From Profile to Surface Monitoring: SPC for Cylindrical Surfaces Via Gaussian Processes

Abstract

Quality of machined products is often related to the shapes of surfaces that are constrained by geometric tolerances. In this case, statistical quality monitoring should be used to quickly detect unwanted deviations from the nominal pattern. The majority of the literature has focused on statistical profile monitoring, while there is little research on surface monitoring. This paper faces the challenging task of moving from profile to surface monitoring. To this aim, different parametric approaches and control charting procedures are presented and compared with reference to a real case study dealing with cylindrical surfaces obtained by lathe-turning. In particular, a novel method presented in this paper consists of modeling the manufactured surface via Gaussian processes models and monitor the deviations of the actual surface from the target pattern estimated in Phase I. Regardless of the specific case study in this paper, the proposed approach is quite general and can be easily extended to deal with different kinds of surface or profiles.

Multisensor data fusion via Gaussian process models for dimensional and geometric verification

“…Among the different models that can be assumed for this term, a Gaussian Process (GP) model [23][24][25] is considered in this work.…”

Statistical monitoring of multiple profiles simultaneously using Gaussian processes

“…In this model, represents the measurement noise, the mean function is usually taken to be zero, and the model is parameterized by defining a positive definite covariance function. In this study, as in most other practical applications, the covariance function is chosen to be a Gaussian kernel where Here is defined as the maximum allowable covariance and λ i , m is the shape parameter for sample m of profile i . Considering the Gaussian covariance function, the covariance matrix for the observations of profile i can be constructed.…”

“…The Gaussian kernels do not require many parameters to be estimated which makes them a perfect choice for the scenario in which there is scarcity of data . Also, their ability to model different spatial features and achieve reasonable performance in different applications has made them a common choice in the literature . Thus, considering Equation , the Gaussian kernel used in this study is as follows: where s , μ ϵ R D and L ui is a D × D positive definite matrix.…”

“…24 Also, their ability to model different spatial features and achieve reasonable performance in different applications has made them a common choice in the literature. 4,14,25 Thus, considering Equation (11), the Gaussian kernel used in this study is as follows:…”

On‐line monitoring of extreme values of geometric profiles in finite horizon processes

“…The need of accounting for the within‐profile spatial autocorrelation has been discussed in Zhen et al, who used GPs to model the dependency among successive measurements. Similarly, Wang et al and Colosimo et al used Gaussian‐Kriging processes to model surfaces by means of random fields: In these papers, autocorrelation has been accounted for by means of a parametric exponential function that is similar to that investigated by Ogilvy, Ogilvy and Foster and later discussed by Zhao et al to model wafer surfaces. In particular, Wang et al et al also discussed the importance of investigating the semivariogram of the correlation function of observations to fit correctly the autocorrelation.…”