A homogenously weighted moving average scheme for observations under the effect of serial dependence and measurement inaccuracy

2021 ◽  
Vol 12 (4) ◽  
pp. 401-414 ◽  
Author(s):  
Maonatlala Thanwane ◽  
Sandile C. Shongwe ◽  
Muhammad Aslam ◽  
Jean-Claude Malela-Majika ◽  
Mohammed Albassam
Keyword(s):  
Measurement Errors ◽  
Moving Average ◽  
Length Distribution ◽  
Real Life ◽  
Sampling Strategy ◽  
Serial Dependence ◽  
Statistical Efficiency ◽  
Average Scheme ◽  
Run Length Distribution ◽  
Weighted Moving Average

The combined effect of serial dependency and measurement errors is known to negatively affect the statistical efficiency of any monitoring scheme. However, for the recently proposed homogenously weighted moving average (HWMA) scheme, the research that exists concerns independent and identically distributed observations and measurement errors only. Thus, in this paper, the HWMA scheme for monitoring the process mean under the effect of within-sample serial dependence with measurement errors is proposed for both constant and linearly increasing measurement system variance. Monte Carlo simulation is used to evaluate the run-length distribution of the proposed HWMA scheme. A mixed-s&m sampling strategy is incorporated to the HWMA scheme to reduce the negative effect of serial dependence and measurement errors and its performance is compared to the existing Shewhart scheme. An example is given to illustrate how to implement the proposed HWMA scheme for use in real-life applications.

Combined effect of autocorrelation and measurement errors on the adaptive X¯ monitoring schemes

2020 ◽  
pp. 014233122093529 ◽  
Author(s):  
Sandile Charles Shongwe ◽  
Jean-Claude Malela-Majika
Keyword(s):  
Measurement Errors ◽  
Length Distribution ◽  
Real Life ◽  
Adaptive Designs ◽  
Combined Effect ◽  
Sampling Strategies ◽  
Run Length ◽  
Variable Sampling ◽  
Negative Effect ◽  
Run Length Distribution

For independent and identically distributed observations, and those with measurement errors only, the adaptive designs (i.e. variable sampling sizes (VSS), variable sampling intervals (VSI) and the latter two combined to form VSSI) have been thoroughly discussed. However, no research exists for processes under the combined effect of autocorrelation and measurement errors; thus, such adaptive Shewhart [Formula: see text] schemes are proposed. The Markov chain approach for adaptive designs are used to evaluate the run-length distribution properties with two special sampling strategies (i.e. s-skip and multiple measurements) incorporated to reduce the combined negative effect of autocorrelation and measurement inaccuracy. Using numerous run-length metrics, it is shown that the combination of the two sampling strategies with the VSSI design reduces this negative effect considerably and improves the detection ability of the [Formula: see text] scheme by a significant margin as compared with using the fixed sample size and sampling interval (FSSI), VSS and VSI designs. Autocorrelation level has a higher negative effect as compared with the measurement inaccuracy level. For high levels of autocorrelation ([Formula: see text]0.8), the s-skip strategy has little influence in reducing the negative effect; but the VSSI design maintains better performance than the other designs. Finally, a real-life example is used to illustrate its implementation.

scholarly journals A synthetic exponentially weighted moving average control chart to monitor process median based on ranked set sampling

2021 ◽  
Vol 36 ◽  
pp. 01002
Author(s):  
Jing Wen Ng ◽  
Voon Hee Wong ◽  
Sook Theng Pang
Keyword(s):  
Control Chart ◽  
Moving Average ◽  
Length Distribution ◽  
Ranked Set Sampling ◽  
Exponentially Weighted Moving Average ◽  
Process Mean ◽  
Run Length ◽  
Ewma Chart ◽  
Run Length Distribution ◽  
Weighted Moving Average

Exponentially Weighted Moving Average (EWMA) control charts yield insights into data in a way more comprehensible to the practitioners and researchers because of its capability in discovering small to moderate process mean shifts. EWMA control chart is incorporated with conforming run length (CRL) chart, named synthetic EWMA chart, to enhance the performance of the chart in detecting the out-of-control signal. Synthetic EWMA chart based on ranked set sampling (RSS) for monitoring process mean has been proposed as it advanced the detection of chart over a series of mean shifts. With the situation that normality assumption is scarcely attain in practice, we proposed synthetic EWMA median chart based on RSS. Rather than select average run length (ARL) as sole performance evaluating tool, the median and percentiles of run-length distribution are used to examine the performance of the proposed chart as it provides more information on the entire run-length distribution. Near-optimal parameters of the proposed chart will be acquired by setting the incontrol ARL at a designated value. The run length performances of the proposed chart are then compared with the existing charts such as EWMA median chart based on RSS.

scholarly journals The effect of measurement errors on the performance of the homogenously weighted moving average X¯ monitoring scheme

2020 ◽  
pp. 014233122097356
Author(s):  
Maonatlala Thanwane ◽  
Jean-Claude Malela-Majika ◽  
Philippe Castagliola ◽  
Sandile Charles Shongwe
Keyword(s):  
Measurement Errors ◽  
Moving Average ◽  
Real Life ◽  
Error Model ◽  
Measuring Instruments ◽  
Monitoring Scheme ◽  
Real Life Situation ◽  
Negative Effect ◽  
Multiple Measurements ◽  
Weighted Moving Average

Monitoring schemes are typically designed under the assumption of perfect measurements. However, in real-life applications, data tend to be subjected to measurement errors, that is, a difference between the real quantities and the measured ones mostly exist even with highly sophisticated advanced measuring instruments. Thus, in this paper, the negative effect of measurement errors on the performance of the homogenously weighted moving average (HWMA) scheme is studied using the linear covariate error model for constant and linearly increasing variance. Monte Carlo simulations are used to evaluate the performance of the proposed HWMA scheme in terms of the run-length characteristics. It is observed that as the smoothing parameter increases, measurement errors have a higher negative effect on the performance of the HWMA [Formula: see text] scheme. More importantly, it is shown that the negative effect of measurement errors is reduced by using multiple measurements and/or by increasing the slope coefficient of the covariate error model. Moreover, the performance of the HWMA [Formula: see text] scheme is compared with the corresponding exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) [Formula: see text] schemes. An illustrative example is provided to help in implementing this monitoring scheme in a real-life situation.

scholarly journals Parameter Estimation Effect of the Homogeneously Weighted Moving Average Chart to Monitor the Mean of Autocorrelated Observations With Measurement Errors

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 221352-221366
Author(s):  
Maonatlala Thanwane ◽  
Sandile Charles Shongwe ◽  
Jean-Claude Malela-Majika ◽  
Muhammad Aslam
Keyword(s):  
Parameter Estimation ◽  
Measurement Errors ◽  
Moving Average ◽  
Autocorrelated Observations ◽  
The Mean ◽  
Weighted Moving Average

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.

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