¹King Fahad University of Petroleum and Minerals, Department of Mathematics and Statistics, Dhahran, Saudi Arabia. Professor. Email: riazm@kfupm.edu.sa
²King Fahad University of Petroleum and Minerals, Department of Mathematics and Statistics, Dhahran, Saudi Arabia. Professor. Email: saddamaa@kfupm.edu.sa

In monitoring process parameters, we assume normality of the quality characteristic of interest, which is an ideal assumption. In many practical situations, we may not know the distributional behavior of the data, and hence, the need arises use nonparametric techniques. In this study, a nonparametric double EWMA control chart, namely the NPDEWMA chart, is proposed to ensure efficient monitoring of the location parameter. The performance of the proposed chart is evaluated in terms of different run length properties, such as average, standard deviation and percentiles. The proposed scheme is compared with its recent existing counterparts, namely the nonparametric EWMA and the nonparametric CUSUM schemes. The performance measures used are the average run length (ARL), standard deviation of the run length (SDRL) and extra quadratic loss (EQL). We observed that the proposed chart outperforms the said existing schemes to detect shifts in the process mean level. We also provide an illustrative example for practical considerations.

Key words: ARL, Control charts, DEWMA, EQL, Nonparametric, Process location, Run length sistribution, SDRL.

En el seguimiento de los parámetros del proceso, asumimos normalidad de la característica de calidad de interés que es un supuesto ideal. En muchas situaciones prácticas, no podemos conocer el comportamiento de distribución de los datos y por lo tanto, surge la necesidad de técnicas no paramétricas. En este estudio, un gráfico de control EWMA doble paramétrico, a saber, la carta NPDEWMA, se propone para una vigilancia eficaz en el parámetro de localización. El rendimiento del gráfico propuesto se evalúa en términos de propiedades diferentes de longitud de ejecución, como promedio, desviación estándar y percentiles. El esquema propuesto se compara con sus homólogos de los últimos existentes, a saber, la EWMA no paramétrico y los esquemas de CUSUM no paramétricas. Las medidas de desempeño utilizadas son la longitud promedio de carreras (ARL), la desviación estándar de la longitud de ejecución (SDRL) y pérdida cuadrática extra (EQL). Se observa que el gráfico propuesto supera a dichos regímenes existentes para detectar cambios en el proceso de nivel medio. También se proporciona un ejemplo ilustrativo para consideraciones prácticas.

Palabras clave: ARL, gráficas de control, DEWMA, EQL, no paramétrica, ubicación proceso, ejecutar distribución de longitud, SDRL.

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