Tempo médio até o sinal em gráficos de controle para médias móveis exponencialmente distribuídas usando a abordagem de cadeias de Markov

Abstract

This monograph sought to reproduce the results presented by (LUCAS; SACCUCCI, 1990a) for calculating the Average Run Length (ARL) in Exponentially Weighted Moving Average (EWMA) control charts. In the methodological approach employed, the control intervals were discretized and modeled as a discrete Markov Chain. This technique enabled the precise calcu- lation of the ARL for both the Zero State — where the process is assumed to start at the target value — and the Steady State - which reflects the chart’s performance after an extended period of operation. Based on an in-depth understanding of the numerical method used by the original authors, new source codes were developed in the R programming language, providing a modern and accessible alternative to the original algorithms written in Fortran. This study validates the efficiency of discretization in process monitoring and provides updated computational tools for performance analysis in statistical quality control.