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Interval Estimation Of Capability Index C_(pmk) For Manufacturing Processes With Asymmetric Tolerances

机译:具有不对称公差的制造过程的能力指数C_(pmk)的区间估计

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摘要

The index C_(pmk) combines the merits of the three earlier indices C_p, C_(pk), C_(pm) and alerts the user if the process variance increases and/or the process mean deviates from its target value. In practice, treat the calculated estimate C_(pmk) as true value and ignore the effect on asymmetric tolerances may lead to misinterpretation of process capability. Pearn et al. [Pearn, W. L., Chen, K. S. & Lin, P. C. (1999). On the generalizations of the capability index C_(pmk) for asymmetric tolerances. Far East Journal of Theoretical Statistics, 3(1), 47-66.] introduced a generalization of C_(pmk), which referred to as C"_(pmk) to handle processes with asymmetric tolerances. However, the sampling distribution of the estimator C"_(pmk) is exceedingly complex and the derivation of an interval estimation of C"_(pmk) is mathematically intractable. In this paper, we reformulate the explicit formulas and propose a heuristic algorithm to compute a lower confidence bound on C"_(pmk), which presents a measure on the minimum capability of the process, to enhance the applicability of the theoretical results. Tables are provided to assist the practitioners for a wide range of real world situation involving processes capability analysis. Equations and tables to estimate approximate sample size necessary to achieve a desired confidence limit with a specified confidence level are also developed. An application example on the trench capacitor etch process is also presented for illustrating the applicability of the generalization.
机译:指标C_(pmk)结合了三个较早指标C_p,C_(pk),C_(pm)的优点,并在过程方差增加和/或过程均值偏离其目标值时警告用户。在实践中,将计算出的估计值C_(pmk)视为真实值,而忽略对不对称公差的影响可能会导致对过程能力的误解。 Pearn等。 [Pearn,W. L.,Chen,K. S.&Lin,P. C.(1999)。关于不对称公差的能力指标C_(pmk)的一般化。远东理论统计杂志,3(1),47-66。]引入了C_(pmk)的泛化,称为C“ _(pmk),用于处理具有非对称公差的过程。但是,估计量C“ _(pmk)极其复杂,并且对C” _(pmk)的区间估计值的推导在数学上是棘手的。在本文中,我们重新制定了显式公式,并提出了一种启发式算法来计算C的下置信度“ _(pmk),提出了对过程最小能力的一种度量,以增强理论结果的适用性。提供表格以帮助从业人员应对涉及过程能力分析的各种实际情况。还开发了方程和表格,以估算达到指定置信度水平所需的置信度极限所需的近似样本量。还给出了沟槽电容器蚀刻工艺的一个应用实例,以说明该概括的适用性。

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