scholarly journals On the Efficient Monitoring of Multivariate Processes with Unknown Parameters

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 823 ◽  
Author(s):  
Nasir Abbas ◽  
Muhammad Riaz ◽  
Shabbir Ahmad ◽  
Muhammad Abid ◽  
Babar Zaman
Keyword(s):  
Control Charts ◽  
Average Run Length ◽  
Quality Characteristics ◽  
Quadratic Loss ◽  
Unknown Parameters ◽  
Efficient Manner ◽  
Data Set ◽  
Run Length ◽  
Length Standard ◽  
Usual Scheme

Control charts are commonly used tools that deal with monitoring of process parameters in an efficient manner. Multivariate control charts are more practical and are of greater importance for timely detection of assignable causes in multiple quality characteristics. This study deals with multivariate memory control charts to address smaller shifts in process mean vector. By adopting a new homogeneous weighting scheme, we have designed an efficient structure for multivariate process monitoring. We have also investigated the effect of an estimated variance covariance matrix on the proposed chart by considering different numbers and sizes of subgroups. We have evaluated the performance of the newly proposed multivariate chart under different numbers of quality characteristics and varying sample sizes. The performance measures used in this study include average run length, standard deviation run length, extra quadratic loss, and relative average run length. The performance analysis revealed that the proposed control chart outperforms the usual scheme under both known and estimated parameters. An application of the study proposal is also presented using a data set related to Olympic archery, for the monitoring of the location of arrows over the concentric rings on the archery board.

scholarly journals Multivariate Statistical Quality Control Based on Ranked Set Sampling

2017 ◽  
Vol 14 (1) ◽  
pp. 1
Author(s):  
Hakan Eygü ◽  
M. Suphi Özçomak
Keyword(s):  
Control Charts ◽  
Sampling Methods ◽  
Average Run Length ◽  
Ranked Set Sampling ◽  
Multivariate Statistical ◽  
Run Length ◽  
Hotelling's T2 ◽  
Median Ranked Set Sampling ◽  
Hotelling’S T2 ◽  
T2 Control Chart

The sample of the study was formed using simple random sampling, ranked set sampling, extreme ranked set sampling and median ranked set sampling. At the end of this process, the researcher created Hotelling’s T2 control charts, a multivariate statistical process control method. The performances of SRS, RSS, ERSS and MRSS sampling methods were compared to one another using these control charts. A simulation was performed to see the average run-length values for Hotelling’s T2 control charts, and these findings were also used for the comparison of the sampling performances.At the end of the study, the researcher formed a sample using median ranked set sampling and created the Hotelling’s T2 control chart. As a result of this operation, the researcher found that there was an out-of-control signal in the process, while there was no such signal in other sampling methods. When the average run-length values obtained from Hotelling’s T2 control charts were compared, it was seen that a shift in the process was detected by the ranked set sampling earlier, when compared to other sampling methods. This paper it can be said that the methods used are unique to the literature because they are applied to multivariate data.

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 new alternative Hotelling’s T2 control chart using MEWMA to monitor minimal mean deviation

2021 ◽  
Vol 336 ◽  
pp. 09021
Author(s):  
Kunyun Wang ◽  
Qianqian Li ◽  
Guangdong Li
Keyword(s):  
Production Process ◽  
Control Chart ◽  
Average Run Length ◽  
Quality Characteristics ◽  
Mean Deviation ◽  
Sample Sizes ◽  
Forgetting Factor ◽  
Good Efficiency ◽  
Run Length ◽  
T2 Control Chart

Hotelling T2 control chart not only reflects the correla-tions between different quality characteristics but also has good efficiency on monitoring multivariate quality characteristics in production process. A new alternative control chart was constructed after the original products data are processed by using multivariate exponentially weighted moving average for cumulating failure effects because T2 control chart is ineffective on detecting minimal mean deviations. Exemplified by bivariate quality characteristics, we compared the monitoring effects of Hotelling T2 control chart and new control chart which is called as T2MEWMA control chart. Paper showed the improved T2MEWMA control chart has smaller average run length than Hotelling T2 control chart on monitoring minimal mean deviation and that also studied the relationships between T2MEWMA control chart’s forgetting factor, sample sizes N and type II error. It indicated the smaller forgetting factor is more sensitive to minimal mean value deviation and that average run length tended to become bigger gradually along with increase of sample sizes N when production process is out of control.

scholarly journals Nonparametric Double EWMA Control Chart for Process Monitoring

2016 ◽  
Vol 39 (2) ◽  
pp. 167 ◽  
Author(s):  
Muhammad Riaza ◽  
Saddam Akber Abbasib
Keyword(s):  
Standard Deviation ◽  
Control Chart ◽  
Average Run Length ◽  
Location Parameter ◽  
Quality Characteristic ◽  
Quadratic Loss ◽  
Run Length ◽  
Ewma Control Chart ◽  
Monitoring Process ◽  
Nonparametric Techniques

<p>In monitoring process parameters, we assume normality of the quality characteristic of interest, which is an ideal assumption. In many practical sit- uations, we may not know the distributional behavior of the data, and hence, the need arises use nonparametric techniques. In this study, a nonparametric double EWMA control chart, namely the NPDEWMA chart, is proposed to ensure efficient monitoring of the location parameter. The performance of the proposed chart is evaluated in terms of different run length properties, such as average, standard deviation and percentiles. The proposed scheme is compared with its recent existing counterparts, namely the nonparametric EWMA and the nonparametric CUSUM schemes. The performance mea- sures used are the average run length (ARL), standard deviation of the run length (SDRL) and extra quadratic loss (EQL). We observed that the pro- posed chart outperforms the said existing schemes to detect shifts in the process mean level. We also provide an illustrative example for practical considerations.</p>

In-control robustness comparison of different control charts

2017 ◽  
Vol 40 (13) ◽  
pp. 3860-3871 ◽  
Author(s):  
Muhammad Abid ◽  
Hafiz Zafar Nazir ◽  
Muhammad Riaz ◽  
Zhengyan Lin
Keyword(s):  
Standard Deviation ◽  
Control Chart ◽  
Control Charts ◽  
Average Run Length ◽  
Location Parameter ◽  
Normal Distributions ◽  
Run Length ◽  
Design Structure ◽  
Control Robustness ◽  
Proper Design

Control charts are widely used to monitor the process parameters. Proper design structure and implementation of a control chart requires its in-control robustness, otherwise, its performance cannot be fairly observed. It is important to know whether a chart is sensitive to disturbances to the model (e.g. normality under which it is developed) or not. This study, explores the robustness of Mixed EWMA-CUSUM (MEC) control chart for location parameter under different non-normal and contaminated environments and compares it with its counterparts. The robustness of the MEC scheme and counterparts is evaluated by using the run length distributions, and for better assessment not only is in-control average run length (ARL) used, but also standard deviation of run length (SDRL) and different percentiles – that is, 5th, 50th and 95th– are considered. A careful insight is necessary in selection and application of control charts in non-normal and contaminated environments. It is observed that the in-control robustness performance of the MEC scheme is quite good in the case of normal, non-normal and contaminated normal distributions as compared with its competitor’s schemes.

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