Simple linear profiles (SLPs) are modeled by a linear functional relationship between a response variable and an explanatory variable. Several studies have proposed process capability indices to evaluate process performance under the assumption of fixed explanatory variables. In certain applications, this assumption may not hold, and one needs to utilize a method based on the assumption of random explanatory variable. This study introduces a functional capability index for SLPs with a random explanatory variable for both symmetric and asymmetric tolerances. The performance of the proposed index is evaluated in terms of accuracy and precision of estimation under two different scenarios, i.e. the uniform and normal explanatory variable distribution functions, through simulation studies. The simulation results show that the proposed index outperforms the existing one in terms of mean absolute error and mean square error metrics. Finally, an illustrative example in the cryptocurrency markets is used to demonstrate the applicability of the proposed method.

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