Collaborative Research: Monitoring Process and Product Quality Profiles

这项拨款为统计方法的发展提供资金，以有效地监测代表过程或产品质量的曲线。在目前工业上的大多数统计过程控制应用中，假设质量可以通过单变量质量特征的分布或由几个相关质量特征组成的向量的一般多变量分布来充分表示。然而，在许多实际情况下，通过响应变量和一个或多个解释变量之间的关系，可以更好地描述和总结过程或产品的质量。因此，在每个采样阶段，人们观察到一组数据点，这些数据点可以用曲线（或剖面）表示。在一些校准应用中，轮廓可以用简单的直线模型充分表示，而在其他应用中则需要更复杂的模型。在这项工作中，将开发和评估控制图，以监测这种过程和产品质量概况。该应用程序将与功能数据分析相关，并将开发用于线性轮廓，非线性轮廓以及目前使用样条和小波处理的轮廓的方法。这项研究的结果将导致更有效地利用工业数据来描述和监测过程和产品的质量。特别是，该方法可用于监控校准关系，避免测量设备的过度校准。这降低了成本，提高了测量精度。在制药工业中存在着监测连续批次药物的非线性剂量-反应曲线的应用。在半导体制造、化学和其他测量过程的校准（包括NASA的一个测量过程）中，已经确定了应用程序并获得了数据。

This grant provides funding for the development of statistical methods for the effective monitoring of curves that represent the quality of a process or product. In most current statistical process control applications in industry it is assumed that that quality can be adequately represented by the distribution of a univariate quality characteristic or by the general multivariate distribution of a vector consisting of several correlated quality characteristics. In many practical situations, however, the quality of a process or product is better characterized and summarized by a relationship between a response variable and one or more explanatory variables. Thus, at each sampling stage one observes a collection of data points that can be represented by a curve (or profile). In some calibration applications, the profile can be represented adequately by a simple straight-line model, while in other applications more complicated models are needed. In this work control charts will be developed and evaluated to monitor such process and product quality profiles. This application will be related to functional data analysis and methods will be developed for linear profiles, nonlinear profiles, and those currently handled using splines and wavelets. The results of this research will lead to more effective use of industrial data to characterize and monitor the quality of processes and products. In particular, the methods can be used to monitor calibration relationships and avoid the over-calibration of measurement devices. This lowers costs and improves measurement accuracy. Applications exist in the pharmaceutical industry in the monitoring of non-linear dose-response curves of successive batches of drugs. Applications have been identified and data have already been obtained in semiconductor manufacturing and in the calibration of chemical and other measurement processes, including one at NASA.