Process monitoring research with various estimator-based MEWMA control charts

This paper can be considered as an extension of the work of Tran et al (for monitoring compositional data using a multivariate exponentially weighted moving average MEWMA-compositional data [CoDa] chart) by taking into account potential measurement errors that are known to highly affect production processes. A linearly covariate error model with a constant error variance is used to study the impact of measurement errors on the MEWMA-CoDa control chart. In particular, the influence of the device parameters (σ M ,b), the number of independent observations m, and the the number of variables p are investigated in terms of the MEWMA optimal couples (r,H) as well as in terms of their corresponding ARLs. A comparison between the Hotelling-CoDa T 2 and the proposed chart is made in order to show that the MEWMA-CoDa chart is more efficient in detecting shifts in the presence of measurement errors. A real-life example of muesli production, using multiple measurements for each composition, is used to estimate the parameters and also to demonstrate how the MEWMA-CoDa can handle measurement errors to detect shifts in the process.

Section: Introductionmentioning

confidence: 99%

Performance of the MEWMA‐CoDa control chart in the presence of measurement errors

Zaidi

Castagliola

Tran

et al. 2020

“…Its properties and design stategies have been thoroughly investigated by many authors. For further details, see, for instance, Runger and Prabhu, 25 Prabhu and Runger, 26 Molnau et al, 27 Lee and Khoo, 28 Reynolds Jr. and Stoumbos, 29 Mahmoud and Maravelakis, 30 Wu et al, 31 and Chen et al 32 As far as we know, up to now, MEWMA-type charts have not been used for monitoring CoDa. Consequently, the purpose of this study is to propose a MEWMA-type control chart (denoted as MEWMA-CoDa control chart) for CoDa, based on the ilr approach, with each subgroup consisting of n > 1 sample units and to investigate its statistical performance.…”

Section: Introductionmentioning

confidence: 99%

“…Its properties and design stategies have been thoroughly investigated by many authors. For further details, see, for instance, Runger and Prabhu, Prabhu and Runger, Molnau et al, Lee and Khoo, Reynolds Jr. and Stoumbos, Mahmoud and Maravelakis, Wu et al, and Chen et al…”

Section: Introductionmentioning

confidence: 99%

Monitoring compositional data using multivariate exponentially weighted moving average scheme

Tran

Castagliola

Celano

et al. 2018

Recently, the monitoring of compositional data by means of control charts has been investigated in the statistical process control literature. In this article, we develop a Phase II multivariate exponentially weighted moving average control chart, for the continuous surveillance of compositional data based on a transformation into coordinate representation. We use a Markov chain approximation to determine the performance of the proposed multivariate control chart. The optimal multivariate exponentially weighted moving average smoothing constants, control limits, and out‐of‐control average run lengths have been computed for different combinations of the in‐control average run lengths and the number of variables. Several tables are presented and enumerated to show the statistical performance of the proposed control chart. An example illustrates the use of this chart on an industrial problem from a plant in Europe.

“…The case of monitoring multivariate nonlinear profiles was also examined in a study by Chou et al In their proposed approach, different profiles are first fitted by B‐splines, and then the deviations of the observed profile from the fitted profile are fed into a multivariate EWMA (MEWMA) control scheme for the purpose of process monitoring. Moreover, in a study by Wu et al, the performance of different population covariance matrix estimators for the MEWMA control charts has been investigated. One limitation of these approaches based on the MEWMA chart is that they also do not consider the heterogeneity in the data.…”

Section: Introductionmentioning

confidence: 99%

Statistical monitoring of multiple profiles simultaneously using Gaussian processes

Jahani

Kontar

Veeramani

et al. 2018

Profile monitoring is the application of control charts to monitor the stability of a process over time when the process can be characterized by a functional relationship between a response variable and 1 or more explanatory variables. Most of the research in profile monitoring has been focused on monitoring univariate profiles, while multivariate profile data are widely observed in practice. In this paper, a monitoring approach based on a multivariate Gaussian process (MGP) model is proposed to monitor multivariate profiles simultaneously. In this regard, using a non‐separable covariance function, a MGP model is fitted to represent the baseline in‐control multivariate profile. Then, the stability of the process is tracked by monitoring a distance measure between the new observations of the multivariate profile and the baseline in‐control model. A key advantage of this method is that it considers correlations both within profiles and between profiles. We also introduce, as a benchmark, a univariate Gaussian process‐based profile monitoring scheme modified for multivariate profiles. The performance of the proposed approaches is investigated and compared through numerical studies and a real‐world case study. The analysis confirms the effectiveness of the MGP‐based monitoring scheme for multivariate profiles.