Monitoring the parameter vector of regression models with time-to-event response in phase II processes

Abstract

Palabras clave: Censuramiento, distribución de valor extremo, distribución Weibull, modelo de regresión, monitoreo de perfiles, razón de verosimilitudes, tiempos de vida. Abbreviations and conventions In the following table, there are listed some abbreviations and conventions used throughout this document. Short expression Extended expression ARL Average run length ARL 0 In-control average run length ARL 1 Out-of-control average run length CL Central line CU SU M Cumulative sum EV RM Extreme value regression model (or models) EW M A Exponentially weighted moving average GLM Generalized linear model LRT Likelihood ratio test LCL Lower control limit M EW M A Multivariate exponentially weighted moving average M LE Maximum likelihood estimator pdf Probability density function SP C Statistical process control U CL Upper control limit W RM Weibull regression model (or models) EV (a; b) The extreme value distribution with parameter vector (a; b) EV (0; 1) The standardized extreme value distribution N (a; b) The normal distribution with parameter vector (a; b) N (0; 1) The standard normal distribution W (a; b) The Weibull distribution with parameter vector (a; b) χ 2 p The chi-square distributions with p degrees of freedom X ∼ D(A) The random variable X follows a known distribution D with parameter vector A Aknowledgements The author expresses his gratitude to all those who have contributed to the development and successful completion of this work. The author would especially like to thank: • Professor J.A.Vargas, advisor of the thesis, for giving the opportunity to work in Staistical Quality Control, • The members of the jury evaluating this work for their comments and contributions that greatly enriched the final version of the thesis manuscript, • The reviewers of the articles and communications in specialized events that are products of this research work, • The executive staff of the Department of Statistics, professors in charge of doctoral courses and activities, coworkers and classmates for the support provided, • Mother and sisters.