Comparing the performance of Kernel PCA Mix Chart with PCA Mix Chart for monitoring mixed quality characteristics

Abstract

Along with the development of information and technology, the quality characteristics of a product cannot be monitored separately in the different types of control charts. In the past, conventional control charts were developed to monitor only one type of quality characteristic. The variable control charts are used to observe the variable or metric quality characteristics. Meanwhile, in monitoring non-metric characteristics or categorical data, attribute control charts are employed. To accommodate these two types of data, the PCA Mix control chart is suggested to simultaneously monitor these two types of data in one chart. However, some drawbacks occur when this chart is applied to monitor non-metric data which has an imbalanced proportion. Therefore, the Kernel PCA Mix control chart is created to overcome the gaps that occurred in the PCA Mix chart. Similar to the previous chart, this chart is also constructed using Hotelling’s T2 statistics with Kernel Density Estimation control limit. Several simulations are used to evaluate the performance of the proposed control charts. The simulation results show that the proposed chart has a better result than the previous control chart, especially for a small mean shift with an imbalanced proportion of non-metric data. However, the PCA Mix chart has a similar performance to the proposed chart when it is applied to monitor the balanced proportion of categorical data with a large mean shift. The application with simulated data with various scenarios and the real-world case also shows that the Kernel PCA Mix chart performs better compared to the performance of the PCA Mix chart.

Economic statistical model of the np chart for monitoring defectives

“…The study also conducts a sensitivity analysis to provide insights into the impact of changes in the design parameters on the performance of the np chart. By identifying the significant factors that influence the expected total cost, the study offers valued (10) Practical implications. The findings of this research hold significant practical implications for manufacturing organizations and service sectors.…”

“…Even though Shewhart charts assess the expenses implicitly by selecting n and h, the resultant charts are not guaranteed to be economically optimal.The performance of statistically designed charts is typically determined in terms of the Average Run Length (ARL) or Average Time to Signal (ATS) where ATS = ARL × h 8,9 . The out-of-control ARL can be defined as the average number of samples required to detect a process shift after it occurs [10][11][12] . Similarly, the out-of-control ATS can be defined as the average time required to detect a process shift after it occurs [13][14][15] .…”

Control Chart T2Qv for Statistical Control of Multivariate Processes with Qualitative Variables

“…Among the contributions related to control charts that incorporate multivariate techniques, the STATIS-based chart for monitoring batch processes in nonparametric environments stands out [28]; robust bagplot diagrams using Dual STATIS and Parallel Coordinates [29]; the PCA-based multivariate control chart for mixed data, which applies a combination of Principal Component Analysis and Multiple Correspondence Analysis [30]; the Density-sensitive Novelty Weight control chart (DNW) that uses the k-Nearest Neighbor (kNN) algorithm [15]; the Kernel PCA Mix-based chart [31,32]; the T 2 chart based on a combination of PCA for continuous and qualitative data with outlier detection [33]; and the PCA-based control charts for nonparametric environments [15,34].…”

Gráfico de control estadístico de procesos multivariantes para variables cualitativas

“…Poisson (Patel, 1973), Gráfico D 2 de control de atributos multivariante (Mukhopadhyay, 2008), Gráfico de control de calidad difuso multivariante (Taleb, Limam y Hirota, 2006), Gráfico de control multivariante basado en la combinación de PCA para características de calidad de atributos y variables (Ahsan, et al, 2018), gráfico T 2 basado en PCA Mix con límite de control de densidad de Kernel para mezclas de datos categóricos y continuos (Ahsan, et al, 2022), PCA Mix Chart para monitorear las características de calidad mixta en presencia de datos atípicos (Ahsan, et al, 2021), Gráfico de control multivariante no paramétrico para variables numéricas y categóricas , el Gráfico de control estadístico de procesos multivariantes para datos cualitativos (Rojas-Preciado, et al, 2023).…”

“…El PCA Mix es eficaz para monitorear simultáneamente variables numéricas y categóricas en un solo gráfico, no obstante, cuando éstas tienen una proporción desequilibrada se producen algunas dificultades. Para superarlas, Ahsan, et al (2022) desarrollaron el gráfico de control Kernel PCA Mix. En este gráfico, los datos categóricos se transforman en variables ficticias (dummy), después se combinan con los datos numéricos para dar lugar a la función Kernel.…”