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

Abstract

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.

Regulation of Requirements for Quality Indicators of Paint Covering

“…Results of check of hypotheses by Pearson , s criterion (significance value α =0,05, number of degrees of freedom 3 shows the numerical values of the actual and normative values of the coefficients of variation and also the maximum possible allowed value (AQD) for some the protective -decorative coverings. Analysis of the data shows that some of coverings are characterized by lower uniformity values of the bond strength, than it is required, proceeding from a ratio of actual and normative coefficients of a variation [16,17,18,19,20]. The maximum allowed value the average-quadratic deviation at statistical controllability of process of painting for some coverings (PVAC, polymerlime, PF-115) must be less than the actual and must correspond to the values from table 3.…”