Variable Sample Size Control Charts for Monitoring the Multivariate Coefficient of Variation Based on Median Run Length and Expected Median Run Length

The monitoring of a well-functioning process system has always held significant importance. In recent times, there has been notable attention towards employing control charts to oversee both univariate and multivariate coefficients of variation (MCV). This shift is in response to the concern of erroneous outcomes that can arise when traditional control charts are applied under the condition of dependent mean and standard deviation, as highlighted by prior research. To address this, the remedy lies in adopting the coefficient of variation. Furthermore, this study underscores the application of MCV in scenarios where multiple quality attributes are simultaneously under surveillance within an industrial process. This aspect has demonstrated considerable enhancement in chart performance, especially when incorporating the variable sample size (VSS) feature into the MCV chart. Adaptive VSS, evaluated through metrics like median run length (MRL) and expected median run length (EMRL), is also integrated for MCV monitoring. In contrast to earlier studies that predominantly focused on average run length (ARL), this research acknowledges the potential inaccuracies in ARL measurement. In this study, two optimal designs for VSS MCV charts are formulated by minimizing two criteria: firstly, MRL; and secondly, EMRL, both accounting for deterministic and unknown shift sizes. Additionally, to assess the distribution's variability in run lengths, the study provides the 5th and 95th percentiles. The research delves into two VSS schemes: one with a defined small sample size (nS), and another with a predetermined large sample size (nL) for the initial subgroup (n(1)). The approach taken involves the development of a Markov chain method for designing and deriving performance measures of the proposed chart. These measures include MRL and EMRL. Moreover, a comparative analysis between the proposed chart's performance and the standard MCV chart (STD) is presented in terms of MRL and EMRL criteria. The outcomes illustrate the superiority of the proposed chart over the STD MCV chart for all shift sizes, whether they are upward or downward, and when n(1) equals nS or nL

Optimal statistical designs of multivariate EWMA and multivariate CUSUM charts based on average run length and median run leng

Carta kawalan multivariat ialah alat yang berkuasa dalam kawalan proses yang melibatkan kawalan serentak beberapa cirian kualiti yang berkorelasi. Carta-carta multivariat hasil tambah longgokan {MCUSUM) dan multivariat purata bergerak berpemberat eksponen (MEWMA) sentiasa dicadangkan dalam kawalan proses apabila pengesanan cepat anjakan tetap yang keciJ atau sederhana dalam vektor min adalah diingini. A multivariate control chart is a powerful tool in process control involving a simultaneous monitoring of several correlated quality characteristics. The multivariate cumulative sum (MCUSUM) and multivariate exponentially weighted moving average (MEWMA) charts are often recommended in process monitoring when a quick detection of small or moderate sustained shifts in the mean vector is desired

Optimal Designs Of Univariate And Multivariate Synthetic Control Charts Based On Median Run Length

Univariate and multivariate control charts are usually optimally designed using average run length (ARL) as a sole measure of the charts’ performances. It is well known that the shape of the run length distribution for the univariate and multivariate charts changes from highly skewed when the process is in-control to approximately symmetric for large process shifts. Therefore, the median run length (MRL) is a more meaningful interpretation of the in-control and out-of-control performances of the charts and provides additional information not given by the average run length (ARL)

Adaptive Control Charts For Monitoring The Univariate And Multivariate Coefficient Of Variation

The first objective of this research is to propose a univariate adaptive CV chart using the variable sample size and sampling interval (VSSI) approach, called the VSSI CV chart, to monitor the process CV. The VSSI CV chart will be optimally designed, where two parameters, namely the sample size and sampling intervals are allowed to vary. In real life scenarios, there are many situations in which a simultaneous monitoring of two or more correlated quality characteristics is necessary. Erroneous conclusions will occur if quality practitioners use univariate control charts to monitor a multivariate process. The second objective of this study is to propose CV charts for monitoring the multivariate process CV (MCV) by adopting the adaptive procedures. Three new charts for monitoring the MCV, namely the variable sampling interval MCV (by varying the sampling interval), variable sample size MCV (by varying the sample size) and VSSI MCV (by varying both the sample size and sampling interval) charts are proposed to improve the performance of the existing MCV chart. All the charts proposed for monitoring the univariate and multivariate CVs are designed using the Markov chain approach. The implementation procedures and optimization designs of these proposed charts are enumerated in this xxiv thesis

Design of side-sensitive double sampling control schemes for monitoring the location parameter

Double sampling procedure is adapted from a statistical branch called acceptance sampling. The first Shewhart-type double sampling monitoring scheme was introduced in the statistical process monitoring (SPM) field in 1974. The double sampling monitoring scheme has been proven to effectively decrease the sampling effort and, at the same time, to decrease the time to detect potential out-of-control situations when monitoring the location, variability, joint location and variability using univariate or multivariate techniques. Consequently, an overview is conducted to give a full account of all 76 publications on double sampling monitoring schemes that exist in the SPM literature. Moreover, in the review conducted here, these are categorized and summarized so that any research gaps in the SPM literature can easily be identified. Next, based on the knowledge gained from the literature review about the existing designs for monitoring the process mean, a new type of double sampling design is proposed. The new charting region design lead to a class of a control charts called a side-sensitive double sampling (SSDS) monitoring schemes. In this study, the SSDS scheme is implemented to monitor the process mean when the underlying process parameters are known as well as when they are unknown. A variety of run-length properties (i.e., the 5th, 25th, 50th, 75th, 95th percentiles, the average run-length (), standard deviation of the run-length (), the average sample size () and the average extra quadratic loss () metrics) are used to design and implement the new SSDS scheme. Comparisons with other established monitoring schemes (when parameters are known and unknown) indicate that the proposed SSDS scheme has a better overall performance. Illustrative examples are also given to facilitate the real-life implementation of the proposed SSDS schemes. Finally, a list of possible future research ideas is given with hope that this will stimulate more future research on simple as well as complex double sampling schemes (especially using the newly proposed SSDS design) for monitoring a variety of quality characteristics in the future.StatisticsM. Sc. (Statistics

Control Charts With Estimated Process Parameters And A Proposed Coefficient Of Variation Chart

Carta kawalan menerima perhatian besar dalam Kawalan Proses Berstatistik (SPC) sebagai alat yang paling berguna dalam pengesanan anjakan proses supaya tindakan pembetulan boleh diambil untuk mengenal pasti dan menyingkirkan sebab-sebab terumpukkan yang hadir. Objektif utama penyelidikan ini adalah untuk menangani masalah anggaran parameter proses bagi carta larian kumpulan dengan kepekaan sisi (carta SSGR) dan carta pensampelan ganda dua sintetik (carta SDS). Kebanyakan carta kawalan memerlukan andaian bahawa nilai sasaran parameter proses dalam kawalan, iaitu min dan sisihan piawai adalah diketahui untuk pengiraan had-had kawalan serta statistik carta kawalan. Malangnya, parameter proses lazimnya tidak diketahui dalam keadaan sebenar, yang mana nilainya dianggarkan daripada set data Fasa-I dalam kawalan. Dalam penyelidikan ini, prestasi carta-carta SSGR dan SDS dengan parameter proses yang dianggarkan dibandingkan dengan prestasi carta-carta yang sepadan apabila parameter proses diketahui. Control charts receive great attention in Statistical Process Control (SPC) as the most useful tool in detecting process shifts so that corrective actions can be taken to identify and eliminate the assignable causes that are present. The main objective of this research is to address the problems of estimation of process parameters for the side sensitive group runs (SSGR) chart and synthetic double sampling (SDS) chart. Most control charts require the assumption that the target values of the in-control process parameters, i.e. the mean and standard deviation are known for the computation of the control charts’ control limits and statistics. Unfortunately, process parameters are usually unknown in real situations, where they are estimated from an in-control Phase-I dataset. In this research, the performances of the SSGR and SDS charts with estimated process parameters are compared with that of their known process parameters counterparts

ISBIS 2016: Meeting on Statistics in Business and Industry

This Book includes the abstracts of the talks presented at the 2016 International Symposium on Business and Industrial Statistics, held at Barcelona, June 8-10, 2016, hosted at the Universitat Politècnica de Catalunya - Barcelona TECH, by the Department of Statistics and Operations Research. The location of the meeting was at ETSEIB Building (Escola Tecnica Superior d'Enginyeria Industrial) at Avda Diagonal 647. The meeting organizers celebrated the continued success of ISBIS and ENBIS society, and the meeting draw together the international community of statisticians, both academics and industry professionals, who share the goal of making statistics the foundation for decision making in business and related applications. The Scientific Program Committee was constituted by: David Banks, Duke University Amílcar Oliveira, DCeT - Universidade Aberta and CEAUL Teresa A. Oliveira, DCeT - Universidade Aberta and CEAUL Nalini Ravishankar, University of Connecticut Xavier Tort Martorell, Universitat Politécnica de Catalunya, Barcelona TECH Martina Vandebroek, KU Leuven Vincenzo Esposito Vinzi, ESSEC Business Schoo

A rare event classification in the advanced manufacturing system: focused on imbalanced datasets

In many industrial applications, classification tasks are often associated with imbalanced class labels in training datasets. Imbalanced datasets can severely affect the accuracy of class predictions, and thus they need to be handled by appropriate data processing before analyzing the data since most machine learning techniques assume that the input data is balanced. When this imbalance problem comes with highdimensional space, feature extraction can be applied. In Chapter 2, we present two versions of feature extraction techniques called CL-LNN and RD-LNN in a time series dataset based on the nearest neighbor combined with machine learning algorithms to detect a failure of the paper manufacturing machinery earlier than its occurrence from the multi-stream system monitoring data. The nearest neighbor is applied to each separate feature instead of the whole 61 features to address the curse of dimensionality. Also, another technique for the skewness between class labels can be solved by either oversampling minorities or downsampling majorities in class. In the chapter 3, we are seeking to find a better way of downsampling by selecting the most informative samples in the given imbalanced dataset through the active learning strategy to mitigate the effect of imbalanced class labels. The data selection for downsampling is performed by the criterion used in optimal experimental designs, from which the generalization error of the trained model is minimized in a sequential manner under the penalized logistic regression as a classification model. We also suggest that the performance is significantly improved, especially with the highly imbalanced dataset, e.g., the imbalanced ratio is greater than ten if tuning hyper-parameter and costweight method are applied to the active downsampling technique. The research is further extended to cover nonlinearity using nonparametric logistic regression, and performance-based active learning (PBAL) is proposed to enhance the performance compared to the existing ones such as D-optimality and A-optimality.Includes bibliographical references

Some theoretical comments regarding the run-length properties of the synthetic and runs-rules monitoring schemes – Part 1: zero-state

Please read abstract in the article.The SARChI Chair at the University of Pretoria, the National Research Foundation (NRF) and Department of Science and Technology’s Innovation Doctoral scholarship, and the Department of Statistics’ STATOMET.hj2020Science, Mathematics and Technology EducationStatistic