chart ◽  
Control Charts ◽  
Continuous Process ◽  
Descriptive Statistics ◽  
Statistical Techniques ◽  
Statistical Control ◽  
Executive Management ◽  
Statistical Process

The present study advocates the application of statistical process control (SPC) as a performance monitoring tool for a PACS. The objective of statistical process control (SPC) differs significantly from the traditional QC/QA process. In the traditional process, the QC/QA tests are used to generate a datum point and this datum point is compared to a standard. If the point is out of specification, then action is taken on the product and action may be taken on the process. To move from the traditional QC/QA process to SPC, a process control plan should be developed, implemented, and followed. Implementing SPC in the PACS environment need not be a complex process. However, if the maximum effect is to be achieved and sustained, PACSSPC must be implemented in a systematic manner with the active involvement of all employees from line associates to executive management. SPC involves the use of mathematics, graphics, and statistical techniques, such as control charts, to analyze the PACS process and its output, so as to take appropriate actions to achieve and maintain a state of statistical control. While SPC is extensively used in the healthcare industry, especially in patient monitoring, it is rarely applied in the PACS environment. One may refer to a recent SPC application that Mercy Hospital (Alegent Health System) initiated after it implemented a PACS in November 2003 (Stockman & Krishnan, 2006). The anticipated benefits characteristic to PACS through the use of SPC include: • Reduced image retake and diagnostic expenditure associated with better process control. • Reduced operating costs by optimizing the maintenance and replacement of PACS equipment components. • Increased productivity by identification and elimination of variation and outof- control conditions in the imaging and retrieval processes. • Enhanced level of quality by controlled applications. SPC involves using statistical techniques to measure and analyze the variation in processes. Most often used for manufacturing processes, the intent of SPC is to monitor product quality and maintain processes to fixed targets. Hence besides the HSSH techniques, the proposed TQM approach would include the use of SPC. Although SPC will not improve the reliability of a poorly designed PACS, it can be used to maintain the consistency of how the individual process is provided and, therefore, of the entire PACS process. A primary tool used for SPC is the control chart, a graphical representation of certain descriptive statistics for specific quantitative measurements of the PACS process. These descriptive statistics are displayed in the control chart in comparison to their “in-control” sampling distributions. The comparison detects any unusual variation in the PACS delivery process, which could indicate a problem with the process. Several different descriptive statistics can be used in control charts and there are several different types of control charts that can test for different causes, such as how quickly major vs. minor shifts in process means are detected. These control charts are also used with service level measurements to analyze process capability and for continuous process improvement efforts.

scholarly journals Application of Statistical Quality Control in Monitoring the Production, Packaging and Marketing Process of Sachet Water

2020 ◽  
pp. 32-45
Author(s):  
Terna Godfrey Ieren ◽  
Samson Kuje ◽  
Abraham Iorkaa Asongo ◽  
Innocent Boyle Eraikhuemen
Keyword(s):  
Quality Control ◽  
Process Control ◽  
Statistical Process Control ◽  
Control Charts ◽  
Statistical Quality Control ◽  
Statistical Control ◽  
Statistical Process ◽  
Marketing Process ◽  
Product Sales ◽  
Sachet Water

Statistical process control is a technique employed to enhance the quality and productivity of processes and the distribution or marketing of its products. Sachet water is a product that has become popular and is being used as a replacement for lack of potable water. It is an alternative that is readily available, affordable but with questions about its purity, production and marketing processes. The objective of this study is to apply statistical control charts in monitoring the production, packaging and distribution or marketing processes of sachet water in Nigeria. This paper employed statistical quality control approach to monitor process stability in a Table Water manufacturing company. Quality control tools such as p-chart, u-chart, X-bar and R charts as well as process capability chart were use to observed field data obtained from the sachet water manufacturing company on important processes of sachet water production and marketing for 30 working days. This was done to check if the processes were in control or out of control and to verify the capability of the marketing process of the product meeting preset specifications. With this, the statistical control charts suitable for the processes were constructed using package “qcc” in R software version 3.6.1. The results from p-chart and u-chart showed that the production and packaging process of the product is not in control and hence the need for further investigations and corrective measures to prevent variability in the process and thus allowing improvement in the quality of the product. Also, the results from X-bar and R charts showed that the marking process was in statistical process control in respects of the product sales recorded by the four independent marketers, with no assignable cause of variation. It also revealed that, the product marketing process has low capability of successfully attending the preset specification limits in respect of the product sales and hence generating low profit for the company.

scholarly journals Statistical Control Charts: Performances of Short Term Stock Trading in Croatia

2015 ◽  
Vol 6 (1) ◽  
pp. 22-35 ◽  
Author(s):  
Ksenija Dumičić ◽  
Berislav Žmuk
Keyword(s):  
Control Charts ◽  
Stock Exchange ◽  
Moving Average ◽  
Portfolio Analysis ◽  
False Alarms ◽  
Statistical Control ◽  
Stock Trading ◽  
Statistical Tool ◽  
Statistical Process ◽  
Short Run

Abstract Background: The stock exchange, as a regulated financial market, in modern economies reflects their economic development level. The stock market indicates the mood of investors in the development of a country and is an important ingredient for growth. Objectives: This paper aims to introduce an additional statistical tool used to support the decision-making process in stock trading, and it investigate the usage of statistical process control (SPC) methods into the stock trading process. Methods/Approach: The individual (I), exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) control charts were used for gaining trade signals. The open and the average prices of CROBEX10 index stocks on the Zagreb Stock Exchange were used in the analysis. The statistical control charts capabilities for stock trading in the short-run were analysed. Results: The statistical control chart analysis pointed out too many signals to buy or sell stocks. Most of them are considered as false alarms. So, the statistical control charts showed to be not so much useful in stock trading or in a portfolio analysis. Conclusions: The presence of non-normality and autocorellation has great impact on statistical control charts performances. It is assumed that if these two problems are solved, the use of statistical control charts in a portfolio analysis could be greatly improved.

Sign in / Sign up

Export Citation Format

Share Document