A phase I multi-modelling approach for profile monitoring of signal data

Abstract

Many industrial processes exhibit multiple in-control signatures, where signal data vary over time without affecting the final product quality. They are known as multimode processes. With regard to profile monitoring methodologies, the existence of multiple in-control patterns entails the study and development of novel monitoring schemes. We propose a method based on coupling curve classification and monitoring that inherits the so-called ‘multi-modelling framework’. The goal is to design a monitoring tool that is able to automatically adapt the control chart parameters to the current operating mode. The proposed approach allows assessing which mode new data belong to before applying a control chart to determine if they are actually in control or not. Contrary to mainstream multi-modelling techniques, we propose extending the classification step to include a novelty detection capability, in order to deal with the possible occurrence of in-control operating modes during the design phase that were not observed previously. The functional data depth paradigm is proposed to design both the curve classification and the novelty detection algorithm. A simulation study is presented to demonstrate the performances of the proposed methodology, which is compared against benchmark methods. A real case study is presented too, which consists of a multimode end-milling process, where different operating conditions yield different cutting force profile patterns

Constructing a Control Chart Using Functional Data

“…In this regard, Reference [42] presents an overview of the recent contributions to the development of Phase I control charts. Among the latest proposals for control charts, the work of Grasso et al [43] is especially interesting taking into account that is a Phase I control chart proposal for profiles based on the use of functional data depth concept (as well as the case of the present proposal). In fact, they proposed a Phase I control chart methodology for profiles belonging to the "multi-modelling framework", that includes the following stages: (1) a classification stage of new profiles into different operating modes or profile patterns using functional classification techniques from functional data depth measures (maximum depth approach based on Mode depth); (2) even the identification of a novel operation mode is included; (3) Once the operation mode corresponding to a new profile is identified, this is assigned to the corresponding control chart and consequently a suitable control charting method is applied to determine if the process remained in control over the period of time where those data were collected.…”

“…The automatic classification of each profile in the corresponding profile pattern could be very useful in the building energy efficiency field and previously to the application of our control chart proposal for Phase I and Phase II. With respect to the work of Grasso et al [43], it is also interesting to mention that the proposed profile monitoring control charting scheme is that based on functional PCA and described in Colosimo and Pacella [57].…”

Robust Functional ANOVA with Application to Additive Manufacturing

“…The mainstream literature devoted to spatter analysis and monitoring in L-PBF relies on video image processing methods to compute synthetic indices that capture salient aspects of the spatter behaviour, e.g., the number of ejected spatters in each video frame, their size, speed, etc. (Grasso et al, 2017;Everton et al, 2016). In the real-case study presented in this section, instead of treating synthetic descriptors of the spatter ejections as univariate or multivariate variables, the spatter behaviour is translated into a functional format by means of the so-called spatter intensity function introduced in Section 1.…”

A functional data analysis approach for the monitoring of ship CO2 emissions

“…Centofanti et al (2020) expand the Mandel's regression control chart (Mandel, 1969) to the functional setting, that is a control chart elaborated on the functional residuals obtained from a function-on-function regression of the quality characteristic profile on concurrent functional covariates. Other relevant contributions in this field include the work of Jin & Shi (1999), Colosimo & Pacella (2007), Colosimo & Pacella (2010), Grasso et al (2017), andBersimis et al (2018).…”