Performance of the mean control charts with generalized sensitizing rules for various probability distribution

The current study highlights and resolves the issues of mean control charts with sensitizing rules. The average run length (ARL)-based mean control charts with sensitizing rules involve a restricted assumption of normality. The restricted assumption has a limitation that in-control ARL deviates from the predefined level when it is violated. Also, false alarm rate (FRL)-based mean control charts with sensitizing rules for various probability distribution results into undesired run length properties. In this study, ARL-based mean control charts (two-sided and one-sided) with generalized sensitizing rules for normal and non-normal distributions are derived. Results indicate that in-control ARL is obtained equal to the predefined level. This shows that the proposed mean control charts have sustained behavior for any choice of sensitizing rules and probability distribution. In addition, we have explained that an optimal choice of the sensitizing rules depend on a process probability distribution. Besides, the proposed control charts are applied in petrochemical process to monitor the diesel oil characteristics.

本研究针对带灵敏性规则的均值控制图所存在的问题展开分析并给出解决方案。采用灵敏性规则的基于平均运行长度（average run length, ARL）的均值控制图，需依赖受限的正态性假设。该受限假设存在局限：当假设被违背时，受控状态下的平均运行长度会偏离预设水平。此外，针对不同概率分布、采用灵敏性规则的基于虚警率（false alarm rate, FRL）的均值控制图，会呈现出非预期的运行长度特性。本研究推导了针对正态与非正态分布、采用广义灵敏性规则的双侧与单侧基于平均运行长度的均值控制图。研究结果显示，此类控制图可获得与预设水平一致的受控状态平均运行长度，表明所提出的均值控制图，无论灵敏性规则与概率分布作何选择，均能保持稳定的受控特性。此外，本文阐明了灵敏性规则的最优选择取决于过程的概率分布。最后，将所提出的控制图应用于石化过程，用于监控柴油的各项特性指标。