Abstract: Traditional control charts are mostly estimated on the basic hypothesis that the distribution of quality characteristic parameter follows the normal distribution. However, in real-applications, the normal distribution assumption cannot be satisfied, and this might lead to the bias from the monitoring process. Motivated by the aforementioned the problems, a series of maximum entropy-based approaches are proposed to approving the existed control charts, Shewhart chart and CUSUM chart, from the perspectives of rebuilding and evaluating method designing. Specifically, conforming to the economy criteria, an improved Shewhart control chart based on maximum entropy distribution is constructed analytically. Then a methodology by combining the Markov Chain and maximum entropy distribution is put forward to evaluating the performances of adaptive CUSUM chart. The simulated case in this paper validates that improved Shewhart chart performs much better than its original one, from the value of average run length. And the results from novel method for the CUSUM evaluation are much closer to the realities. Moreover, the improved Shewhart chart is suitable for large shifts monitoring, whereas the adaptive CUSUM chart is proper for small shifts monitoring.

Key words: maximum entropy, control chart, average run length, control limit