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 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 Application of robust multivariate control chart with Winsorized Mean: a case study

2019 ◽  
Vol 15 (S1) ◽  
pp. 309-318
Author(s):  
Angellys P. Ariza Guerrero ◽  
Rister Barreto Pombo ◽  
Roberto J. Herrera Acosta
Keyword(s):  
Control Chart ◽  
Multivariate Control Chart ◽  
Multivariate Control

A Case Study on the Establishment of Upper Control Limit to Detect Vessel’s Main Engine Failures using Multivariate Control Chart

2018 ◽  
Vol 55 (6) ◽  
pp. 505-513 ◽  
Author(s):  
Young-Mok Bae ◽  
Min-Jun Kim ◽  
Kwang-Jae Kim ◽  
Chi-Hyuck Jun ◽  
Sang-Su Byeon ◽  
...  
Keyword(s):  
Control Chart ◽  
Control Limit ◽  
Multivariate Control Chart ◽  
Main Engine ◽  
Multivariate Control

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 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 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 MULTIVARIATE CONTROL CHARTS BASED ON DATA DEPTH FOR SUBGROUP LOCATION AND SCALE - CASE STUDY

2018 ◽  
Vol 6 ◽  
pp. 1042-1049
Author(s):  
Izabela D. Czabak-Górska
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Quality Characteristics ◽  
Data Depth ◽  
Multivariate Control Charts ◽  
Production Practice ◽  
Classic Approach ◽  
Multivariate Control ◽  
T2 Control Chart

The purpose of the article is to present a method for determining control charts, which allow to control few interrelated quality characteristics. Often, in production practice, there is a need to simultaneously control several interrelated quality characteristics. The use of univariate control charts, separately for each quality characteristics, may lead to inadequate corrective actions of a production process. In such situations, it is recommended to use multivariate control charts, for example, the T2 control chart. However, the use of this classic approach involves making complicated calculations. Therefore, the author of this paper suggests using multivariate control charts based on data depth proposed by Liu.  In this paper, the author presented the idea and principles of the multivariate control chart based on data depth and then, using it to assess the statistical stability of the process in a manufacturing company, engaged in the production of window fittings.

SURVEILLANCE OF DIABETES PREVALENCE RATE THROUGH THE DEVELOPMENT OF A MARKOV-BASED CONTROL CHART

2012 ◽  
Vol 12 (04) ◽  
pp. 1250083
Author(s):  
PERSHANG DOKOUHAKI ◽  
RASSOUL NOOROSSANA
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
High Performance ◽  
Discrete Data ◽  
Correlated Data ◽  
Statistical Process ◽  
Control Charting ◽  
Attribute Quality ◽  
Related Process

In the field of statistical process control (SPC), usually two issues are addressed; the variables and the attribute quality characteristics control charting. Focusing on discrete data generated from a process to be monitored, attributes control charts would be useful. The discrete data could be classified into two categories; the independent and auto-correlated data. Regarding the independence in the sequence of discrete data, the typical Shewhart-based control charts, such as p-chart and np-chart would be effective enough to monitor the related process. But considering auto-correlation in the sequence of the data, such control charts would not workanymore. In this paper, considering the auto-correlated sequence of X1, X2,…, Xt,… as the sequence of zeros or ones, we have developed a control chart based on a two-state Markov model. This control chart is compared with the previously developed charts in terms of the average number of observations (ANOS) measure. In addition, a case study related to the diabetic people is investigated to demonstrate the applicability and high performance of the developed chart.

Improving Phase I Monitoring of Dirichlet Regression Profiles

2018 ◽  
Vol 25 (06) ◽  
pp. 1850030 ◽  
Author(s):  
Hourieh Foroutan ◽  
Amirhossein Amiri ◽  
Reza Kamranrad
Keyword(s):  
Phase I ◽  
Control Chart ◽  
Control Charts ◽  
Compositional Data ◽  
Ratio Test ◽  
Statistical Process ◽  
Explanatory Variables ◽  
Monitoring Procedure ◽  
Multivariate Control

In most statistical process control (SPC) applications, quality of a process or product is monitored by univariate or multivariate control charts. However, sometimes a functional relationship between a response variable and one or more explanatory variables is established and monitored over time. This relationship is called “profile” in SPC literature. In this paper, we specifically consider processes with compositional data responses, including multivariate positive observations summing to one. The relationship between compositional data responses and explanatory variables is modeled by a Dirichlet regression profile. We develop a monitoring procedure based on likelihood ratio test (lrt) for Phase I monitoring of Dirichlet regression profiles. Then, we compare the performance of the proposed method with the best method in the literature in terms of probability of signal. The results of simulation studies show that the proposed control chart has better performance in Phase I monitoring than the competing control chart. Moreover, the proposed method is able to estimate the real time of a change as well. The performance of this feature is also investigated through simulation runs which show the satisfactory performance. Finally, the application of the proposed method is illustrated based on a real case in comparison with the existing method.

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