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.

ZIB-EWMA CONTROL CHART FOR MONITORING RARE HEALTH EVENTS

2011 ◽  
Vol 11 (04) ◽  
pp. 881-895 ◽  
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.

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.

Design and Application of a Modified EWMA Control Chart for Monitoring Process Mean

2021 ◽  
Author(s):  
Yadpirun Supharakonsakun ◽  
Yupaporn Areepong
Keyword(s):  
White Noise ◽  
Control Chart ◽  
Control Charts ◽  
Moving Average ◽  
Autoregressive Process ◽  
Process Mean ◽  
Ewma Chart ◽  
Ewma Control Chart ◽  
Abrupt Shifts ◽  
Run Lengths

The modified exponentially weighted moving average (modified EWMA) control chart is an improvement on the performance of the standard EWMA control chart for detecting small and abrupt shifts in the process mean. In this study, the effect of varying the constant and exponential smoothing parameters for detecting shifts in the mean of an autoregressive process with exogenous variables (ARX(p,r)) with a trend and exponentially distributed white noise on the standard and modified EWMA control chart was investigated. The performances of the two control charts were compared via their average run lengths (ARLs) computed by using explicit formulas and the numerical integrated equation (NIE) technique. A comparative study of the two ARL methods on the modified and traditional EWMA control charts shows that the modified schemes had better detection ability at all levels of shift size. Finally, two examples using real datasets on gold and silver prices are given to illustrate the applicability of the proposed procedure. Our findings advocate that the modified EWMA chart is excellent for monitoring ARX(p,r) processes with exponentially distributed white noise

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.

scholarly journals Monitoring Mortality Caused by COVID-19 Using Gamma-Distributed Variables Based on Generalized Multiple Dependent State Sampling

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Muhammad Aslam ◽  
G. Srinivasa Rao ◽  
Muhammad Saleem ◽  
Rehan Ahmad Khan Sherwani ◽  
Chi-Hyuck Jun
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Average Run Length ◽  
Real Life ◽  
Quality Characteristics ◽  
Statistical Quality Control ◽  
Nonnormal Distributions ◽  
Run Lengths ◽  
Chart Design ◽  
Dependent State

More recently in statistical quality control studies, researchers are paying more attention to quality characteristics having nonnormal distributions. In the present article, a generalized multiple dependent state (GMDS) sampling control chart is proposed based on the transformation of gamma quality characteristics into a normal distribution. The parameters for the proposed control charts are obtained using in-control average run length (ARL) at specified shape parametric values for different specified average run lengths. The out-of-control ARL of the proposed gamma control chart using GMDS sampling is explored using simulation for various shift size changes in scale parameters to study the performance of the control chart. The proposed gamma control chart performs better than the existing multiple dependent state sampling (MDS) based on gamma distribution and traditional Shewhart control charts in terms of average run lengths. A case study with real-life data from ICU intake to death caused by COVID-19 has been incorporated for the realistic handling of the proposed control chart design.

scholarly journals A One-Class Classification-Based Control Chart Using the K-Means Data Description Algorithm

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Walid Gani ◽  
Mohamed Limam
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Nearest Neighbor ◽  
Average Run Length ◽  
Control Sample ◽  
Control Process ◽  
Process Data ◽  
Data Description ◽  
Kernel Distance ◽  
One Class Classification

This paper aims to enlarge the family of one-class classification-based control charts, referred to as OC-charts, and extend their applications. We propose a new OC-chart using the K-means data description (KMDD) algorithm, referred to as KM-chart. The proposed KM-chart gives the minimum closed spherical boundary around the in-control process data. It measures the distance between the center of KMDD-based sphere and the new incoming sample to be monitored. Any sample having a distance greater than the radius of KMDD-based sphere is considered as an out-of-control sample. Phase I and II analysis of KM-chart was evaluated through a real industrial application. In a comparative study based on the average run length (ARL) criterion, KM-chart was compared with the kernel-distance based control chart, referred to as K-chart, and the k-nearest neighbor data description-based control chart, referred to as KNN-chart. Results revealed that, in terms of ARL, KM-chart performed better than KNN-chart in detecting small shifts in mean vector. Furthermore, the paper provides the MATLAB code for KM-chart, developed by the authors.

ZERO INFLATED POISSON EWMA CONTROL CHART FOR MONITORING RARE HEALTH-RELATED EVENTS

2012 ◽  
Vol 12 (04) ◽  
pp. 1250065 ◽  
Author(s):  
AMIR AFSHIN FATAHI ◽  
RASSOUL NOOROSSANA ◽  
PERSHANG DOKOUHAKI ◽  
BABAK FARHANG MOGHADDAM
Keyword(s):  
Control Chart ◽  
Moving Average ◽  
Random Variable ◽  
Performance Measure ◽  
Performance Criteria ◽  
Ewma Chart ◽  
Ewma Control Chart ◽  
Health Related ◽  
Run Lengths ◽  
Approach Zero

Recently, rare health events issue has motivated many researches in the field of control charting. Various methods such as g-type control chart, g-type CUSUM control chart, sets method, CUSCORE method, SHDA method and the Bernoulli CUSUM have been developed in this regard, in which each of them has a specific approach to the problem. As a relatively new approach, zero inflation in Poisson distribution, named ZIP distribution can be applied. In this paper, an exponentially weighted moving average (EWMA) control chart is developed for the ZIP random variable to monitor rare health-related events with a predefined performance measure value. Since the ZIP-EWMA plotted data are dependent, Markov chain approach is applied to calculate average run lengths (ARLs) as the control chart performance criteria. Based on the ARL measure, the ZIP-EWMA chart performs better in comparison with the methods available in the literature. As the main contribution of this paper is the development a control chart which performs better than the previously proposed charts. Also, a motivating real case study related to monitoring needle-stick rare occurrences in a hospital is investigated to show the applicability of the developed chart.

MONITORING AUTOCORRELATED PROCESS MEAN AND VARIANCE USING A GWMA CHART BASED ON RESIDUALS

2008 ◽  
Vol 25 (06) ◽  
pp. 781-792 ◽  
Author(s):  
SHEY-HUEI SHEU ◽  
SHIN-LI LU
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Moving Average ◽  
Autoregressive Process ◽  
Process Mean ◽  
Process Variability ◽  
Autocorrelated Process ◽  
Ewma Control Chart ◽  
Mean And Variance ◽  
Run Lengths

This investigation elucidates the feasibility of monitoring a process for which observational data are largely autocorrelated. Special causes typically affect not only the process mean but also the process variance. The EWMA control chart has recently been developed and adopted to detect small shifts in the process mean and/or variance. This work extends the EWMA control chart, called the generally weighted moving average (GWMA) control chart, to monitor a process in which the observations can be regarded as a first-order autoregressive process with a random error. The EWMA and GWMA control charts of residuals used to monitor process variability and to monitor simultaneously the process mean and variance are considered to evaluate how average run lengths (ARLs) differ in each case.

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

2019 ◽  
pp. 187-198 ◽  
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.  

Nonparametric Control Charts Design and Analysis for Small Lot Production Based on the Moving Average

2014 ◽  
Vol 988 ◽  
pp. 461-466
Author(s):  
Yu Hao Deng ◽  
Hai Ping Zhu ◽  
Guo Jun Zhang ◽  
Hui Yin ◽  
Fan Mao Liu
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Average Run Length ◽  
Moving Average ◽  
Small Samples ◽  
Lot Size ◽  
Small Shift ◽  
Average Sampling ◽  
Run Lengths ◽  
Production Lot Size

This paper designed a moving average sampling method for small samples, further designed moving average (MA) control chart and moving average cumulative sum (MACS) control chart respectively, and calculated the in-control and out-of-control average run length for both charts. The charts are robust, which can monitor the process state effectively without knowing the distribution. Through analyzing the control chart costs and quality loss that is related to the production lot size, the control chart parameters are reasonably optimized. By comparing the average run lengths and some numerical examples, the paper finds that MACS chart has a good performance on detecting small shift within the small samples under the nonparametric condition.

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