A Neural Network Approach to Synthetic Control Chart for the Process Mean

In this project, a multivariate synthetic control chart for monitoring the process mean vector of skewed populations using weighted standard deviations has been proposed. The proposed chart incorporates the weighted standard deviation (WSD) method of Chang and Bai (2004) into the standard multivariate synthetic chart of Ghute and Shirke (2008)

Univariate And Multivariate Synthetic Control Charts For Monitoring The Process Mean Of Skewed Distributions

Alat yang paling berkuasa dalam Kawalan Kualiti Berstatistik (SQC) ialah carta kawalan. The most powerful tool in Statistical Quality Control (SQC) is the control chart. Control charts are now widely accepted and used in industries

A multivariate EWMA control chart for skewed populations using weighted variance method

This article proposes Multivariate Exponential Weighted Moving Average control chart for skewed population using heuristic Weighted Variance (WV) method, obtained by decomposing the variance into the upper and lower segments according to the direction and degree of skewness.This method adjusts the variance-covariance matrix of quality characteristics.The proposed chart, called WV-MEWMA hereafter, reduces to standard multivariate Exponential Weighted Moving Average control chart (standard MEWMA) when the underlying distribution is symmetric.In control and out-of-control ARLs of the proposed WV-MEWMA control chart are compared with those of the weighted standard deviation Exponential Weighted Moving Average (WSD-MEWMA) and (standard MEWMA) control charts for multivariate normal, lognormal and gamma distributions. In general, the simulation results show that the performance of the proposed WV-MEWMA chart is better than WSD-MEWMA and Standard MEWMA charts when the underlying distributions are skewed

A multivariate synthetic control chart for monitoring the process mean vector of skewed populations using weighted standard deviations

This article proposes a multivariate synthetic control chart for skewed populations based on the weighted standard deviation method.The proposed chart incorporates the weighted standard deviation method into the standard multivariate synthetic control chart.The standard multivariate synthetic chart consists of the Hotelling's T 2 chart and the conforming run length chart.The weighted standard deviation method adjusts the variance–covariance matrix of the quality characteristics and approximates the probability density function using several multivariate normal distributions. The proposed chart reduces to the standard multivariate synthetic chart when the underlying distribution is symmetric.In general, the simulation results show that the proposed chart performs better than the existing multivariate charts for skewed populations and the standard T 2 chart, in terms of false alarm rates as well as moderate and large mean shift detection rates based on the various degrees of skewnesses

Robust control charts via winsorized and trimmed estimators

In process control, cumulative sum (CUSUM), exponentially weighted moving average (EWMA), and synthetic control charts are developed to detect small and moderate shifts. Small shifts which are hard to detect can be costly to the process control if left undetected for a long period. These control charts are not reliable under non-normality as the design structure of the charts is based on the sample mean. Sample mean is sensitive to outliers, a common cause of non-normality. In circumventing the problem, this study applied robust location estimators in the design structure of the control charts, instead of the sample mean. For such purpose, four robust estimators namely 20%-trimmed mean, median, modified one-step M-estimator (MOM), and winsorized MOM (WMOM) were chosen. The proposed charts were tested on several conditions which include sample sizes, shift sizes, and different types of non-normal distributions represented by the g-and-h distribution. Random variates for each distribution were obtained using SAS RANNOR before transforming them to the desired type of distribution. Robustness and detection ability of the charts were gauged through average run length (ARL) via simulation study. Validation of the charts’ performance which was done through real data study, specifically on potential diabetic patients at Universiti Utara Malaysia shows that robust EWMA chart and robust CUSUM chart outperform the standard charts. The findings concur with the results of simulation study. Even though robust synthetic chart is not among the best choice as it cannot detect small shifts as quickly as CUSUM or EWMA, its performance is much better than the standard chart under non-normality. This study reveals that all the proposed robust charts fare better than the standard charts under non-normality, and comparable with the latter under normality. The most robust among the investigated charts are EWMA control charts based on MOM and WMOM. These robust charts can fast detect small shifts regardless of distributional shapes and work well under small sample sizes. These characteristics suit the industrial needs in process monitoring