PERFORMANCE OF SENSITIZING RULES ON SHEWHART CONTROL CHARTS WITH AUTOCORRELATED DATA

2001 ◽  
Vol 08 (02) ◽  
pp. 159-171 ◽  
Author(s):  
SANDY D. BALKIN ◽  
DENNIS K. J. LIN
Keyword(s):  
Time Series ◽  
Control Charts ◽  
Moving Average ◽  
Correlated Data ◽  
Autoregressive Moving Average ◽  
Shewhart Control Charts ◽  
Shewhart Control ◽  
The Mean ◽  
Autocorrelated Data ◽  
Using Data

Sensitizing Rules are commonly applied to Shewhart Charts to increase their effectiveness in detecting shifts in the mean that may otherwise go unnoticed by the usual "out-of-control" signals. The purpose of this paper is to demonstrate how well these rules actually perform when the data exhibit autocorrelation compared to non-correlated data. Since most control chart data are collected as time series, it is of interest to examine the performance of Shewhart's [Formula: see text] Chart using data generated from typical time series models. In this paper, measurements arising from autoregressive (AR), moving average (MA) and autoregressive moving average (ARMA) processes are examined using Shewhart Control Charts in conjunction with several sensitizing rules. The results indicate that the rules work well when there are strong autocorrelative relationships, but are not as effective in recognizing small to moderate levels of correlation. We conclude with the recommendation to practitioners that they use a more definitive measure of autocorrelation such as the Sample Autocorrelation Function correlogram to detect dependency.

scholarly journals Design of a Control Chart Using Extended EWMA Statistic

Technologies ◽  
2018 ◽  
Vol 6 (4) ◽  
pp. 108 ◽  
Author(s):  
Muhammad Naveed ◽  
Muhamma Azam ◽  
Nasrullah Khan ◽  
Muhammad Aslam
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Average Run Length ◽  
Moving Average ◽  
Shewhart Control Charts ◽  
Shewhart Control ◽  
Application Data ◽  
Mean And Variance ◽  
The Mean ◽  
Working Procedure

In the present paper, we propose a control chart based on extended exponentially weighted moving average (EEWMA) statistic to detect a quick shift in the mean. The mean and variance expression of the proposed EEWMA statistic are derived. The proposed EEWMA statistic is unbiased and simulation results show a smaller variance as compared to the traditional EWMA. The performance of the proposed control chart with the existing chart based on the EWMA statistic is evaluated in terms of average run length (ARL). Various tables were constructed for different values of parameters. The comparison of the EEWMA control chart with the traditional EWMA and Shewhart control charts illustrates that the proposed control chart performs better in terms of quick detection of the shift. The working procedure of the proposed control chart was also illustrated by simulated and application data.

Single-Subgroup Performance Measures and Diagnostic Procedures for X-Bar Control Charts

1994 ◽  
Vol 116 (2) ◽  
pp. 216-224
Author(s):  
G. E. Rahn ◽  
S. G. Kapoor ◽  
R. E. DeVor
Keyword(s):  
Performance Measures ◽  
Control Charts ◽  
Simulated Data ◽  
Diagnostic Procedures ◽  
Shewhart Control Charts ◽  
Operational Characteristics ◽  
Shewhart Control ◽  
The Mean ◽  
Measures Of Performance ◽  
Tremendous Impact

Although Shewhart control charts have had a tremendous impact on quality improvement, the inability to precisely measure chart performance has limited their role, and subsequently overall effectiveness in the control of manufacturing processes. Measures of performance in terms of operational characteristics (OC) are defined on two distinct levels: (a) single-subgroup level, which examines the probability of a rule violation at any given subgroup (b) multiple-subgroup level, which considers the probability of one or more rule violations throughout process monitoring. Single-subgroup performance measures for X-bar charts that employ four rules are formulated. These measures are exact expressions of operational characteristics, except for the numerical approximation to the integral of the normal distribution. Applications of these models to simulated data demonstrate their accuracy in predicting chart performance. In addition, a diagnostic methodology is described which utilizes the derived performance measures to predict the mean of a shifted distribution. The proposed diagnostic procedure is illustrated in validation and application examples.

Economic design of Shewhart control charts for monitoring autocorrelated data with skip sampling strategies

2014 ◽  
Vol 151 ◽  
pp. 121-130 ◽  
Author(s):  
Bruno Chaves Franco ◽  
Giovanni Celano ◽  
Philippe Castagliola ◽  
Antonio Fernando Branco Costa
Keyword(s):  
Control Charts ◽  
Economic Design ◽  
Sampling Strategies ◽  
Shewhart Control Charts ◽  
Shewhart Control ◽  
Autocorrelated Data ◽  
Skip Sampling

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.

SHEWHART CHARTS FOR THE DETECTION OF LINEAR TRENDS AND OF SHIFTS IN AN AUTOREGRESSION MODEL

2000 ◽  
Vol 07 (04) ◽  
pp. 309-330 ◽  
Author(s):  
RAINER GÖB
Keyword(s):  
Control Charts ◽  
Linear Trend ◽  
Average Run Length ◽  
Model Parameters ◽  
Adjustment Policy ◽  
Shewhart Control Charts ◽  
Shewhart Control ◽  
Autoregression Model ◽  
The Mean ◽  
Biased Estimates

The paper considers a univariate characteristic of a manufacturing process which is measured at discrete time points. The characteristic exhibits a linear trend under an AR(1) disturbance. If the slope of the linear trend and the autoregression coefficient are known, the process characteristic can be adjusted to vary as white noise around its target. However, the adjustment policy is very sensitive to departures from model assumptions and fails to achieve its objective in case of shifted model parameters, e.g., in case of biased estimates or external assignable causes which change the parameters. A discussion of the behaviour of the adjusted process shows that parameter shifts can have harmful consequences. As a protection against parameter shifts, additional statistical monitoring of the process is indispensable. The paper introduces various Shewhart control charts for the detection of shifts in the mean, the trend parameter, or the autoregression parameter. The performance of the charts is analyzed by the average run length criterion.

scholarly journals Control charts for monitoring drip irrigation with different hydraulic heads

2020 ◽  
Vol 15 (4) ◽  
pp. 1
Author(s):  
Allan Remor Lopes ◽  
Marcio Antonio Vilas Boas ◽  
Felix Augusto Pazuch ◽  
Diane Aparecida Ostroski ◽  
Marta Juliana Schmatz
Keyword(s):  
Control Chart ◽  
Drip Irrigation ◽  
Control Charts ◽  
Irrigation System ◽  
Moving Average ◽  
Drip Irrigation System ◽  
State University ◽  
Shewhart Control Charts ◽  
Agricultural Engineering ◽  
Shewhart Control

This study monitored a drip irrigation system with different hydraulic heads, using control charts. The study included 25 tests, and was conducted at the Experimental Nucleus of Agricultural Engineering of the State University of Western Paraná, located in the municipality of Cascavel, Paraná. The drip irrigation system was operated by gravity, and had four hydraulic heads (10, 11, 12 and 15 kPa). The uniformity of the system was determined based on uniformity distribution. Uniformity monitoring was performed using Shewhart and exponentially weighted moving-average (EWMA) control charts. An increase in the hydraulic head increased uniformity. The use of 12 and 15 kPa hydraulic heads yielded good performance, whereas 10 and 11 kPa yielded regular performance. The use of control charts proved to be efficient; the Shewhart control chart was more robust, whereas the EWMA control chart, which indicated trends and deviations not shown by Shewhart control charts, was more sensitive.

The Enhanced EWMA Control Chart with Autocorrelation

2014 ◽  
Vol 71 (5) ◽  
Author(s):  
Abbas Umar Farouk ◽  
Ismail Mohamad
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Average Run Length ◽  
Independence Assumption ◽  
Shewhart Control Charts ◽  
Ewma Chart ◽  
Ewma Control Chart ◽  
Shewhart Control ◽  
Autocorrelated Data ◽  
The Given

Control charts are effective tool with regard to improving process quality and productivity, Shewhart control charts are efficiently good at detecting large shifts in a given process but very slow in detecting small and moderate shifts, such problem could be tackled through design of sensitizing rules. It has been observed that autocorrelation has an advert effect on the control charts developed under the independence assumption [1]. In this article a new EWMA control chart has been introduced with autocorrelation and some run rule schemes were introduced to enhanced the performance of the EWMA control chart when autocorrelated. The three-out-of three EWMA scheme and three-out-of- four EWMA schemes were introduced and the generated data with induced autocorrelation were used to construct the EWMA chart to sensitize the shifts presence.  Simulation of autocorrelated data were carried out for the proposed schemes which detects the shifts as soon as it occurs in the given process, the performance were evaluated using the ARL (average run length) and the results were compared with the published results of Steiner (1991) and the Saccucci (1990) which were designed for large, small and moderate shift. The results indicates that the proposed schemes are more sensitive to the shifts at ARL0=500, 300 and 200 with autocorrelation of 0.2, 0.5 and 0.9 considered in the study.

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