Evaluation of Cpm estimators in ranked set sampling designs

Abstract

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 Cpm (or Taguchi) index. In this work we propose the estimation of Cpm 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 Cpm 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 Cpm 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.