scholarly journals A Nonparametric HEWMA-p Control Chart for Variance in Monitoring Processes

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 356 ◽  
Author(s):  
Muhammad Aslam ◽  
G. Rao ◽  
Ali AL-Marshadi ◽  
Chi-Hyuck Jun
Keyword(s):  
Normal Distribution ◽  
Control Chart ◽  
Control Charts ◽  
Average Run Length ◽  
Moving Average ◽  
Asymmetric Distribution ◽  
Unknown Distribution ◽  
Shewhart Control ◽  
Average Proportion ◽  
Significant Measure

Control charts are considered as powerful tools in detecting any shift in a process. Usually, the Shewhart control chart is used when data follows the symmetrical property of a normal distribution. In practice, the data from the industry may follow a non-symmetrical distribution or an unknown distribution. The average run length (ARL) is a significant measure to assess the performance of the control chart. The ARL may mislead when the statistic is computed from an asymmetric distribution. To handle this issue, in this paper, an ARL-unbiased hybrid exponentially weighted moving average proportion (HEWMA-p) chart is proposed for monitoring the process variance for a non-normal distribution or an unknown distribution. The efficiency of the proposed chart is compared with the existing chart in terms of ARLs. The proposed chart is more efficient than the existing chart in terms of ARLs. A real example is given for the illustration of the proposed chart in the industry.

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.

Design of a Variable Sampling Interval EWMA Median Control Chart

2019 ◽  
Vol 26 (05) ◽  
pp. 1950021 ◽  
Author(s):  
Kim Phuc Tran ◽  
Philippe Castagliola ◽  
Thi Hien Nguyen ◽  
Anne Cuzol
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Food Production ◽  
Average Run Length ◽  
Moving Average ◽  
Sampling Interval ◽  
Performance Comparison ◽  
Variable Sampling Interval ◽  
Variable Sampling ◽  
Weighted Moving Average

In the literature, median type control charts have been widely investigated as easy and efficient means to monitor the process mean when observations are from a normal distribution. In this work, a Variable Sampling Interval (VSI) Exponentially Weighted Moving Average (EWMA) median control chart is proposed and studied. The Markov chains are used to calculate the average run length to signal (ARL). A performance comparison with the original EWMA median control chart is made. The numerical results show that the proposed chart is considerably more effective as it is faster in detecting process shifts. Finally, the implementation of the proposed chart is illustrated with an example in food production process.

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.  

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

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.

scholarly journals A New X-Bar Control Chart for Using Neutrosophic Exponentially Weighted Moving Average

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 957 ◽  
Author(s):  
Muhammad Aslam ◽  
Ali Hussein AL-Marshadi ◽  
Nasrullah Khan
Keyword(s):  
Monte Carlo Simulation ◽  
Control Chart ◽  
Control Charts ◽  
Symmetry Property ◽  
Average Run Length ◽  
Moving Average ◽  
Exponentially Weighted Moving Average ◽  
Uncertainty Environment ◽  
Weighted Moving Average ◽  
Exponentially Weighted

The existing Shewhart X-bar control charts using the exponentially weighted moving average statistic are designed under the assumption that all observations are precise, determined, and known. In practice, it may be possible that the sample or the population observations are imprecise or fuzzy. In this paper, we present the designing of the X-bar control chart under the symmetry property of normal distribution using the neutrosophic exponentially weighted moving average statistics. We will first introduce the neutrosophic exponentially weighted moving average statistic, and then use it to design the X-bar control chart for monitoring the data under an uncertainty environment. We will determine the neutrosophic average run length using the neutrosophic Monte Carlo simulation. The efficiency of the proposed plan will be compared with existing control charts.

Average Run Lengths in Shewhart Type Charts for 2-Order Autoregressive Process

2010 ◽  
Vol 139-141 ◽  
pp. 1860-1863
Author(s):  
Qiu Xia Sun ◽  
Jian Li Zhao ◽  
Qi Sheng Gao
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Average Run Length ◽  
Correlation Coefficients ◽  
Autoregressive Process ◽  
Run Length ◽  
Shewhart Control ◽  
Control Schemes ◽  
Run Lengths ◽  
Residual Control

In this paper the average run length is adopted as the tool to describe the performance of control charts. The respective methods for calculating the average run length of the modified Shewhart control chart and the Shewhart residual control chart for 2-order autoregressive process are derived and shown in detail. By the proposed approach some numerical results of average run lengths of both Shewhart type charts are formulated and discussed. We analyze and compare that the influence of the correlation coefficients of the 2-order autoregressive process on the performance of both charts based on the estimated data. Several clear and main points of the issue are summed up. Lastly, we give some recommendations for the choice of both Shewhart type control schemes.

scholarly journals Moving Average control charts for Burr X and Inverse Gaussian distributions

2020 ◽  
Vol 30 (4) ◽  
Author(s):  
Ambreen Shafqat ◽  
Muhammad Aslam ◽  
Mohammed Albassam
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Average Run Length ◽  
Moving Average ◽  
Inverse Gaussian ◽  
Life Test ◽  
Run Length ◽  
Truncated Life Test ◽  
Average Control ◽  
Better Than

The Burr X and Inverse Gaussian (IG) distributions are considered in this paper to design an attribute control chart for time truncated life test with Moving Average (MA) scheme w. The presentation of the MA control chart is estimated in terms of average run length (ARL) by using the Monte Carlo simulation. The ARL is decided for different values of sample sizes, MA statistics size, parameters’ values, and specified average run length. The performance of this new MA attribute control chart is compared with the usual time truncated control chart for Burr X and IG distributions. The performance of a new control chart is better than the existing control chart.

scholarly journals A New Generalized Range Control Chart for the Weibull Distribution

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Osama H. Arif ◽  
Muhammad Aslam
Keyword(s):  
Weibull Distribution ◽  
Control Chart ◽  
Control Charts ◽  
Average Run Length ◽  
Moving Average ◽  
Comparison Study ◽  
Exponentially Weighted Moving Average ◽  
Run Length ◽  
Weighted Moving Average ◽  
Exponentially Weighted

In this study, a generalized range control chart is designed for the Weibull distribution using generally weighted moving average statistics. The proposed chart is based on minimum generally weighted moving average statistic and maximum generally weighted moving average statistics. We utilize the inverse erf function to transform the Weibull data to normal data. The necessary measures are given to assess the performance of the proposed control chart. The comparison study shows that the proposed control chart outperforms the existing control charts based on exponentially weighted moving average statistic in terms of the average run length. A real example is given for applying the proposed chart in the industry.

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.

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