scholarly journals Robust Multivariate Shewhart Control Chart Based on the Stahel-Donoho Robust Estimator and Mahalanobis Distance for Multivariate Outlier Detection

Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2772
Author(s):  
Ishaq Adeyanju Raji ◽  
Nasir Abbas ◽  
Mu’azu Ramat Abujiya ◽  
Muhammad Riaz
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Real Life ◽  
Robust Estimator ◽  
Estimation Of Parameters ◽  
Run Length ◽  
Control Charting ◽  
Shewhart Control ◽  
Multivariate Control Chart ◽  
Multivariate Control

While researchers and practitioners may seamlessly develop methods of detecting outliers in control charts under a univariate setup, detecting and screening outliers in multivariate control charts pose serious challenges. In this study, we propose a robust multivariate control chart based on the Stahel-Donoho robust estimator (SDRE), whilst the process parameters are estimated from phase-I. Through intensive Monte-Carlo simulation, the study presents how the estimation of parameters and presence of outliers affect the efficacy of the Hotelling T2 chart, and then how the proposed outlier detector brings the chart back to normalcy by restoring its efficacy and sensitivity. Run-length properties are used as the performance measures. The run length properties establish the superiority of the proposed scheme over the default multivariate Shewhart control charting scheme. The applicability of the study includes but is not limited to manufacturing and health industries. The study concludes with a real-life application of the proposed chart on a dataset extracted from the manufacturing process of carbon fiber tubes.

scholarly journals On multivariate control charts

Production ◽  
2011 ◽  
Vol 21 (2) ◽  
pp. 235-241 ◽  
Author(s):  
Marianne Frisén
Keyword(s):  
Control Chart ◽  
Industrial Production ◽  
Control Charts ◽  
Multivariate Control Charts ◽  
Multivariate Control Chart ◽  
Multivariate Control

Industrial production requires multivariate control charts to enable monitoring of several components. Recently there has been an increased interest also in other areas such as detection of bioterrorism, spatial surveillance and transaction strategies in finance. In the literature, several types of multivariate counterparts to the univariate Shewhart, EWMA and CUSUM methods have been proposed. We review general approaches to multivariate control chart. Suggestions are made on the special challenges of evaluating multivariate surveillance methods.

scholarly journals Comparison of short runs control chart and T2 Hotelling control chart for monitoring sunergy glass production process

2021 ◽  
Vol 2106 (1) ◽  
pp. 012019
Author(s):  
M Qori’atunnadyah ◽  
Wibawati ◽  
W M Udiatami ◽  
M Ahsan ◽  
H Khusna
Keyword(s):  
Production Process ◽  
Control Chart ◽  
Mass Production ◽  
Control Charts ◽  
Manufacturing Industry ◽  
Average Run Length ◽  
Glass Production ◽  
Short Run ◽  
Multivariate Control Chart ◽  
Multivariate Control

Abstract In recent years, the manufacturing industry has tended to reduce mass production and produce in small quantities, which is called “Short Run Production”. In such a situation, the course of the production process is short, usually, the number of productions is less than 50. Therefore, a control chart for the short run production process is required. This paper discusses the comparison between multivariate control chart for short run production (V control chart) and T2 Hotelling control chart applied to sunergy glass data. Furthermore, a simulation of Average Run Length (ARL) was carried out to determine the performance of the two control charts. The results obtained are that the production process has not been statistically controlled using either the V control chart or the T2 Hotelling control chart. The number of out-of-control on the control chart V using the the EWMA test is more than the T2 Hotelling control chart. Based on the ARL value, it shows that the V control chart is more sensitive than the T2 Hotelling control chart.

scholarly journals A Fuzzy EWMA Attribute Control Chart to Monitor Process Mean

Information ◽  
2018 ◽  
Vol 9 (12) ◽  
pp. 312 ◽  
Author(s):  
Muhammad Zahir Khan ◽  
Muhammad Farid Khan ◽  
Muhammad Aslam ◽  
Seyed Taghi Akhavan Niaki ◽  
Abdur Razzaque Mughal
Keyword(s):  
Fuzzy Control ◽  
Control Chart ◽  
Control Charts ◽  
Moving Average ◽  
Real Life ◽  
Fuzzy Data ◽  
Process Mean ◽  
Statistical Process ◽  
Control Charting ◽  
Real Life Data

Conventional control charts are one of the most important techniques in statistical process control which are used to assess the performance of processes to see whether they are in- or out-of-control. As traditional control charts deal with crisp data, they are not suitable to study unclear, vague, and fuzzy data. In many real-world applications, however, the data to be used in a control charting method are not crisp since they are approximated due to environmental uncertainties and systematic ambiguities involved in the systems under investigation. In these situations, fuzzy numbers and linguistic variables are used to grab such uncertainties. That is why the use of a fuzzy control chart, in which fuzzy data are used, is justified. As an exponentially weighted moving average (EWMA) scheme is usually used to detect small shifts, in this paper a fuzzy EWMA (F-EWMA) control chart is proposed to detect small shifts in the process mean when fuzzy data are available. The application of the newly developed fuzzy control chart is illustrated using real-life data.

scholarly journals Study on Likelihood-Ratio-Based Multivariate EWMA Control Chart Using Lasso

2021 ◽  
Vol 25 (1) ◽  
pp. 3-15
Author(s):  
Takumi Saruhashi ◽  
Masato Ohkubo ◽  
Yasushi Nagata
Keyword(s):  
Covariance Matrix ◽  
Likelihood Ratio ◽  
Control Chart ◽  
Control Charts ◽  
Ewma Chart ◽  
Regularization Parameters ◽  
Multivariate Control Chart ◽  
Multivariate Control ◽  
Mean Vector ◽  
Variance Covariance Matrix

Purpose: When applying exponentially weighted moving average (EWMA) multivariate control charts to multivariate statistical process control, in many cases, only some elements of the controlled parameters change. In such situations, control charts applying Lasso are useful. This study proposes a novel multivariate control chart that assumes that only a few elements of the controlled parameters change. Methodology/Approach: We applied Lasso to the conventional likelihood ratio-based EWMA chart; specifically, we considered a multivariate control chart based on a log-likelihood ratio with sparse estimators of the mean vector and variance-covariance matrix. Findings: The results show that 1) it is possible to identify which elements have changed by confirming each sparse estimated parameter, and 2) the proposed procedure outperforms the conventional likelihood ratio-based EWMA chart regardless of the number of parameter elements that change. Research Limitation/Implication: We perform sparse estimation under the assumption that the regularization parameters are known. However, the regularization parameters are often unknown in real life; therefore, it is necessary to discuss how to determine them. Originality/Value of paper: The study provides a natural extension of the conventional likelihood ratio-based EWMA chart to improve interpretability and detection accuracy. Our procedure is expected to solve challenges created by changes in a few elements of the population mean vector and population variance-covariance matrix.

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 Propuesta de Carta de Control Multivariada utilizando la Media Winsorizada basada en la Carta |S| / Proposed Multivariate Control Chart using Winsorized Mean based on the |S| Chart

2018 ◽  
Vol 29 (1) ◽  
pp. 65-79
Author(s):  
Rister Junior Barreto Pombo ◽  
Angellys Paola Ariza Guerrero ◽  
Roberto José Herrera Acosta
Keyword(s):  
Covariance Matrix ◽  
Control Chart ◽  
Control Charts ◽  
Quality Monitoring ◽  
Multivariate Control Charts ◽  
Global Quality ◽  
Simultaneous Evaluation ◽  
Multivariate Control Chart ◽  
Implementation Methodology ◽  
Multivariate Control

Resumen— El monitoreo global de la calidad de un producto está sujeto a la evaluación simultánea de varias de sus características; es necesario bajo estas condiciones la implementación de las cartas de control tipo multivariadas. La variabilidad, en este caso la matriz de varianza covarianza, es sin duda el más importante de los estadísticos desde la perspectiva multivariada, que puede ser monitoreada con distintas cartas. Entre éstas se encuentran: las cartas Shewhart, CUSUM y EWMA. En este artículo se desarrolla una metodología de implementación de la Media Winsorizada en la carta de control multivariada de varianza efectiva |S|, encontrando una gran utilidad en procesos con valores extremos.  El estudio muestra además una comparación entre la carta de control tradicional multivariante y la carta propuesta, que muestra mayor sensibilidad.Abstract— The global quality monitoring of a product is often subject to the simultaneous evaluation of several of its features; under these circumstances it is necessary to implement multivariate control charts. Variability, in this particular case, the variance-covariance matrix is indisputably the most important of the statistics from the multivariate perspective and it can be monitored with different charts, among these: Shewhart, CUSUM and EWMA. This article develops the Winsorized Mean in the effective variance multivariate control |S|-chart implementation methodology and it was demonstrated that the modification was more efficient when the sample hat outliers. This study shows a comparison between the traditional multivariate control chart and a proposed chart which was found to have more sensitivity. 

scholarly journals Multiple Dependent State Repetitive Sampling-Based Control Chart for Birnbaum–Saunders Distribution

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Muhammad Aslam ◽  
Ambreen Shafqat ◽  
G. Srinivasa Rao ◽  
Jean-Claude Malela-Majika ◽  
Sandile C. Shongwe
Keyword(s):  
Control Chart ◽  
Simulation Study ◽  
Control Charts ◽  
Average Run Length ◽  
Real Life ◽  
Detection Ability ◽  
Run Length ◽  
Comprehensive Comparison ◽  
Shift Detection ◽  
Dependent State

This paper proposes a new control chart for the Birnbaum–Saunders distribution based on multiple dependent state repetitive sampling (MDSRS). The proposed control chart is a generalization of the control charts based on single sampling, repetitive sampling, and multiple dependent state sampling. Its sensitivity is evaluated in terms of the average run length (ARL) using both exact formulae and simulations. A comprehensive comparison between the Birnbaum–Saunders distribution control chart based on the MDSRS method and other existing competing methods is provided using a simulation study as well as a real-life illustration. The results reveal that the proposed chart outperforms the existing charts considered in this study by having better shift detection ability.

scholarly journals Shewhart-Type Charts for Masked Data: A Strategy for Handling the Privacy Issue

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Said Farooq Shah ◽  
Zawar Hussain ◽  
Muhammad Riaz ◽  
Salman Arif Cheema
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Data Privacy ◽  
Average Run Length ◽  
Real Life ◽  
Performance Measure ◽  
Privacy Issue ◽  
Control Charting ◽  
Data Masking ◽  
Randomized Response Techniques

Data privacy is a serious issue and therefore needs our attention. In this study, we propose masking through randomized response techniques (RRTs) to ensure the privacy and thus to avoid falsification. We assume that the process characteristic is of sensitive nature, and due to privacy issue, the actual measurements cannot be shared with the monitoring team. In such situations, the producer is very likely to falsify the measurements. Consequently, the usual control charting techniques will mislead about the process status. We discuss different data masking strategies to be used with Shewhart-type control charts. The usual Shewhart-type control chart appears to be a subchart of the proposed charts. Average run length (ARL) is used as a performance measure of the study proposals. We have evaluated the performance of the proposed charts for different shift sizes and under different intensities of masking. We have also carried out a comparative analysis for various models under varying sensitivity parameters. We have also compared the performance of the proposals with the traditional Shewhart chart. It is observed that the B-L control chart under the RRT model performs better for smaller shifts and for larger shift sizes, the G-B chart under an unrelated question model tperforms better. A real-life application of the study proposal is also considered where monitoring of thickness of paint on refrigerators is of interest.

scholarly journals Multivariate Control Chart and Lee–Carter Models to Study Mortality Changes

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2093
Author(s):  
Gisou Díaz-Rojo ◽  
Ana Debón ◽  
Jaime Mosquera
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Causes Of Death ◽  
Mortality Model ◽  
Probability Of Death ◽  
Multivariate Control Chart ◽  
Model Residuals ◽  
Multivariate Control ◽  
Carter Model

The mortality structure of a population usually reflects the economic and social development of the country. The purpose of this study was to identify moments in time and age intervals at which the observed probability of death is substantially different from the pattern of mortality for a studied period. Therefore, a mortality model was fitted to decompose the historical pattern of mortality. The model residuals were monitored by the T2 multivariate control chart to detect substantial changes in mortality that were not identified by the model. The abridged life tables for Colombia in the period 1973–2005 were used as a case study. The Lee–Carter model collects information regarding violence in Colombia. Therefore, the years identified as out-of-control in the charts are associated with very early or quite advanced ages of death and are inversely related to the violence that did not claim as many victims at those ages. The mortality changes identified in the control charts pertain to changes in the population’s health conditions or new causes of death such as COVID-19 in the coming years. The proposed methodology is generalizable to other countries, especially developing countries.

scholarly journals On Performance of Two-Parameter Gompertz-Based X¯ Control Charts

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Johnson A. Adewara ◽  
Kayode S. Adekeye ◽  
Olubisi L. Aako
Keyword(s):  
Control Chart ◽  
Coverage Probability ◽  
Control Charts ◽  
Average Run Length ◽  
Real Life ◽  
Correction Method ◽  
Gompertz Distribution ◽  
Real Life Data ◽  
Control Limits ◽  
Two Parameter

In this paper, two methods of control chart were proposed to monitor the process based on the two-parameter Gompertz distribution. The proposed methods are the Gompertz Shewhart approach and Gompertz skewness correction method. A simulation study was conducted to compare the performance of the proposed chart with that of the skewness correction approach for various sample sizes. Furthermore, real-life data on thickness of paint on refrigerators which are nonnormal data that have attributes of a Gompertz distribution were used to illustrate the proposed control chart. The coverage probability (CP), control limit interval (CLI), and average run length (ARL) were used to measure the performance of the two methods. It was found that the Gompertz exact method where the control limits are calculated through the percentiles of the underline distribution has the highest coverage probability, while the Gompertz Shewhart approach and Gompertz skewness correction method have the least CLI and ARL. Hence, the two-parameter Gompertz-based methods would detect out-of-control faster for Gompertz-based X¯ charts.

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