¹Universidad Industrial de Santander, Facultad de Ciencias, Escuela de Matemáticas, Bucaramanga, Colombia. Associate Professor. Email: gmorenoa@uis.edu.co
²Universidad de Córdoba, Facultad de Ciencias, Departamento de Matemáticas y Estadística, Montería, Colombia. Professor. Email: gmartinez@correo.unicordoba.edu.co
³Instituto Tecnológico Metropolitano, Facultad de Ciencias Exactas y Aplicadas, Medellin, Colombia. Associate Professor. Email: carlosbarrera@itm.edu.co

Birnbaum & Saunders (1969b) used a probability distribution to explain the lifetime data and stress produced in materials. Based on this distribution, we propose a generalization of the Birnbaum-Saunders distribution, referred to as the proportional hazard Birnbaum-Saunders distribution, which includes a new parameter that provides more flexibility in terms of skewness and kurtosis than existing models. We derive the main properties of the model. We discuss maximum likelihood estimation of the model parameters. As a natural step, we define the log-linear proportional hazard Birnbaum-Saunders regression model. An empirical application to a real data set is presented in order to illustrate the usefulness of the proposed model. The results showed that the proportional hazard Birnbaum-Saunders model can be used quite effectively in analyzing survival data, reliability problems and fatigue life studies.

Key words: Birnbaum-Saunders Distribution, Proportional Hazard, Reliability, Survival Data.

Birnbaum & Saunders (1969b) presentaron una distribución de probabilidad para explicar los datos de supervivencia y estrés producidos sobre los materiales. Basados en esta distribución, proponemos una generalización de la distribución Birnbaum-Saunders, la cual llamamos distribución Birnbaum-Saunders de riesgo proporcional, incluyendo un nuevo parámetro que proporciona una mayor flexibilidad en términos de asimetría y curtosis comparado con los modelos existentes. Derivamos las principales propiedades del modelo. Discutimos la estimación de máxima verosimilitud de los parámetros del modelo. Como un paso natural, definimos el modelo de regresion log-lineal Birnbaum-Saunders de riesgo proporcional. Presentamos una aplicación con un conjunto de datos reales con el propósito de ilustrar la utilidad del modelo propuesto. Los resultados mostraron que el modelo Birnbaum-Saunders de riesgo proporcional puede ser utilizado efectivamente en el análisis de datos de supervivencia, problemas de confiabilidad y estudios de resistencia a la fatiga.

Palabras clave: distribución Birnbaum-Saunders, riesgo proporcional, confiabilidad, datos de supervivencia.

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