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Entropy 2017, 19(8), 406; https://doi.org/10.3390/e19080406

Statistical Process Control for Unimodal Distribution Based on Maximum Entropy Distribution Approximation

1
School of Management, Shanghai University, Shanghai 200444, China
2
College of Economics & Management, China Jiliang University, Hangzhou 310018, China
3
School of Management, Shenzhen Polytechnic, Shenzhen 518055, China
*
Author to whom correspondence should be addressed.
Received: 21 June 2017 / Revised: 18 July 2017 / Accepted: 4 August 2017 / Published: 7 August 2017
(This article belongs to the Special Issue Maximum Entropy and Bayesian Methods)
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Abstract

In statistical process control, the control chart utilizing the idea of maximum entropy distribution density level sets has been proven to perform well for monitoring the quantity with multimodal distribution. However, it is too complicated to implement for the quantity with unimodal distribution. This article proposes a simplified method based on maximum entropy for the control chart design when the quantity being monitored is unimodal distribution. First, we use the maximum entropy distribution to approximate the unknown distribution of the monitored quantity. Then we directly take the value of the quantity as the monitoring statistic. Finally, the Lebesgue measure is applied to estimate the acceptance regions and the one with minimum volume is chosen as the optimal in-control region of the monitored quantity. The results from two cases show that the proposed method in this article has a higher detection capability than the conventional control chart techniques when the monitored quantity is asymmetric unimodal distribution. View Full-Text
Keywords: maximum entropy distribution; control chart; acceptance region; type II error rate maximum entropy distribution; control chart; acceptance region; type II error rate
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Fang, X.; Song, M.; Chen, Y. Statistical Process Control for Unimodal Distribution Based on Maximum Entropy Distribution Approximation. Entropy 2017, 19, 406.

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