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In recent research endeavors, discrete models have gained considerable attention, even in cases where the observed variables are continuous. These variables can often be effectively approximated by a normal distribution. Given the prevalence of processes requiring robust quality control, models associated with the normal distribution have found widespread applicability; nevertheless, there remains a persistent need for enhanced accuracy in normality analysis, prompting the exploration of novel and improved solutions. This paper introduces a discrete parameter-free distribution linked to the normal distribution, derived from a quality control methodology rooted in the renowned '3-sigma' rule. The development of a novel normality test, based on this distribution, is presented. A comprehensive examination encompasses mathematical derivation, distribution tables generated through Monte Carlo simulation studies, properties, power analysis, and comparative analysis, all with key features illustrated graphically. Notably, the proposed normality test surpasses conventional methods in performance. Termed the 'Zone distribution', this newly introduced distribution, along with its accompanying 'Zone test', demonstrates superior efficacy through illustrative examples. This research contributes a valuable tool to the field of normality analysis, offering a robust alternative for applications requiring precise and reliable assessments. [ABSTRACT FROM AUTHOR]

In recent research endeavors, discrete models have gained considerable attention, even in cases where the observed variables are continuous. These variables can often be effectively approximated by a normal distribution. Given the prevalence of processes requiring robust quality control, models associated with the normal distribution have found widespread applicability; nevertheless, there remains a persistent need for enhanced accuracy in normality analysis, prompting the exploration of novel and improved solutions. This paper introduces a discrete parameter-free distribution linked to the normal distribution, derived from a quality control methodology rooted in the renowned ‘3-sigma’ rule. The development of a novel normality test, based on this distribution, is presented. A comprehensive examination encompasses mathematical derivation, distribution tables generated through Monte Carlo simulation studies, properties, power analysis, and comparative analysis, all with key features illustrated graphically. Notably, the proposed normality test surpasses conventional methods in performance. Termed the ‘Zone distribution’, this newly introduced distribution, along with its accompanying ‘Zone test’, demonstrates superior efficacy through illustrative examples. This research contributes a valuable tool to the field of normality analysis, offering a robust alternative for applications requiring precise and reliable assessments.

Lithium battery is a complex nonlinear time-varying system with several inconsistencies. The fault diagnosis method has difficulty making an early diagnosis of battery faults without obvious abnormalities. In fact, voltage inconsistency is a representative fault response. Therefore, the monitoring of voltage inconsistency is highly important for the safe and reliable operation of lithium batteries in E-vehicles. The entropy method does not rely on an accurate analysis model and expert experience. Moreover, it does not consider the complex fault mechanism and system structure. Hence, it has gradually attracted widespread attention. Given such attention, a hybrid fault diagnosis method combining multiscale permutation entropy (MPE) and coefficient of variation (CV) is presented in this paper, and the improved MPE fault diagnosis model based on 3-sigma is emphasized. First, MPE and the 3-sigma rule are used to calculate the threshold, and the voltage inconsistency of the battery is judged by the threshold. Then, the location of the faulty cells is located by the CV. The superiority of the proposed method is proven by experimental data from the Yunzhitong platform of CRRC Electric Vehicle Co., Ltd. and a comparison of frontier methods. The proposed approach is feasible and promising in real E-vehicle applications.