Tr(R
            <sup>2</sup>
            ) control charts based on kernel density estimation for monitoring multivariate variability process

Mashuri, Muhammad; Haryono, Haryono; Aksioma, Diaz Fitra; Wibawati, Wibawati; Ahsan, Muhammad; Khusna, Hidayatul

doi:10.1080/23311916.2019.1665949

Cited by 17 publications

(7 citation statements)

References 62 publications

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“…Recently, Apsemidis et al 35 provided a comprehensive review on about 90 articles after 2002 that include the combination of kernel-based approaches with other ML techniques. Mashuri et al 36 proposed a T r(R2) control chart based on the squared correlation matrix with the trace operator and used the kernel density estimation method to calculate the better control limit for the proposed chart. Chinnam 37 demonstrates that SVMs can be extremely effective in minimizing both Type-I errors and Type-II errors and in detecting shifts in both the non-correlated processes ou autocorrelated processes.…”

Section: Kernel-based Learning Methodsmentioning

confidence: 99%

Application of Machine Learning in Statistical Process Control Charts: A Survey and Perspective

Tran¹,

Nadi

Nguyễn

et al. 2021

Springer Series in Reliability Engineering

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Over the past decades, control charts, one of the essential tools in Statistical Process Control (SPC), have been widely implemented in manufacturing industries as an effective approach for Anomaly Detection (AD). Thanks to the development of technologies like the Internet of Things and Artificial Intelligence (AI), Smart Manufacturing (SM) has become an important concept for expressing the end goal of digitization in manufacturing. However, SM requires a more automatic procedure with capabilities to deal with huge data from the continuous and simultaneous process. Hence, traditional control charts of SPC now find difficulties in reality activities including designing, pattern recognition, and interpreting stages. Machine Learning (ML) algorithms have emerged as powerful analytic tools and great assistance that can be integrating to control charts of SPC to solve these issues. Therefore, the purpose of this chapter is first to presents a survey on the applications of ML techniques in the stages of designing, pattern recognition, and interpreting of control charts respectively in SPC especially in the context of SM for AD. Second, difficulties and challenges in these areas are discussed. Third, perspectives of ML techniquesbased control charts for AD in SM are proposed. Finally, a case study of an ML-based control chart for bearing failure AD is also provided in this chapter.

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Section: Kernel-based Learning Methodsmentioning

confidence: 99%

Application of Machine Learning in Statistical Process Control Charts: A Survey and Perspective

Tran¹,

Nadi

Nguyễn

et al. 2021

Springer Series in Reliability Engineering

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“…where x 1 ×n is the first - row vector of X m 1 ×n , (similarly Q -index can be computed for all the row vectors of X rd m 1 ×n ). The threshold values of T 2 -statistic and Q -index for the training data set, which defines the normal operating region (NOR), are computed for a 99% confidence interval using normal kernel density function, 41,42 by…”

Section: Theoretical Background Of Pcamodel–based Crack Detection Andmentioning

confidence: 99%

Detection and localization of fatigue-induced transverse crack in a rotor shaft using principal component analysis

Prasad

Sekhar

2020

Structural Health Monitoring

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Rotor shafts subjected to severe operating stresses are prone to develop transverse fatigue cracks at the localized stress raisers. Therefore, the ability to identify and locate the incipient fatigue crack is imperative in order to avoid catastrophic failure. The literature on rotor crack detection discussed the importance of monitoring the steady-state 1X, 2X and 3X harmonic response components of rotors. However, the other rotor faults such as misalignment and unbalance, exhibit similar symptoms. Thus, the main aim is to develop new independent fault-related features which measure the driving principle governing the behaviour of various rotor faults. In this article, the application of principal component analysis–based statistical pattern analysis, as a tool for early detection and localization of fatigue-induced transverse crack in a rotor shaft is investigated. To perform this study, accelerated fatigue experiments are conducted on a customized setup. This developed test rig is novel and unique by itself that facilitates generating a fatigue crack in a shaft, under conditions that mimic a real in-service loading environment of industrial rotors. Unlike conventional methods, noise in the acquired vibration and strain data is denoised via classical principal component analysis method. Time- and frequency-domain statistical features extracted from different vibration and strain sensor signals are used for this study. Damage indices such as Hotelling’s T2-statistic and Q-index are used to detect the presence of the crack. It is observed that irrespective of the sensor location, damage index such as Q-statistic of all the sensors is very effective to detect the presence and time of incipient crack. Partial decomposition contributions method is found to be very effective in identifying the location of the crack. This article provides the most significant vibration-based statistical features, which are sensitive to shaft transverse cracks, for different sensor types and their mounting location. Finally, a new fused health indicator which is highly sensitive to the presence of rotor shaft crack is defined and is found successful when applied to a new experimental data.

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“…11 Khoo and Quah 12 suggested the use of a dispersion control chart for multivariate individual observations. Djauhari 13 and Djauhari et al 14 introduced the improved GV and vector variance control charts, respectively, and Mashuri et al 15 proposed the trace (R 2 ) control chart.…”

Section: Introductionmentioning

confidence: 99%

“…Djauhari 13 and Djauhari et al 14 . introduced the improved GV and vector variance control charts, respectively, and Mashuri et al 15 . proposed the trace ( R 2 ) control chart.…”

Section: Introductionmentioning

confidence: 99%

The effectiveness of Max‐half‐Mchart over Max‐Mchart in simultaneously monitoring process mean and variability of individual observations

Kruba

Mashuri

Prastyo

2021

Quality & Reliability Eng

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Control charts are widely used in industrial environments for the simultaneous or separate monitoring of the process mean and process variability. The Max-Mchart is a multivariate Shewhart-type simultaneous control chart that is used when monitoring subgroups. While this sampling design allows the computation of the generalized variance (GV) used to calculate the process variability, a GV chart cannot be plotted for individual observations. Hence, we cannot compute the single statistic in the Max-Mchart. This study aims to overcome the aforementioned issue. To this end, first, we develop a new Max-Mchart for individual observations by utilizing the statistic in the dispersion control chart. Second, instead of the standard normal distribution, we propose a new transformation using a half-normal distribution to calculate the statistic for the process mean and process variability. Thus, the proposed chart is called the Max-Half-Mchart, whose control limit is calculated using the bootstrap approach. An evaluation based on the average run length values shows the robustness of the Max-Half-Mchart for the simultaneous monitoring of the process mean and process variability. The single statistic in the Max-Half-Mchart is more consistent with the statistic in Hotelling's 2 and the dispersion chart than that of the Max-Mchart.

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Tr(R ² ) control charts based on kernel density estimation for monitoring multivariate variability process

Cited by 17 publications

References 62 publications

Application of Machine Learning in Statistical Process Control Charts: A Survey and Perspective

Application of Machine Learning in Statistical Process Control Charts: A Survey and Perspective

Detection and localization of fatigue-induced transverse crack in a rotor shaft using principal component analysis

The effectiveness of Max‐half‐Mchart over Max‐Mchart in simultaneously monitoring process mean and variability of individual observations

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Tr(R 2 ) control charts based on kernel density estimation for monitoring multivariate variability process

Cited by 17 publications

References 62 publications

Application of Machine Learning in Statistical Process Control Charts: A Survey and Perspective

Application of Machine Learning in Statistical Process Control Charts: A Survey and Perspective

Detection and localization of fatigue-induced transverse crack in a rotor shaft using principal component analysis

The effectiveness of Max‐half‐Mchart over Max‐Mchart in simultaneously monitoring process mean and variability of individual observations

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Product

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Tr(R ² ) control charts based on kernel density estimation for monitoring multivariate variability process