In industrial environments, process capability indices are daily employed as numerical metrics to summarize the performance of a process according to a predefined set of specification limits. Neglecting gauge measurement errors is a common phenomenon in process capability evaluations by researchers in laboratory investigations and by practitioners in daily operations. However, this common negligence is far from reality regardless of the employment of highly modern measuring tools, and may notably influence the efficiency of the measuring method for assessing the performance of a manufacturing process. In this paper, a linear covariate error model is applied to investigate the effects of gauge measurement errors on the classical and fuzzy estimation approaches of the multivariate process capability index $S_{pk}^T$ for univariate and multivariate normally distributed quality characteristics with precise specification limits. Moreover, lower confidence bounds are also derived for the yield index $S_{pk}^T$ in the presence of measurement errors and based on a fuzzy approach. In addition to the theoretical results, extensive simulations have been conducted to analyze how the behavior of the test statistic and lower confidence bound (LCB) for assessing the performance of the process is affected by different sources of the measurement errors. The obtained results indicate that a serious underestimation of the process capability occurs when the data is contaminated with measurement errors. It is also shown that the underestimation problem is somewhat solved by taking multiple measurements from the identical item. Moreover, comparative analyses show that the proposed method is superior to Scagliarini’s method and Wang’s way such that the negative effects of errors on underestimating the LCB are reduced in the proposed plan. This paper also extends the application of the introduced method to correlated variables. Finally, three practical examples are discussed to demonstrate the use of the proposed method in industrial applications.

在工业环境中，过程能力指数每天都被用作数字指标，以根据一组预定义的规范限制来总结过程的性能。忽略量规测量误差是实验室调查研究人员和日常操作中的从业人员在过程能力评估中的常见现象。然而，无论使用高度现代化的测量工具如何，这种常见的疏忽都远非现实，并且可能会显着影响评估制造过程性能的测量方法的效率。在本文中，应用线性协变量误差模型来研究量规测量误差对多元过程能力指数的经典和模糊估计方法的影响${\mathrm{小号}}_{pķ}^{吨}$用于具有精确规格限制的单变量和多变量正态分布质量特征。此外，还得出了收益率指数的置信下限${\mathrm{小号}}_{pķ}^{吨}$在存在测量误差的情况下并基于模糊方法。除了理论结果之外，还进行了广泛的模拟来分析用于评估过程性能的测试统计量和置信下限 (LCB) 的行为如何受到不同来源的测量误差的影响。所得结果表明，当数据被测量误差污染时，会严重低估过程能力。它还表明，通过对同一项目进行多次测量，可以在一定程度上解决低估问题。此外，比较分析表明，所提出的方法优于 Scagliarini 的方法和 Wang 的方法，从而在所提出的计划中减少了错误对 LCB 低估的负面影响。本文还将所介绍的方法的应用扩展到相关变量。最后，讨论了三个实际示例，以证明所提出的方法在工业应用中的使用。