The Enhanced EWMA  Control Chart with Autocorrelation

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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Monitoring process mean with a new EWMA control chart

Production ◽

10.1590/s0103-65132011005000026 ◽

2011 ◽

Vol 21 (2) ◽

pp. 217-222 ◽

Cited By ~ 4

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.

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Design of a Control Chart Using Extended EWMA Statistic

Technologies ◽

10.3390/technologies6040108 ◽

2018 ◽

Vol 6 (4) ◽

pp. 108 ◽

Cited By ~ 3

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.

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ZIB-EWMA CONTROL CHART FOR MONITORING RARE HEALTH EVENTS

Journal of Mechanics in Medicine and Biology ◽

10.1142/s0219519411004125 ◽

2011 ◽

Vol 11 (04) ◽

pp. 881-895 ◽

Cited By ~ 7

Author(s):

RASSOUL NOOROSSANA ◽

AMIR AFSHIN FATAHI ◽

PERSHANG DOKOUHAKI ◽

MASSOUD BABAKHANI

Keyword(s):

Control Chart ◽

Control Charts ◽

Average Run Length ◽

Moving Average ◽

Cusum Chart ◽

Health Events ◽

Ewma Chart ◽

Ewma Control Chart ◽

Significant Public Health ◽

Health Related

Monitoring rare health events, as a significant public health subject, has been considered recently by different authors. In this regard, different statistical methods such as g-type control chart, Poisson CUSUM control chart, sets-based methods, and Bernoulli CUSUM chart have been developed. Zero-inflated binomial (ZIB) distribution, due to its structure, can also be considered to develop methods for monitoring rare health-related events. If zero inflation is considered in the sampling data, and the sampling subgroup size is mandatory greater than 1, then the data best fits the ZIB distribution and the aforementioned control charts cannot be applied. ZIB distribution assumes that random shocks, corresponding to rare health events, occur and then number of failures in each subgroup fits a binomial distribution. In this paper, an exponentially weighted moving average (EWMA) control chart is applied for ZIB data to develop a ZIB-EWMA chart. Since ZIB-EWMA statistic values are not independent, Markov chain approach is considered to evaluate the performance of the proposed control chart in terms of average run length (ARL). According to the ARL measure, this ZIB-EWMA chart has a better performance in comparison with the methods available in the literature. In addition, a real case study related to rare infections in a hospital is investigated to show the applicability of the proposed control chart.

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Comparison of fixed versus variable samplmg interval shewhart control charts in the presence of positively autocorrelated data

Communications in Statistics - Simulation and Computation ◽

10.1080/03610919708813369 ◽

1997 ◽

Vol 26 (1) ◽

pp. 83-106 ◽

Cited By ~ 7

Author(s):

Victor R. Prybutok ◽

Howard R. Clayton ◽

Martha M. Harvey

Keyword(s):

Control Charts ◽

Shewhart Control Charts ◽

Shewhart Control ◽

Autocorrelated Data

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A Fuzzy Control Chart Approach for Attributes and Variables

Engineering, Technology & Applied Science Research ◽

10.48084/etasr.2192 ◽

2018 ◽

Vol 8 (5) ◽

pp. 3360-3365 ◽

Cited By ~ 1

Author(s):

N. Pekin Alakoc ◽

A. Apaydin

Keyword(s):

Quality Control ◽

Fuzzy Control ◽

Control Chart ◽

Control Charts ◽

Fuzzy Numbers ◽

Fuzzy Theory ◽

New Approach ◽

Shewhart Control Charts ◽

Shewhart Control ◽

Quality Control Chart

The purpose of this study is to present a new approach for fuzzy control charts. The procedure is based on the fundamentals of Shewhart control charts and the fuzzy theory. The proposed approach is developed in such a way that the approach can be applied in a wide variety of processes. The main characteristics of the proposed approach are: The type of the fuzzy control charts are not restricted for variables or attributes, and the approach can be easily modified for different processes and types of fuzzy numbers with the evaluation or judgment of decision maker(s). With the aim of presenting the approach procedure in details, the approach is designed for fuzzy c quality control chart and an example of the chart is explained. Moreover, the performance of the fuzzy c chart is investigated and compared with the Shewhart c chart. The results of simulations show that the proposed approach has better performance and can detect the process shifts efficiently.

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A control chart for severity index to detect drought compares favourably to logistic regression

Hydrology Research ◽

10.2166/nh.2010.013 ◽

2011 ◽

Vol 42 (1) ◽

pp. 1-9

Author(s):

Jared Townsley ◽

Justin R Chimka

Keyword(s):

Logistic Regression ◽

Control Chart ◽

Control Charts ◽

Severity Index ◽

Drought Severity ◽

Prediction Errors ◽

Shewhart Control Charts ◽

Shewhart Control ◽

Accessible Method ◽

Made In

We describe the discovery of how a traditional control chart for the Palmer Drought Severity Index (PDSI) to detect drought compares favourably to a theoretically appropriate statistical (logistic regression) model of drought as a function of PDSI. Our empirical results are based on monthly observations of PDSI, precipitation and temperature made in Kansas since 1895. Results from the study suggest that a relatively simple statistical approach based on Shewhart control charts may provide a more accessible method for relevant government agencies to predict droughts, improving resource management and preparation. Moreover, utilizing such an approach over more sophisticated methods may come at little expense regarding prediction errors.

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Improving Benchmarking Student Learning Outcomes Using Repetitive Sampling Control Chart

Journal of Computational and Theoretical Nanoscience ◽

10.1166/jctn.2016.5668 ◽

2016 ◽

Vol 13 (10) ◽

pp. 7036-7039

Author(s):

Nawal G Alghamdi ◽

Muhammad Aslam

Keyword(s):

Control Chart ◽

Control Charts ◽

Assessment Tool ◽

Educational Programs ◽

Management Program ◽

Pass Rate ◽

Shewhart Control Charts ◽

Process Understanding ◽

Shewhart Control

In recent years research on the application of Shewhart control charts in evaluating the performance of educational programs have gain sufficient grounds. These control charts aid in process understanding and identify changes that indicate either improvement or deterioration in quality of the program. Current research proposes control charts using repetitive sampling on the data taken from Weber State University’s construction management program, which uses the Associate Constructor Level 1 exam as an assessment tool. A code was developed to run the proposed control charts. Both the traditional and proposed charts were plotted using R software. The results indicate that the proposed control charts are comparatively more efficient than the traditional control charts in assessment of educational programs and minimizing false positives. At the end comparison of the benchmark—pass rate and traditional control chart with the proposed control chart has also been elucidated so that the proposed control charts may be readily employed in evaluating any educational program by academic counsellors.

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Application of Statistical Monitoring Using Autocorrelated Data and With the Influence of Multicollinearity in a Steel Process

International Journal of Statistics and Probability ◽

10.5539/ijsp.v10n4p96 ◽

2021 ◽

Vol 10 (4) ◽

pp. 96

Author(s):

Cristie Diego Pimenta ◽

Messias Borges Silva ◽

Fernando Augusto Silva Marins ◽

Aneirson Francisco da Silva

Keyword(s):

Control Chart ◽

Control Charts ◽

Stable Process ◽

Industrial Process ◽

Original Data ◽

Practical Application ◽

Statistical Monitoring ◽

Ewma Control Chart ◽

Autocorrelated Data ◽

Special Causes

The purpose of this article is to demonstrate a practical application of control charts in an industrial process that has data auto-correlated with each other. Although the control charts created by Walter A. Shewhart are very effective in monitoring processes, there are very important statistical assumptions for Shewhart's control charts to be applied correctly. Choosing the correct Control Chart is essential for managers to be able to make coherent decisions within companies. With this study, it was possible to demonstrate that the original data collected in the process, which at first appeared to have many special causes of variation, was actually a stable process (no anomalies present). However, this finding required the use of autoregressive models, multivariate statistics, autocorrelation and normality tests, multicollinearity analysis and the use of the EWMA control chart. It was concluded that it is of fundamental importance to choose the appropriate control chart for monitoring industrial processes, to ensure that changes in processes do not incorporate non-existent variations and do not cause an increase in the number of defective products.

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HYBRID EXPONENTIALLY WEIGHTED MOVING AVERAGE (HEWMA) CONTROL CHART BASED ON EXPONENTIAL TYPE ESTIMATOR OF MEAN

Journal of Reliability and Statistical Studies ◽

10.13052/jrss2229-5666.12214 ◽

2019 ◽

pp. 187-198 ◽

Cited By ~ 1

Author(s):

Syed Muhammad Muslim Raza ◽

Maqbool Hussain Sial ◽

Muhammad Haider ◽

Muhammad Moeen Butt

Keyword(s):

Control Chart ◽

Exponential Type ◽

Control Charts ◽

Average Run Length ◽

Moving Average ◽

Exponentially Weighted Moving Average ◽

Ewma Chart ◽

Weighted Moving Average ◽

Better Than ◽

Exponentially Weighted

In this paper, we have proposed a Hybrid Exponentially Weighted Moving Average (HEWMA) control chart. The proposed control chart is based on the exponential type estimator for mean using two auxiliary variables (cf. Noor-ul-Amin and Hanif, 2012). We call it an EHEWMA control chart because it is based on the exponential estimator of the mean. From this study, the fact is revealed that E-HEWMA control chart shows more efficient results as compared to traditional/simple EWMA chart and DS.EWMA control chart (cf. Raza and Butt, 2018). The comparison of the E-HEWMA control chart is also performed with the DS-EWMA chart. The proposed chart also outperforms the other control chartsin comparison. The E-HEWMA chart can be used for efficient monitoring of the production process in manufacturing industries.A simulated example has been used to compare the proposed and traditional/simple EWMA charts and DS.EWMA control chart. The control charts' performance is measured using the average run length-out of control (ARL1). It is observed that the proposed chart performs better than existing EWMA control charts.

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On Shewhart Control Charts for Zero-Truncated Negative Binomial Distributions

Pakistan Journal of Engineering Technology & Science ◽

10.22555/pjets.v4i1.521 ◽

2016 ◽

Vol 4 (1) ◽

Author(s):

Anwer Khurshid ◽

Ashit B Chakraborty

Keyword(s):

Negative Binomial Distribution ◽

Binomial Distribution ◽

Control Charts ◽

Negative Binomial ◽

Average Run Length ◽

Shewhart Control Charts ◽

Binomial Distributions ◽

Shewhart Control ◽

Cusum Charts ◽

Number Of Individuals

The negative binomial distribution (NBD) is extensively used for the description of data too heterogeneous to be fitted by Poisson distribution. Observed samples, however may be truncated, in the sense that the number of individuals falling into zero class cannot be determined, or the observational apparatus becomes active when at least one event occurs. Chakraborty and Kakoty (1987) and Chakraborty and Singh (1990) have constructed CUSUM and Shewhart charts for zero-truncated Poisson distribution respectively. Recently, Chakraborty and Khurshid (2011 a, b) have constructed CUSUM charts for zero-truncated binomial distribution and doubly truncated binomial distribution respectively. Apparently, very little work has specifically addressed control charts for the NBD (see, for example, Kaminsky et al., 1992; Ma and Zhang, 1995; Hoffman, 2003; Schwertman. 2005). The purpose of this paper is to construct Shewhart control charts for zero-truncated negative binomial distribution (ZTNBD). Formulae for the Average run length (ARL) of the charts are derived and studied for different values of the parameters of the distribution. OC curves are also drawn.

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