A NewS2-EWMA Control Chart for Monitoring the Process Variance

Abstract

This article demonstrates how a three-parameter logarithmic transformation combined with an exponentially weighted moving average (EWMA) approach can be used to monitor the sample variance of a process. The computation of the parameters of the logarithmic transformation and the control limits are explained. An easy-to-use table is provided and an illustrative example is given. The performance of the logarithmic transformation is evaluated under the assumption of normality. An optimal design strategy based on the ARL is presented and comparisons with other procedures are performed.

Comparación de las Cartas de Control Univariadas con Transformación en la Medida de Variabilidad

“…Alwan [1] proposes the study to improve the sensitivity in univariate control charts by transforming the measure of variability transformation taking the standard deviation for the logarithmic EWMA chartsproposed by Crowder [2], fi nding an improvement in sensitivity to small changes in variability. This sensitivity improves in HV CUSUM proposal which applies a transformation to the standard deviation of three parameters [3] fi rst proposed by Castagliola [3]. …”

“…Presenta además mayor sensibilidad en detectar señales de alarma que el esquema EWMA propuesto por Castagliola [3].…”

“…Alwan [1] plantea el estudio del mejoramiento de la sensibilidad en las cartas de control univariado mediante la transformación de la medida de variabilidad tomando la transformación de la desviación estándar para las cartas EWMA logarítmica propuesta por Crowder [2] encontrando una mejora de la sensibilidad a los cambios pequeños de la variabilidad. Esta sensibilidad mejora en la propuesta de CUSUM HV que aplica una transformación triparamétrica a la desviación estándar [3] propuesta inicialmente por Castagliola [3]. Palabras clave: Medida de variabilidad, Transformación, Sensibilidad, Simulación R, ARL y Señales de alarma.…”

New Memory-Type Control Charts for Monitoring Process Mean and Dispersion

“…The proposed charts are based on the usual mean standardization of X for the location and a three-parameter logarithmic transformation to S 2 (cf., [17]) for the dispersion statistic. This section is divided into four parts for the four proposals discussed below.…”

“…The charts are developed by replacing the statistic that monitors the process dispersion of the Max-EWMA, Max-CUSUM, SS-EWMA, and SS-CUSUM with the three parameters' logarithmic transformation to S 2 , suggested by Castagliola [17].…”