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A Study of Cumulative Quantity Control Chart for a Mixture of Rayleigh Model under a Bayesian Framework
Un estudio de cartas de control de cantidades acumuladas por mixturas de modelos Rayleigh bajo un enfoque Bayesiano
DOI:
https://doi.org/10.15446/rce.v39n2.58915Keywords:
Quality control, Inverse Transformation Method, Loss Functions and Bayes Estimators, MRCQC-Chart, SRCQC-Char (en)Control de calidad, Método de la transformación, Función de pérdida, Estimador bayesiano, Carta MRCQC, Carta SRCQC (es)
This study deals with the cumulative charting technique based on a simple and a mixture of Rayleigh models. The respective charting schemes are referred as the SRCQC-chart and the MRCQC-chart. These are stimulated from existing statistical control charts in this direction i.e. the cumulative quantity control (CQC) chart, based on exponential and Weibull models, and the cumulative count control (CCC) chart, based on the simple geometricmodel. Another motivation for this study is the mixture cumulative count control (MCCC) chart based on the two component geometric model. The use of mixture cumulative quantity is an attractive approach for process monitoring. The design structure of the proposed control chart is derived by using the cumulative distribution function of simple, and two components of mixture distribution(s). We observed that the proposed charting structure
is efficient in detecting the changes in process parameters. The application of the proposed scheme is illustrated using a real dataset.
Este estudio trata con cartas de control acumuladas basadas en distribuciones Rayleigh y en mixturas de estas mismas. Las cartas se denominan SRCQC y MRCQC, respectivamente. Estas se fundamentan en cartas existentes como la carta de control de cantidades acumuladas (CQC), basada en modelos exponencial y Weibull en la carta de control de conteos acumulados (CCC), soportada en un modelo geométrico. Otra propuesta del estudio es la carta de control de mixtura de conteos acumulados (MCCC). Esta última es muy atractiva en procesos de monitoreo. La estructura de diseño de las cartas propuestas se deriva usando la función de distribución acumulada simple y la mixtura de dos distribuciones acumuladas. Se observa que las cartas propuestas son eficientes para detectar cambios en los parámetros del proceso. La aplicación del esquema propuesto es ilustrada usando un conjunto
de datos reales.
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