Statistical monitoring of nonlinear product and process quality profiles

Abstract

In many quality control applications, use of a single (or several distinct) quality characteristic(s) is insufficient to characterize the quality of a produced item. In an increasing number of cases, a response curve (profile) is required. Such profiles can frequently be modeled using linear or nonlinear regression models. In recent research others have developed multivariate T 2 control charts and other methods for monitoring the coefficients in a simple linear regression model of a profile. However, little work has been done to address the monitoring of profiles that can be represented by a parametric nonlinear regression model. Here we extend the use of the T 2 control chart to monitor the coefficients resulting from a parametric nonlinear regression model fit to profile data. We give three general approaches to the formulation of the T 2 statistics and determination of the associated upper control limits for Phase I applications. We also consider the use of non-parametric regression methods and the use of metrics to measure deviations from a baseline profile. These approaches are illustrated using the vertical board density profile data presented in Walker and Wright (Comparing curves using additive models.

Adaptive Charting Techniques: Literature Review and Extensions

“…Instead, modelbased methods have been developed to model profile data for SPC. For example, Williams et al (2007) advocated fitting nonlinear models to profiles first and then monitoring fitted parameters.…”

“…Table 1 summarizes the above discussion and classifies the literature based on their primary purposes. (2000), Kim et al (2003)) Nonlinear profile models (Williams et al (2007)) Surface (Wang and Tsung (2005) …”

A New Process Monitoring Method Based on Waveform Signal by Using Recurrence Plot

“…Colosimo et al [8] developed a regression model with spatial autoregressive errors for monitoring the bidimensional profiles of manufactured products. Williams et al [9] proposed to monitor the dose-response profiles by developing a four-parameter logistic regression model. However, these approaches are parametric with an assumption that the profile data should follow a specified functional form.…”

“…There is a limitation of the parametric model that the parameters may remain the same when the profile data has a small change. Thus, the parametric model could not represent the profile data change well [9].…”

A Retrospective on Volume 23 of Quality and Reliability Engineering International

“…The journal published many noteworthy papers in this area, including the work by Wu et al 3 on adaptive Cusum schemes for monitoring the mean and variance, use of cuscores by Nembhard and Changpetch 4 , Nembhard and Valverde-Ventura 5 , and Nembhard and Chen 6 , and the important works on monitoring profiles by Mahmoud et al 7 and Williams et al 8 . Other interesting and useful papers include work on change points by Perry et al 9 , control charting dependent attribute data by Shepherd et al 10 , and multivariate quality control by Guh 11 and Bersimis et al 12 .…”