Análise do desempenho de gráficos de controle com regras suplementares de decisão

Abstract

The most important objectives of industrial and non-industrial companies are related to cost, time and quality. On the one hand, the control charts represents an important quality tool, showing if the process is in control or out of control. On the other hand, the Markov chains can be used with the control charts, modeling the process under analysis. Thus, this research aims to analyze the performance of control charts with supplementary signaling rules through the comparison of the average run length. To do so, the process of literature under investigation was analyzed and modeled through a Markov chain. Following that, the average run length was calculated for distinct scenarios. The control charts under analysis refer to a capability index chart with supplementary signaling rule, a 𝑋 chart with supplementary signaling rule and a 𝑋 chart with basic signaling rule. The results obtained allowed the conduction of two distinct analysis. The first analysis demonstrated that, when it comes to mean shifts, the calculation complexity resulted from the introduction of the capability index does not always generate the best results. The second analysis demonstrated that, when it comes to mean shifts, the calculation complexity resulted from the introduction of the supplementary signaling rule does in general generate the best results. In some cases the capability index chart with supplementary signaling rule was the chart with the best performance among the three under analysis and in other cases the 𝑋 chart with supplementary signaling rule was the chart with the best performance among the three under analysis. Finally, the results reassured that the 𝑋 control chart does not display good performance when it comes to small mean shifts.