scholarly journals Bagan Kendali Robust Multivariat untuk Pengamatan Individual

2018 ◽  
Vol 15 (2) ◽  
pp. 34
Author(s):  
Erna Tri Herdiani
Keyword(s):  
Covariance Matrix ◽  
Extreme Point ◽  
Control Chart ◽  
Minimum Covariance Determinant ◽  
Individual Observation ◽  
Calculation Results ◽  
Multivariate Control ◽  
Mean Vector ◽  
Group Observation

AbstractThe most widely used of control chart in multivariate control processing is control chart T2 Hotelling. There are 2 kinds of control chart T2 Hotelling, namely T2 Hotelling for group observation and T2 Hotelling  for individual observation. In this paper, discuss the control chart T2 Hotelling for individual observation. This control chart is used for monitoring of mean vector and sample of covariance matrix.   Mean vector and sample of covariance matrix are very sensitive with respect to extreme point (outliers). Therefore, it is needed  an estimator of mean vector and has a stocky population covariance matrix to the outliers data. One method that can be used to detect data that contains outliers is  Minimum Covariance Determinant (MCD). From the calculation results, obtained that  control chart T2 Hotelling by using Fast-MCD algorithm is more sensitive to detect outliers data  than  T2 Hotelling classically.Keyword: T2 Hotelling, Minimum Covariance Determinant (MCD), robust, outlier AbstrakBagan kendali yang  paling banyak digunakan dalam pengendalian proses secara multivariat adalah bagan kendali T2 Hotelling. Ada 2 jenis dari bagan kendali  Hotelling yaitu bagan kendali  Hotelling untuk pengamatan kelompok dan individual. Pada tulisan ini membahas bagan kendali  Hotelling untuk pengamatan individual. Bagan kendali ini digunakan untuk memonitor vektor  rata-rata dan matriks kovariansi sampel. Vektor rata-rata dan matriks kovariansi sampel sangat sensitif terhadap titik ekstrim (outliers). Oleh karena itu dibutuhkan estimator vektor rata-rata dan matriks kovariansi populasi yang kekar terhadap data outliers. Salah satu metode yang dapat digunakan untuk mendeteksi data yang mengandung outliers adalah Minimum Covariance Determinant (MCD). Dari hasil perhitungan diperoleh bahwa bagan kendali T2 Hotelling dengan algoritma Fast-MCD lebih sensitif mendeteksi data outliers daripada T2 Hotelling klasik.Kata Kunci: T2 Hotelling, Minimum Covariance Determinant (MCD), robust, outlier.

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.

scholarly journals New Robust MEWMA Control Chart for Monitoring Contaminated Data

2019 ◽  
Vol 8 (10) ◽  
pp. 2773-2780
Keyword(s):  
False Alarm ◽  
Covariance Matrix ◽  
Control Chart ◽  
Time Series Data ◽  
Simulated Data ◽  
Series Data ◽  
Random Pattern ◽  
Contaminated Data ◽  
Mewma Control Chart ◽  
Mean Vector

Multivariate Exponential Weighted Moving Average (MEWMA), E 2 control chart is a popular multivariate control chart for monitoring the stability of time series data (non-random pattern). However, in this paper, we have shown that the existing MEWMA, E 2 control chart is sensitive in contaminated data or in the presence of outliers. To address this problem, this paper proposed an alternative MEWMA E 2 control chart using robust mean vector and covariance matrix instead of the classical mean vector and covariance matrix respectively. The classical mean vector in MEWMA E 2 control chart is replaced by Winsorized Modified One-step M-estimator (WM) while the classical covariance matrix is replaced by the Winsorized covariance matrix. The proposed MEWMA E 2 control chart known as robust MEWMA control chart, denoted as RE2 control chart. The control limit for the RE2 control chart was calculated based on simulated data. The performance of RE2 and existing MEWMA E 2 control charts are based on the false alarm rate. The result revealed that the RE2 control chart is more effective in controlling false alarm rates as compared to the existing MEWMA, E 2 control chart. The zinc-lead flotation data show that the RE2 performs better in application.

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. 

POWER PROPERTIES OF THE T2 CONTROL CHART

1995 ◽  
Vol 02 (01) ◽  
pp. 1-14 ◽  
Author(s):  
SIEBRAND J. WIERDA ◽  
TON STEERNEMAN
Keyword(s):  
Covariance Matrix ◽  
Correlation Coefficient ◽  
Control Chart ◽  
Bivariate Case ◽  
Control Situation ◽  
The Mean ◽  
The Impact ◽  
T2 Control Chart ◽  
Mean Vector ◽  
Over Time

The T2 control chart is a multivariate SPC tool that monitors the mean vector of a process and that examines whether it remains stable over time. This paper examines the probability that the T2 control chart signals for an out-of-control situation. This probability is called the power of the chart. We study the effect on the power consequent on a change in the sample sizes, the dimension, or the level. For the bivariate case, we consider the impact on the power consequent on a change in the correlation coefficient. Finally, we examine what happens if the assumption that the covariance matrix is stable over time is violated.

A Robust MEWMA Control Chart Based on FAST-MCD Algorithm

2012 ◽  
Vol 562-564 ◽  
pp. 1907-1911
Author(s):  
Zhe Li ◽  
Rui Miao ◽  
Chuan Qi Wei ◽  
Ze Feng Li ◽  
Zhi Bin Jiang
Keyword(s):  
Covariance Matrix ◽  
Control Chart ◽  
Robust Statistics ◽  
Sample Covariance Matrix ◽  
Initial Sample ◽  
Multivariate Process ◽  
Sample Covariance ◽  
Sample Data ◽  
Mewma Control Chart ◽  
Mean Vector

MEWMA control chart is generally used to monitor slight deviation of mean vector for multivariate process. Sample covariance matrix S is often applied to estimate population covariance . When the initial sample data contains outliers, the results may be impacted and then weak the probabilities of control chart signals since the conventional mean vector and covariance matrix are not robust statistics. In this paper, FAST-MCD algorithm is used to build a robust covariance matrix to improve the robustness of MEWMA control chart. From the analysis of samples, the robust MEMWA control chart based on FAST-MCD algorithm has better immunity to small amount of noise in the initial samples.

On the multivariate progressive control chart for effective monitoring of covariance matrix

2021 ◽  
Author(s):  
Jimoh Olawale Ajadi ◽  
Kevin Hung ◽  
Muhammad Riaz ◽  
Nurudeen Ayobami Ajadi ◽  
Tahir Mahmood
Keyword(s):  
Covariance Matrix ◽  
Control Chart
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