Quality testing and monitoring advancements have allowed modern production processes to achieve extremely low failure rates, especially in the era of Industry 4.0. Such processes are known as high‐yield processes, and their data set consists of an excess number of zeros. Count models such as Poisson, Negative Binomial (NB), and Conway‐Maxwell‐Poisson (COM‐Poisson) are usually considered good candidates to model such data, but the excess zeros are larger than the number of zeros, which these models fit inherently. Hence, the zero‐inflated version of these count models provides better fitness of high‐quality data. Usually, linearly/non‐linearly related variables are also associated with failure rate data; hence, regression models based on zero‐inflated count models are used for model fitting. This study is designed to propose deep learning (DL) based control charts when the failure rate variables follow the zero‐inflated COM‐Poisson (ZICOM‐Poisson) distribution because DL models can detect complicated non‐linear patterns and relationships in data. Further, the proposed methods are compared with existing control charts based on neural networks, principal component analysis designed based on Poisson, NB, and zero‐inflated Poisson (ZIP) and non‐linear principal component analysis designed based on Poisson, NB, and ZIP. Using run length properties, the simulation study evaluates monitoring approaches, and a flight delay application illustrates the implementation of the research. The findings revealed that the proposed methods have outperformed all existing control charts.