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

Nonparametric statistical process control : an overview and some results

An overview of the literature on some nonparametric or distribution-free quality control procedures is presented for univariate data. A nonparametric control chart is defined along with some general motivations and formulations. Various advantages of these charts are highlighted while some disadvantages of the more traditional, distribution-based. control charts are pointed out. Specific observations are made in the course of the review of articles and constructive criticism is offered. so that opportunities for further research can be identified. Connections to some areas of active research are made. such as sequential analysis, that are of relevance to process control. It is hoped that this article would lead to a wider acceptance of distribution-free control charts among the practitioners and would serve as an impetus to future research and development in this area

On the Bayesian optimization and robustness of event detection methods in NILM

A basic but crucial step to increase efficiency and save energy in residential settings is to have an accurate view of energy consumption. To monitor residential energy consumption cost-effectively, i.e., without relying on per-device monitoring equipment, non-intrusive load monitoring (NILM) provides an elegant solution. The aim of NILM is to disaggregate the total power consumption (as measured, e.g., by smart meters at the grid connection point of the household) into individual devices' power consumption, using machine learning techniques. An essential building block of NILM is event detection: detecting when appliances are switched on or off. Current state-of-the-art methods face two open issues. First, they are typically not robust to differences in base load power consumption and secondly, they require extensive parameter optimization. In this paper, both problems are addressed. First two novel and robust algorithms are proposed: a modified version of the chi-squared goodness-of-fit (x(2) GOF) test and an event detection method based on cepstrum smoothing. Then, a workflow using surrogate-based optimization (SBO) to efficiently tune these methods is introduced. Benchmarking on the BLUED dataset shows that both suggested algorithms outperform the standard x2 GOF test for traces with a higher base load and that they can be optimized efficiently using SBO. (C) 2017 Elsevier B.V. All rights reserved

Optimal Designs Of The Double Sampling X Chart Based On Parameter Estimation

Control charts, viewed as the most powerful and simplest tool in Statistical Process Control (SPC), are widely used in manufacturing and service industries. The double sampling (DS) X chart detects small to moderate process mean shifts effectively, while reduces the sample size. The conventional application of the DS X chart is usually investigated assuming that the process parameters are known. Nevertheless, the process parameters are usually unknown in practical applications; thus, they are estimated from an in-control Phase-I dataset. In this thesis, the effects of parameter estimation on the DS X chart’s performance are examined. By taking into consideration of the parameter estimation, the run length properties of the DS X chart are derived. Since the shape and the skewness of the run length distribution change with the magnitude of the process mean shift, the number of Phase-I samples and sample size, the widely applicable performance measure, i.e. the average run length (ARL) should not be used as a sole measure of a chart’s performance. For this reason, the ARL, the standard deviation of the run length (SDRL), the median run length (MRL), the percentiles of the run length distributions and the average sample size (ASS) are recommended to effectively evaluate the proposed DS X chart with estimated parameters

Optimal Design of a Revised Double Sampling X Chart Based on Median Run Length

In process control, it is very important to have a tool that is able to detect small shifts of a process mean. The revised double samplin

Optimal Designs Of The Double Sampling X Chart Based On Parameter Estimation

Control charts, viewed as the most powerful and simplest tool in Statistical Process Control (SPC), are widely used in manufacturing and service industries. The double sampling (DS) X chart detects small to moderate process mean shifts effectively, while reduces the sample size. The conventional application of the DS X chart is usually investigated assuming that the process parameters are known. Nevertheless, the process parameters are usually unknown in practical applications; thus, they are estimated from an in-control Phase-I dataset. In this thesis, the effects of parameter estimation on the DS X chart’s performance are examined. By taking into consideration of the parameter estimation, the run length properties of the DS X chart are derived. Since the shape and the skewness of the run length distribution change with the magnitude of the process mean shift, the number of Phase-I samples and sample size, the widely applicable performance measure, i.e. the average run length (ARL) should not be used as a sole measure of a chart’s performance. For this reason, the ARL, the standard deviation of the run length (SDRL), the median run length (MRL), the percentiles of the run length distributions and the average sample size (ASS) are recommended to effectively evaluate the proposed DS X chart with estimated parameters

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)