Weibull-Based Process Capability Modeling for Construction Quality Control under Non-Normality: A Reliability–Statistical Framework

Conventional process capability indices (Cp, Cpk) assume normality and can yield misleading assessments when construction quality data exhibit skewness and heavy tails. This study develops a Weibull-based capability framework integrating distribution-specific assessment, failure probability, reliability estimation, and bootstrap validation. The methodology was evaluated on 149 concrete compressive strength records with a 20 MPa lower specification limit (LSL). Normality tests confirmed significant departure from normality (p < 0.001). Maximum likelihood estimation yielded Weibull shape and scale parameters of 15.6992 and 24.5448. The resulting Weibull Reliability Capability Index (WRCI) was 0.5059, contrasting sharply with the conventional lower capability index (Cpl = 1.0508). The Weibull model revealed a 3.94% nonconformance probability (96.06% reliability). Bootstrap validation (1,000 replications) confirmed metric stability (95% CI: 0.4472–0.6163). The framework provides an accurate, risk-informed quality control alternative without requiring normalizing transformations.