¹Universidad de Valpara\'{\i}so, Departamento de Estad\'{i}stica, Valpara\'{\i}so, Chile. Profesor titular. Email: victor.leiva@uv.cl
²Instituto Nacional de Estadísticas, Santiago, Chile. Ingeniero estadístico. Email: gerson.soto@ine.cl
³Universidad de Valpara\'{\i}so, Departamento de Estad\'{i}stica, Valpara\'{\i}so, Chile. Pontificia Universidad Católica de Valpara\'{\i}so, Instituto de Estad\'{i}stica, Valpara\'{\i}so, Chile. Profesor adjunto. Email: enrique.cabrera@uv.cl
⁴Pontificia Universidad Católica de Valpara\'{\i}so, Escuela de Ingeniería Informática, Valpara\'{\i}so, Chile. Profesor permanente. Email: guillermo.cabrera@ucv.cl

l modelo Birnbaum-Saunders (BS) es una distribución de vida que tiene propiedades interesantes y aplicaciones en varias áreas. Esto la ha convertido en un foco de investigación importante en el último tiempo. Sin embargo, la suma de variables aleatorias independientes BS (BSsum) no sigue una distribución BS. A través de la distribución BSsum, se pueden monitorear los tiempos de vida de productos expuestos a fallas mediante una carta de control de calidad. Los procedimientos clásicos de cartas de control suponen normalidad en la distribución de los datos. No obstante, una de las características principales de los tiempos de vida es que éstos generalmente siguen distribuciones asimétricas. Por tanto, si se quiere monitorear estos tiempos, se deben considerar cartas de control para distribuciones asimétricas, como es el caso de la distribución BS. El monitoreo de los tiempos de vida se realiza generalmente mediante el tiempo acumulado o el tiempo promedio hasta la ocurrencia de cierto número de fallas. Entonces, usando la distribución BSsum, desarrollamos, implementamos y aplicamos una nueva metodología para cartas de control basada en la distribución BS.

Palabras clave: lenguaje de computación R, métodos de verosimilitud, tiempos de vida.

The Birnbaum-Saunders (BS) model is a life distribution with interesting properties and applications in several fields. This has transformed the BS model in an important research focus in recent decades. However, the sum of BS (BSsum) independent random variables does not follow a BS distribution. By means of the BSsum distribution, we can monitor the lifetime of products subject to failures using a quality control chart. Classic procedures for control charts assume normality in the distribution of the data. Nevertheless, one of the main characteristics of the lifetimes is that them generally follow asymmetric distributions. Therefore, if we want to monitor these lifetimes, we must consider control charts for asymmetric distributions, such as it is the case of the BS distribution. The monitoring of the lifetimes is carried out generally by the accumulated lifetime or the lifetime average until than a number of failures occurs. Thus, by using the BSsum distribution, we develop, implement and apply a new methodology for control charts based on the BS distribution.

Key words: Lifetime data, Likelihood methods, R computer language.

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