On the effect of measurement errors in simultaneous monitoring of mean vector and covariance matrix of multivariate processes

2016 ◽  
Vol 40 (1) ◽  
pp. 318-330 ◽  
Author(s):  
Amirhossein Amiri ◽  
Reza Ghashghaei ◽  
Mohammad Reza Maleki
Keyword(s):  
Measurement Errors ◽  
Control Charts ◽  
Moving Average ◽  
Real Data ◽  
Simulation Studies ◽  
Process Mean ◽  
Extensive Simulation ◽  
Monitoring Procedure ◽  
Mean Vector ◽  
Weighted Moving Average

In this paper, we investigate the misleading effect of measurement errors on simultaneous monitoring of the multivariate process mean and variability. For this purpose, we incorporate the measurement errors into a hybrid method based on the generalized likelihood ratio (GLR) and exponentially weighted moving average (EWMA) control charts. After that, we propose four remedial methods to decrease the effects of measurement errors on the performance of the monitoring procedure. The performance of the monitoring procedure as well as the proposed remedial methods is investigated through extensive simulation studies and a real data example.

scholarly journals Exponentially Weighted Moving Average Control Charts for the Process Mean Using Exponential Ratio Type Estimator

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Hina Khan ◽  
Saleh Farooq ◽  
Muhammad Aslam ◽  
Masood Amjad Khan
Keyword(s):  
Control Charts ◽  
Sampling Design ◽  
Control Structure ◽  
Moving Average ◽  
Auxiliary Information ◽  
Ranked Set Sampling ◽  
Process Mean ◽  
Average Control ◽  
The Mean ◽  
Weighted Moving Average

This study proposes EWMA-type control charts by considering some auxiliary information. The ratio estimation technique for the mean with ranked set sampling design is used in designing the control structure of the proposed charts. We have developed EWMA control charts using two exponential ratio-type estimators based on ranked set sampling for the process mean to obtain specific ARLs, being suitable when small process shifts are of interest.

Dynamic Response of Residuals of a Controlled Cutting Process to Shifts in the Process Mean

1998 ◽  
Vol 05 (02) ◽  
pp. 157-168
Author(s):  
Jiangbin Yang ◽  
Viliam Makis
Keyword(s):  
Control Charts ◽  
Moving Average ◽  
Cutting Process ◽  
Process Mean ◽  
Autocorrelated Process ◽  
Recursive Procedures ◽  
Statistical Behavior ◽  
Run Lengths ◽  
Cusum Control Charts ◽  
Weighted Moving Average

A usual approach to monitoring an autocorrelated process is to apply a control chart to the process residuals. In this paper, we study the statistical behavior of the residuals of a controlled second-order autoregressive (AR(2)) cutting process when a special-cause shift occurs to the process mean. Shewhart, exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) control charts are applied to the residuals to monitor the cutting process. Formulas, integral equations and recursive procedures for computing the average run lengths (ARLs) of the charts are derived. Numerical results are presented and the relative performance of the charts is investigated.

scholarly journals Modified One-Sided EWMA Charts without- and with Variable Sampling Intervals for Monitoring a Normal Process

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 159
Author(s):  
Xuelong Hu ◽  
Suying Zhang ◽  
Guan Sun ◽  
Jianlan Zhong ◽  
Shu Wu
Keyword(s):  
Control Charts ◽  
Moving Average ◽  
Real Data ◽  
Simulation Method ◽  
Monte Carlo Simulation Method ◽  
Variable Sampling ◽  
Distributed Process ◽  
Sampling Intervals ◽  
The One ◽  
Weighted Moving Average

Much research has been conducted on two-sided Exponentially Weighted Moving Average (EWMA) control charts, while less work has been devoted to the one-sided EWMA charts. Traditional one-sided EWMA charts involve resetting the EWMA statistic to the target whenever it falls below or above the target, or truncating the observations above or below the target and further applying the EWMA statistic to the truncated samples. In order to further improve the performance of traditional one-sided EWMA mean (X¯) charts, this paper studies the performance of the Modified One-sided EWMA (MOEWMA) X¯ charts to monitor a normally distributed process. The Monte-Carlo simulation method is used to obtain the zero- and steady-state Run Length (RL) properties of the proposed control charts. Through extensive simulations and comparisons with other charts, it is shown that the proposed MOEWMA X¯ charts compare favorably with some existing competing charts. Moreover, by attaching the variable sampling intervals (VSI) feature to the MOEWMA X¯ charts, it is shown that the VSI MOEWMA charts outperform the corresponding charts without the VSI feature. Finally, a real data example from manufacturing process shows the implementation of the proposed one-sided charts.

scholarly journals The Performance of Robust Multivariate Ewma Control Charts

2018 ◽  
pp. 52-58
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Moving Average ◽  
Statistical Tool ◽  
M Estimator ◽  
One Step ◽  
Exponential Weighted Moving Average ◽  
Mewma Control Chart ◽  
Mean Vector ◽  
Weighted Moving Average

Multivariate Exponential Weighted Moving Average (MEWMA) control chart is a popular statistical tool for monitoring multivariate process over time. However, this chart is sensitive to the presence of outliers arising from the use of classical mean vector and covariance matrix in estimating the MEWMA statistic. These classical estimators are known to be sensitive to the outliers. To address this problem, robust MEWMA control charts based on modified one-step M-estimator (MOM) and Winsorized modified one-step M-estimator (WM) are proposed. Their performance is then compared with the standard MEWMA control chart in various situations. The findings revealed that the proposed robust MEWMA control charts are more effective in controlling false alarm rates especially for large sample sizes and high percentage of outliers.

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