The Design of GLR Control Chart for Monitoring the Geometric Observations Using Sequential Sampling Scheme

Shahzad, Faisal; Huang, Zhensheng; Shafqat, Ambreen

doi:10.3390/sym12121964

Cited by 4 publications

(2 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Moreover, Mohammadian et al [13] utilized riskadjusted schemes to monitor health-care systems. Researchers are conducting further exploration into monitoring the parameter of geometric distribution (see Quesenberry [14], Schwertman [15], Majeed et al [16], KazemiNia [17], Shahzad et al [18], Park et al [19]).…”

Section: Introductionmentioning

confidence: 99%

Weighted-Likelihood-Ratio-Based EWMA Schemes for Monitoring Geometric Distributions

Zhang,

Cai,

Zhang

2024

Axioms

View full text Add to dashboard Cite

Monitoring the parameter of discrete distributions is common in industrial production. Also, it is often crucial to monitor the parameter of geometric distribution, which is often regarded as the nonconforming item rate. To enhance the detection of nonconforming item, we designed an exponentially weighted moving average (EWMA) scheme based on the weighted likelihood ratio test (WLRT) method, and this scheme is denoted as the EWLRT scheme, specifically designed for monitoring the increase of the parameter in geometric distribution. Moreover, the optimal statistical design of the EWLRT scheme is presented when the shift is known. Results from numerical comparisons through Monte Carlo simulations indicates that the EWLRT scheme performs better than the competing schemes in some scenarios. Additionally, the designed scheme is characterized by its simplicity and ease of use, making it ideally suited for scenarios involving single observation. An example is illustrated to demonstrate the effectiveness of the EWLRT scheme.

show abstract

Section: Introductionmentioning

confidence: 99%

Weighted-Likelihood-Ratio-Based EWMA Schemes for Monitoring Geometric Distributions

Zhang,

Cai,

Zhang

2024

Axioms

View full text Add to dashboard Cite

show abstract

“…Godase and Mahadik 19 introduced a charting procedure for the monitoring of scale parameter. Shahzad et al 20 . developed a new generalized likelihood ratio control (GLR) chart based on the SS scheme for monitoring the changes in the geometric observations.…”

Section: Introductionmentioning

confidence: 99%

On designing efficient sequential schemes to monitor non‐normal processes

Riaz

Khaliq

Abid

et al. 2021

Quality & Reliability Eng

View full text Add to dashboard Cite

The process monitoring techniques play an essential role to improve the overall performance of processes. The control chart is an essential monitoring tool used to detect changes in the process parameters. The Shewhart charts are famous for detecting larger shifts, while exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) control charts are famous for detecting small‐to‐moderate shifts. The separate control schemes are required for the quick identification of the changes in the process parameters because sometimes testing is too expensive or time taking and a practitioner may not afford any kind of defects or loss. With this motivation, the dynamic feature of this article is to introduce an efficient sequential probability ratio test (SPRT) decision‐based Tukey CUSUM design. The performance of the proposal is judged by using several run lengths (RLs) performance measures such as average, median, standard deviation, and percentile RLs. Based on the comparative analysis, it is revealed that the proposed chart offers more sensitivity towards the changes in process location than its competitor's charts for several probability models. The study proposal may find applications in packaging, manufacturing, decision‐making, finance and economics modeling, image processing and automation. A case study from steel rods manufacturing is included to demonstrate the application of the proposed design.

show abstract

Process Monitoring Using Kernel PCA and Kernel Density Estimation-Based SSGLR Method for Nonlinear Fault Detection

2022

View full text Add to dashboard Cite

Fault monitoring is often employed for the secure functioning of industrial systems. To assess performance and enhance product quality, statistical process control (SPC) charts such as Shewhart, CUSUM, and EWMA statistics have historically been utilized. When implemented to multivariate procedures, unfortunately, such univariate control charts demonstrate low fault sensing ability. Due to some limitations of univariate charts, numerous process monitoring techniques dependent on multivariate statistical approaches such as principal component analysis (PCA) and partial least squares (PLS) have been designed. Yet, in some challenging scenarios in industrial chemical and biological processes with notably nonlinear properties, PCA works poorly, according to its presumption that the dataset generally be linear. However, Kernel Principal Component Analysis (KPCA) is a reliable and precise nonlinear process control methodology, but the interaction mainly through upper control limits (UCLs) dependent on the Gaussian distribution may weaken its output. This article introduces time-varying statistical error tracking through Kernel Principal Component Analysis (KPCA) based on Generalized Likelihood Ratio statistics (GLR) using a sequential sampling scheme named KPCA-SSGLR for nonlinear fault detection. The main issue of employing just T2 and Q statistic in KPCA is that they cannot correctly give practitioners the change point of the system fault, preventing practitioners from diagnosing the issue. Based on this perspective, this study attempts to incorporate KPCA with sequential sampling Generalized Likelihood Ratio (SSGLR) for monitoring the nonlinear fault in multivariate systems. The KPCA is utilized for dimension reduction, while the SSGLR is employed as a tracking statistic. The kernel density estimation (KDE) was employed to approximate UCLs for variational system operation relying on KPCA. The testing efficiency of the corresponding KPCA-KDE-SSGLR technique was then analyzed and competed with KPCA and kernel locality preserving projection (KLPP), the UCLs of which were focused on the Gaussian distribution. The purpose of this analysis is to enhance the development of KPCA-KDE-SSGLR to accomplish future enhancements and to advance the practical use of the established model by implementing the sequential sampling GLR approach. The fault monitoring efficiency is demonstrated through different simulation scenarios, one utilizing synthetic data, the other from the Tennessee Eastman technique, and lastly through a hot strip mill. The findings indicate the applicability of the KPCA-KDE-based SSGLR system over the KLPP and KPCA-KDE methods by its two T2 and Q charts to recognize the faults.

show abstract

The Design of GLR Control Chart for Monitoring the Geometric Observations Using Sequential Sampling Scheme

Cited by 4 publications

References 38 publications

Weighted-Likelihood-Ratio-Based EWMA Schemes for Monitoring Geometric Distributions

Weighted-Likelihood-Ratio-Based EWMA Schemes for Monitoring Geometric Distributions

On designing efficient sequential schemes to monitor non‐normal processes

Process Monitoring Using Kernel PCA and Kernel Density Estimation-Based SSGLR Method for Nonlinear Fault Detection

Contact Info

Product

Resources

About