A Hybrid Fuzzy-Statistical Framework for Process Capability Analysis under Non-Normality and Asymmetric Tolerances

Abstract

This paper proposes a methodology for estimating process capability indices (PCIs) when data deviate from normality and the tolerances of quality characteristics are both asymmetric and imprecise. A fuzzy logic approach was applied to address uncertainty in tolerances. The methodology has five steps: (1) Fit a heavy-tailed distribution to the process data, (2) Select the best-fitting distribution, (3) Generate random samples from the selected distribution, (4) Construct triangular fuzzy numbers using the distribution parameters, and (5) Calculate the PCIs and analyze the results. The proposed methodology offers a more accurate assessment of process capability, benefiting industries that manage non-normal data and asymmetric specifications under uncertain conditions. In the applied case, the proposed methodology reduced the relative error in estimating the process capability index value by an average of 49% compared to the traditional method. The primary contribution of this paper is the integration of fuzzy logic with PCIs estimation to address imprecision and asymmetry, thereby enhancing process capability analysis under conditions closer to the reality of process quality control.