Capability analysis allows evaluating the conformity of the production to the project specifications in industrial processes. Different indices can be used to assess the process capability, among them the $C_{pm}$ (or Taguchi) index. In this work we propose the estimation of $C_{pm}$ for normally distributed processes using ranked set sampling (RSS) and two extensions: pair ranked set sampling (PRSS), as an economical alternative; and double ranked set sampling (DRSS), as a more efficient (and expensive) strategy. Also, three different $C_{pm}$ estimators were considered. Their performances regarding bias, mean squared error, and relative efficiency were evaluated through Monte Carlo simulation. The results indicated that: (i) There was a substantial variation in performances for different $C_{pm}$ estimators, particularly for small samples; (ii) RSS based estimators outperformed their simple random sampling counterparts; (iii) DRSS estimator presented the lowest mean square error; and (iv) PRSS estimator showed competitive performance to its counterparts in different scenarios.