Herbal medicines (HMs), which offer a plethora of treatment options for complex diseases, have become increasingly popular worldwide in recent years. HM formulae, which are the combinations of two or more types of herbs, and therefore contain chemical compounds from each of the individual herbs, are the main form of HMs used in clinic. In this work, this type of sample matrix is regarded as a compound matrix, which is a mixture of their constituting ingredients. Similarly, a dietary supplement can also be regarded as a compound matrix if it is composed of multiple nutrients and/or extracts from several types of foods/plants. HPLC is the most commonly used method to analyze compound matrices in various fields. [1][2][3][4][5][6][7][8] However, due to the complexity of the matrices, chromatographic separation for these samples is challenging. Comprehensive pre-experiments to optimize the analytical parameters (e.g., gradient and pH of the mobile phase) are often needed to achieve good separation performance, which makes HPLC method development complicated and time-consuming. In the commonly used approach, the analytical parameters are optimized one by one in a process that is dependent on the experience of the researchers.Although many HPLC experiments are conducted and large amounts of raw data are acquired during method development, the rules of how the analytical parameters impact chromatographic separation are not effectively summarized and recorded. Consequently, when the composition of the compound matrix changes, a new analytical method must be developed from the very beginning if the performance of the original method becomes undesirable.An efficient approach to develop HPLC methods for compound matrices is needed.Since a compound matrix is the combination of its constituting ingredients, and HPLC methods for the individual ingredients have usually been developed before method development for the compound matrix, a question is raised: Are there any mutual retention rules between the compound matrix and its ingredients? If the answer is yes, then based on the retention rules acquired from the constituting ingredients, the impacts of the analytical parameters on the chromatographic separation of the compound matrix are predictable, which will enable rapid optimization of the analytical parameters for the compound matrix. When analyzing compound matrices and their constituting ingredients with the same HPLC analytical parameters, the same chemical compounds in these different samples have the same chromatographic parameters like retention time (tR) and peak width. Therefore, the relationships between the analytical parameters and these chromatographic parameters can be defined as the mutual retention rules between the compound matrices and their constituting ingredients. By effectively acquiring and utilizing the retention rules, the HPLC method development efficiency can be increased.In recent years, the analytical quality by design (AQbD) approach was proposed and has been successfully applied in the develo...