Abstract: This article extends the recent work of V¨annman and Albing (2007) regarding the new family of quantile based process capability indices (qPCI) CMA(τ, v). We develop both asymptotic parametric and nonparametric confidence limits and testing procedures of CMA(τ, v). The kernel density estimator of process was proposed to find the consistent estimator of the variance of the nonparametric consistent estimator of CMA(τ, v). Therefore, the proposed procedure is ready for practical implementation to any processes. Illustrative examples are also provided to show the steps of implementing the proposed methods directly on the real-life problems. We also present a simulation study on the sample size required for using asymptotic results.