arXiv subjects

Mohsen Ebadi

Publications and source records attributed to Mohsen Ebadi.

5 recordsLinked to original sources

arXiv2023

On Monitoring High-Dimensional Processes with Individual Observations

Modern data collecting methods and computation tools have made it possible to monitor high-dimensional processes. In this article, Phase II monitoring of high-dimensional processes is investigated when the available number of samples collected in Phase I is limitted in comparison to the number of variables. A new charting statistic for high-dimensional multivariate processes based on the diagonal elements of the underlying covariance matrix is introduced and a unified procedure for Phase I and II by employing a self-starting control chart is proposed. To remedy the effect of outliers, we adopt a robust procedure for parameter estimation in Phase I and introduce the appropriate consistent estimators. The statistical performance of the proposed method is evaluated in Phase II through average run length (ARL) criterion in the absence and presence of outliers and reveals that the proposed control chart scheme effectively detects various kinds of shifts in the process mean. Finally, we illustrate the applicability of our proposed method via a real-world example.

stat.ME↗

arXiv2022

Phase I Analysis of High-Dimensional Processes in the Presence of Outliers

One of the significant challenges in monitoring the quality of products today is the high dimensionality of quality characteristics. In this paper, we address Phase I analysis of high-dimensional processes with individual observations when the available number of samples collected over time is limited. Using a new charting statistic, we propose a robust procedure for parameter estimation in Phase I. This robust procedure is efficient in parameter estimation in the presence of outliers or contamination in the data. A consistent estimator is proposed for parameter estimation and a finite sample correction coefficient is derived and evaluated through simulation. We assess the statistical performance of the proposed method in Phase I in terms of the probability of signal criterion. This assessment is carried out in the absence and presence of outliers. We show that, in both phases, the proposed control chart scheme effectively detects various kinds of shifts in the process mean. Besides, we present two real-world examples to illustrate the applicability of our proposed method.

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arXiv2021

Statistical Monitoring of the Covariance Matrix in Multivariate Processes: A Literature Review

Monitoring several correlated quality characteristics of a process is common in modern manufacturing and service industries. Although a lot of attention has been paid to monitoring the multivariate process mean, not many control charts are available for monitoring the covariance matrix. This paper presents a comprehensive overview of the literature on control charts for monitoring the covariance matrix in a multivariate statistical process monitoring (MSPM) framework. It classifies the research that has previously appeared in the literature. We highlight the challenging areas for research and provide some directions for future research.

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arXiv2017

Remarks on Bayesian Control Charts

There is a considerable amount of ongoing research on the use of Bayesian control charts for detecting a shift from a good quality distribution to a bad quality distribution in univariate and multivariate processes. It is widely claimed that Bayesian control charts are economically optimal; see, for example, Calabrese (1995) [Bayesian process control for attributes. Management Science, DOI: 10.1287/mnsc.41.4.637] and Makis (2008) [Multivariate Bayesian control chart. Operations Research, DOI: 10.1287/opre.1070.0495]. Some researchers also generalize the optimality of controls defined based on posterior probabilities to the class of partially observable Markov decision processes. This note points out that the existing Bayesian control charts cannot generally be optimal because many years ago an analytical counterexample was provided by Taylor (1965) [Markovian sequential replacement processes. The Annals of Mathematical Statistics, DOI: 10.1214/aoms/1177699796].

stat.AP↗

arXiv2017

Economic Design of Memory-Type Control Charts: The Fallacy of the Formula Proposed by Lorenzen and Vance (1986)

The memory-type control charts, such as EWMA and CUSUM, are powerful tools for detecting small quality changes in univariate and multivariate processes. Many papers on economic design of these control charts use the formula proposed by Lorenzen and Vance (1986) [Lorenzen, T. J., & Vance, L. C. (1986). The economic design of control charts: A unified approach. Technometrics, 28(1), 3-10, DOI: 10.2307/1269598]. This paper shows that this formula is not correct for memory-type control charts and its values can significantly deviate from the original values even if the ARL values used in this formula are accurately computed. Consequently, the use of this formula can result in charts that are not economically optimal. The formula is corrected for memory-type control charts, but unfortunately the modified formula is not a helpful tool from a computational perspective. We show that simulation-based optimization is a possible alternative method.

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