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.

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 Univariate statistical process control of super saver beans: a case of RMV supermarket, zimbabwe.

2015 ◽  
Vol 1 (3) ◽  
pp. 238-248
Author(s):  
Romeo Mawonik ◽  
Vinscent Nkomo
Keyword(s):  
Time Series ◽  
Process Control ◽  
Statistical Process Control ◽  
Control Charts ◽  
Moving Average ◽  
Process Quality ◽  
Correlated Data ◽  
Statistical Process ◽  
Monitoring Process ◽  
Common Causes

Statistical Process Control (SPC) uses statistical techniques to improve the quality of a process reducing its variability. The main tools of SPC are the control charts. The basic idea of control charts is to test the hypothesis that there are only common causes of variability versus the alternative that there are special causes. Control charts are designed and evaluated under the assumption that the observations from the process are independent and identically distributed (IID) normal. However, the independence assumption is often violated in practice. Autocorrelation may be present in many procedures, and may have a significant effect on the properties of the control charts.Thus, traditional SPC charts are inappropriate for monitoring process quality. In this study, wepresent methods for process control that deal with auto correlated data and a method based on time series ARIMA models (Box Jenkins Methodology). We apply the typical Cumulative Sum (CUSUM) and Exponentially Weighted Moving Average (EWMA) charts as SPC techniques and the time-series method in determining packaging process quality.

scholarly journals On the Effect of Estimation Error for the Risk-Adjusted Charts

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-21
Author(s):  
Sajid Ali ◽  
Naila Altaf ◽  
Ismail Shah ◽  
Lichen Wang ◽  
Syed Muhammad Muslim Raza
Keyword(s):  
Control Charts ◽  
Negative Binomial ◽  
Average Run Length ◽  
Moving Average ◽  
Estimation Error ◽  
Bootstrap Method ◽  
Negative Binomial Regression ◽  
Data Sets ◽  
Statistical Process ◽  
The Impact

Control charts are a popular statistical process control (SPC) technique for monitoring to detect the unusual variations in different processes. Contrary to the classical charts, control charts have also been modified to include covariates using regression approaches. This study assesses the performance of risk-adjusted control charts under the complexity of estimation error by considering logistic and negative binomial regression models. To be more precise, risk-adjusted Cumulative Sum (CUSUM) and Exponentially Weighted Moving Average (EWMA) charts are used to evaluate the impact of the estimation error. To compute the average run length (ARL), Markov Chain Monte Carlo simulations are conducted. Furthermore, a bootstrap method is also used to compute the ARL assuming different Phase-I data sets to minimize the effect of estimation error on risk-adjusted control charts. The results for cardiac surgery and respiratory disease data sets show that the modified control charts improve the performance in detecting small shifts.

scholarly journals The Modified Mixed Exponentially Weighted Moving Average-Cumulative Sum Control Charts for Autocorrelated Process

2021 ◽  
Author(s):  
Dushyant Tyagi ◽  
Vipin Yadav
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Average Run Length ◽  
Moving Average ◽  
Statistical Process ◽  
Autocorrelated Process ◽  
Independent Process ◽  
Cumulative Sum Control ◽  
Process Observation ◽  
Control Limits

Statistical Process Control (SPC) is an efficient methodology for monitoring, managing, analysing and recuperating process performance. Implementation of SPC in industries results in biggest benefits, as enhanced quality products and reduced process variation. While dealing with the theory of control chart we generally move with the assumption of independent process observation. But in practice usually, for most of the processes the observations are autocorrelated which degrades the ability of control chart application. The loss caused by autocorrelation can be obliterated by making modifications in the traditional control charts. The article presented here refers to a combination of EWMA and CUSUM charting techniques supplementing modifications in the control limits. The performance of the referred scheme is measured by comparing average run length (ARL) with existing control charts. Also, the referred scheme is found reasonably well for detecting particularly smaller displacements in the process.

scholarly journals Monitoring of mechanical sugarcane harvesting through control charts

2015 ◽  
Vol 35 (6) ◽  
pp. 1079-1092 ◽  
Author(s):  
Murilo A. Voltarelli ◽  
Rouverson P. da Silva ◽  
Cristiano Zerbato ◽  
Carla S. S. Paixão ◽  
Tiago de O. Tavares
Keyword(s):  
Process Control ◽  
Statistical Process Control ◽  
Control Chart ◽  
Control Charts ◽  
Moving Average ◽  
Grinding Wheel ◽  
Individual Values ◽  
Statistical Process ◽  
Minas Gerais State ◽  
Weighted Moving Average

ABSTRACT Statistical process control in mechanized farming is a new way to assess operation quality. In this sense, we aimed to compare three statistical process control tools applied to losses in sugarcane mechanical harvesting to determine the best control chart template for this quality indicator. Losses were daily monitored in farms located within Triângulo Mineiro region, in Minas Gerais state, Brazil. They were carried over a period of 70 days in the 2014 harvest. At the end of the evaluation period, 194 samples were collected in total for each type of loss. The control charts used were individual values chart, moving average and exponentially weighted moving average. The quality indicators assessed during sugarcane harvest were the following loss types: full grinding wheel, stumps, fixed piece, whole cane, chips, loose piece and total losses. The control chart of individual values is the best option for monitoring losses in sugarcane mechanical harvesting, as it is of easier result interpretation, in comparison to the others.

scholarly journals Monitoring process mean with a new EWMA control chart

Production ◽  
2011 ◽  
Vol 21 (2) ◽  
pp. 217-222 ◽  
Author(s):  
Yang Su-Fen ◽  
Tsai Wen-Chi ◽  
Huang Tzee-Ming ◽  
Yang Chi-Chin ◽  
Cheng Smiley
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Population Distribution ◽  
Average Run Length ◽  
Process Data ◽  
Ewma Chart ◽  
Ewma Control Chart ◽  
Simple Statistic ◽  
Run Lengths ◽  
Proper Values

In practice, sometimes the process data did not come from a known population distribution. So the commonly used Shewhart variables control charts are not suitable since their performance could not be properly evaluated. In this paper, we propose a new EWMA Control Chart based on a simple statistic to monitor the small mean shifts in the process with non-normal or unknown distributions. The sampling properties of the new monitoring statistic are explored and the average run lengths of the proposed chart are examined. Furthermore, an Arcsine EWMA Chart is proposed since the average run lengths of the Arcsine EWMA Chart are more reasonable than those of the new EWMA Chart. The Arcsine EWMA Chart is recommended if we are concerned with the proper values of the average run length.

scholarly journals X̅ and R control charts based on marshall-olkin inverse log-logistic distribution for positive skewed data

2020 ◽  
Vol 1 (1) ◽  
pp. 9-16
Author(s):  
O. L. Aako ◽  
J. A. Adewara ◽  
K. S Adekeye ◽  
E. B. Nkemnole
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Average Run Length ◽  
Logistic Distribution ◽  
Skewed Data ◽  
Process Data ◽  
And Performance ◽  
Set Up ◽  
Control Limits ◽  
Normally Distributed

The fundamental assumption of variable control charts is that the data are normally distributed and spread randomly about the mean. Process data are not always normally distributed, hence there is need to set up appropriate control charts that gives accurate control limits to monitor processes that are skewed. In this study Shewhart-type control charts for monitoring positively skewed data that are assumed to be from Marshall-Olkin Inverse Loglogistic Distribution (MOILLD) was developed. Average Run Length (ARL) and Control Limits Interval (CLI) were adopted to assess the stability and performance of the MOILLD control chart. The results obtained were compared with Classical Shewhart (CS) and Skewness Correction (SC) control charts using the ARL and CLI. It was discovered that the control charts based on MOILLD performed better and are more stable compare to CS and SC control charts. It is therefore recommended that for positively skewed data, a Marshall-Olkin Inverse Loglogistic Distribution based control chart will be more appropriate.

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.

scholarly journals Nonparametric EWMA-Type Control Charts for Monitoring Industrial Processes: An Overview

2021 ◽  
Vol 6 (3) ◽  
pp. 708-751
Author(s):  
Ioannis S. Triantafyllou ◽  
Mangey Ram
Keyword(s):  
Probability Distribution ◽  
Statistical Process Control ◽  
Crucial Role ◽  
Control Charts ◽  
Moving Average ◽  
Industrial Processes ◽  
Statistical Process ◽  
Practical Applications ◽  
Memory Type ◽  
Weighted Moving Average

In the present paper we provide an up-to-date overview of nonparametric Exponentially Weighted Moving Average (EWMA) control charts. Due to their nonparametric nature, such memory-type schemes are proved to be very useful for monitoring industrial processes, where the output cannot match to a particular probability distribution. Several fundamental contributions on the topic are mentioned, while recent advances are also presented in some detail. In addition, some practical applications of the nonparametric EWMA-type control charts are highlighted, in order to emphasize their crucial role in the contemporary online statistical process control.

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