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Efecto del incumplimiento de la hipótesis de normalidad en los gráficos de control de la media || Effect of non-compliance with the normality hypothesis on the mean control charts

Author

Listed:
  • Moya Fernández, Pablo

    (Universidad de Granada)

  • Álvarez-Verdejo, Encarnación

    (Universidad de Granada)

  • Blanco-Encomienda, Francisco Javier

    (Universidad de Granada)

Abstract

Los gráficos de control son ampliamente usados para monitorizar la calidad de procesos industriales. Tradicionalmente se asume que la variable aleatoria que representa la característica de calidad se distribuye de forma normal y los límites de control se definen de forma que la probabilidad de obtener una falsa alarma es 0.0027. Sin embargo, en la práctica la característica de calidad podría seguir otra distribución y este hecho podría afectar a la eficiencia del gráfico de control. En el presente trabajo se realiza un estudio de simulación Monte Carlo con el objetivo de evaluar empíricamente el impacto del incumplimiento del supuesto de normalidad en el gráfico de control para la media. Se consideran distintas distribuciones probabilísticas para analizar diferentes grados de incumplimiento. Adicionalmente, se han considerado situaciones en los que el proceso está bajo control y fuera de control. Los resultados sugieren que los gráficos de control son una herramienta efectiva cuando la distribución de la característica de calidad tiene una leve asimetría. Sin embargo, para obtener una efectividad similar a la obtenida bajo normalidad es necesario aumentar levemente el número de muestras o el tamaño de las mismas. En el caso de que la característica de calidad siga una distribución con un grado de asimetría mayor es necesario aumentar los tamaños muestrales para obtener resultados aceptables. Por último, no es recomendable utilizar los gráficos de control en situaciones extremas de falta de normalidad.|| Control charts are widely used to monitor the quality of industrial processes. It is quite common to assume that the random variable associated to the quality characteristic has a Normal distribution, and the control limits are defined so that the probability of obtaining a false alarm is 0.0027. However, the quality characteristic could follow a different distribution in practice, and this fact could have an impact on the efficiency of the control chart. In this paper, a Monte Carlo simulation study is carried out to evaluate empirically the impact of the lack of the normality assumption on the control chart for the mean. Different probabilistic distributions are considered. In addition, under control and out of control processes are considered. The results derived from the simulation study suggest that control charts are an effective tool when the distribution of the quality characteristic is slightly asymmetric. However, a large number of samples or larger sample sizes are required to obtain similar results to the case of symmetric distributions. In the case of asymmetric distributions, it is necessary to increase the sample sizes to obtain acceptable results. Finally, control charts are not recommended under evident cases of non-normality.

Suggested Citation

  • Moya Fernández, Pablo & Álvarez-Verdejo, Encarnación & Blanco-Encomienda, Francisco Javier, 2021. "Efecto del incumplimiento de la hipótesis de normalidad en los gráficos de control de la media || Effect of non-compliance with the normality hypothesis on the mean control charts," Revista de Métodos Cuantitativos para la Economía y la Empresa = Journal of Quantitative Methods for Economics and Business Administration, Universidad Pablo de Olavide, Department of Quantitative Methods for Economics and Business Administration, vol. 31(1), pages 128-143, June.
  • Handle: RePEc:pab:rmcpee:v:31:y:2021:i:1:p:128-143
    DOI: https://doi.org/10.46661/revmetodoscuanteconempresa.4307
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    More about this item

    Keywords

    control estadístico de procesos; simulación Monte Carlo; longitud media de las rachas; error tipo I; monitorizar; statistical process control; Monte Carlo simulation; average run length; type I error; monitor.;
    All these keywords.

    JEL classification:

    • M11 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Administration - - - Production Management

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