In this study, a new process capability index is proposed. The new index is quantile-based, can be used in normal and non-normal measurements, and is a general form of the conventional Cpm. The new index is investigated by relying on the Weibull distribution, which holds significant importance in quality control and reliability studies. Point estimation for the index is discussed with parametric and non-parametric approaches. Moreover, several estimators based on methods such as Bayesian and bootstrap are suggested for interval estimation. A Monte Carlo simulation study is conducted to evaluate the performance of methodologies in both on-target and off-target processes. In addition, numerical examples are provided to evaluate two real-world problems where the measurements follow both the Weibull and normal distributions. The usability of the index is particularly evident when evaluating the ball size data in the first real data analysis, where the classical Cpm index is not used.