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 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.

摘要

能力分析允许评估生产是否符合工业过程中的项目规范。可以使用不同的指标来评估过程能力，其中包括C _pm（或 Taguchi）指标。在这项工作中，我们建议使用排序集抽样 (RSS) 和两个扩展来估计正态分布过程的C _{pm ：对排序集抽样 (PRSS)，作为一种经济的替代方案；}和双排集抽样（DRSS），作为一种更有效（且成本更高）的策略。此外，三个不同的C _pm估计器被考虑。通过蒙特卡罗模拟评估了它们在偏差、均方误差和相对效率方面的表现。结果表明： (i) 不同C _pm估计器的性能存在很大差异，特别是对于小样本；(ii) 基于 RSS 的估计器优于其简单随机抽样对应的估计器；(iii) DRSS 估计器呈现最低的均方误差；(iv) PRSS 估计器在不同情况下显示出与其对应的竞争性能。