A modelagem de gráficos de controle de aceitação condicionados aos índices de capabilidade de processos : uma abordagem prática e econômica

Abstract

Modified and acceptance control charts allow a new approach to statistical process monitoring. This research topic is little explored in the academic world, thus, this thesis contributes to the advancement of statistical process monitoring methods, both in theory and practice. Some decisions about the quality of processes and products are based on a set of economic and practical factors that involve their context, not just a probability, p-value. Statistical significance considers the theoretical decision probability of the statistical hypothesis test, and does not take into account trade-offs when choosing a decision alternative. In this work, when studying the X-bar R/S graphs, the hypothesis is that the limits of statistical control can be determined considering practical aspects. The model proposed in this thesis will be based on the acceptance graphs and on the capacitance indices, Cp and Cpk. The use of these indices is justified because they are widely used by the manufacturing industry, and these represent the practical aspect in the decisions about processes and products. The performance of control charts was evaluated via ARL (Average Run Length). An ARL model was developed when parameters are unknown, including the capability indexes. The results indicated that the proposed graph performs better than Shewhart's traditional charts. An implementation method was proposed and an illustrative case was carried out. In the illustrative example, the proposed method provided a smaller type I error, making it possible to improve the quality level in the process result.