Advanced Statistical Characterization and Correlation Analysis of Process Performance Indicators for Optimized Engineering Decisions

ABSTRACT This study develops a rigorous statistical framework for the systematic characterization and comparative evaluation of process performance indicators, with the objective of informing optimized engineering decision‐making under uncertainty. System behavior is analyzed across multiple operational categories using a structured suite of descriptive and comparative statistical techniques applied to three primary indicators: performance result R, processing time T, and error margin E. The analytical methodology integrates raw observations with aggregated statistical descriptors, including arithmetic means, variances, standard deviations, medians, ranges, coefficients of variation, and Pearson correlation coefficients. This multi‐level characterization enables precise assessment of expected performance, operational effort, uncertainty, and relative stability, which together define the system performance vector (R, E, T). The results reveal pronounced category‐dependent performance profiles and demonstrate a strong performance–effort coupling between R and T, together with moderate associations involving E, thereby elucidating inherent trade‐offs between output magnitude, efficiency, and precision. In addition to static statistical analysis, the study examines learning efficiency and convergence behavior through a comparative evaluation of quantum‐inspired reinforcement learning (QI‐RL) and classical ε‐greedy strategies. The results indicate enhanced exploration capability and accelerated convergence in complex decision spaces. The influence of environmental uncertainty modeling is further investigated, showing that temporally correlated stochastic disturbances substantially increase performance variability relative to uncorrelated assumptions. Overall, the proposed framework provides a coherent and extensible analytical basis that integrates statistical robustness, correlation structure, adaptive learning behavior, and uncertainty sensitivity. It offers a principled foundation for performance evaluation, resource allocation, and adaptive optimization in complex engineering systems and establishes clear directions for future extensions toward dynamic modeling and data‐driven control architectures.