Eficiência entre os gráficos de controle por grupos para a média e o tradicional de Shewhart em processos com fluxos correlacionados

Abstract

The use of Shewhart charts as a tool for process monitoring, whose products come from various production flows (parallel processes), should be viewed with caution because the samples could be determined based on items from different populations. In the construction of these charts, is not recommended mix different sources of process variation, because such an attitude can lead to wrong conclusions and thus reduce the power of the chart in detecting assignable causes. One solution to this problem is the use of a control chart for each stream, which makes control difficult and bureaucratic. Another alternative is to adopt the Groups Charts, which allows control of multiple streams from a single graph. The presence of a correlation structure in the production process, inserted in both types of charts, can compromise the analysis violating the restriction of independence of samples. The literature is lacking in studies of this nature. Given this scenario, the objective of this work is to develop a study through simulation using the Software R, Group Charts in terms of its performance and efficiency, as an alternative to Model Shewhart in parallel processes with correlated streams. The study is an analysis of the change in the mean and the variance of the process individually and jointly. This work then contextualizes the importance of Statistical Control in the Process (SPC) logistics and its contribution to the theory and practice SPC within the proposed objective. Results indicate that the efficiency of GG compared to traditional increases as the correlation grows. Furthermore, for small disturbances, with 3 flows, the GG becomes 55% slower as to detect a displacement set average and the variance of the process compared to the traditional of Shewhart. Note also that, for 10 streams, the GG has outperformed GCS in the order of 36% correlation to 0:5, giving evidence that, for a large number of flows (k >= 10), the GG is better than the GCS in the presence of correlation between the streams.