Measurement Systems Analysis for Curve Data Astrid Ruck

Measurement Systems Analysis for Curve Data Astrid Ruck, Senior Specialist in Statistics, Autoliv B. V. & Co. KG Chris Gotwalt, JMP Director of Statistical Research and Development, SAS Laura Lancaster, JMP Principal Research Statistician Developer, SAS 1 October 2020 Measurement Systems Analysis for Curve Data Copyright Autoliv Inc. , All Rights Reserved Americas JMP Discovery Summit 2020

Contents § Measurement Systems Analysis (MSA) § Influence of Uncertainty and Part Selection § Functional Data Analysis § Motivation and Background § Objective § GRR Study Design § Methodology § Result § Outlook § Conclusion 2 October 2020 Measurement Systems Analysis for Curve Data, A. Ruck, C. Gotwalt, L. Lancaster Copyright Autoliv Inc. , All Rights Reserved Americas JMP Discovery Summit 2020

Measurement Systems Analysis (MSA) MSA is a measurement process consisting not only of the measurement system, equipment and parts, but also the operators, methods and techniques involved in the entire procedure of measuring. Automotive industry guidelines such as AIAG or VDA investigate a one-dimensional output per test, but they do not describe how to deal with data curves as output. We will show to perform a gauge repeatability and reproducibility Study (Type-2 GRR study) based on force versus distance output curves. Thereby, § Repeatability is associated with the equipment variation § Reproducibility is associated with the variation of operator and operator*part interaction. MSA procedure 3 October 2020 Measurement Systems Analysis for Curve Data, A. Ruck, C. Gotwalt, L. Lancaster Copyright Autoliv Inc. , All Rights Reserved Americas JMP Discovery Summit 2020

Influence of Uncertainty and Part Selection If one has good accuracy, then … § the uncertainty will be low § high probability of right decision of whether good or bad parts are in the neighbourhood of the upper and lower specification limit(s), USL and LSL, respectively. The more different the master and/or reference parts are, the better the accuracy of the measurement system will be understood. In contrast to SPC parts at the specification limit(s) are very valuable. Influence of increasing Uncertainty Part selection according to the reference figure (RF) These ideas can also be used for output curves and their specification bound(s) 4 October 2020 Measurement Systems Analysis for Curve Data, A. Ruck, C. Gotwalt, L. Lancaster Copyright Autoliv Inc. , All Rights Reserved Americas JMP Discovery Summit 2020

Functional Data Explorer (FDE) § Data often comes as a function, curve or profile, referred to functional data. § Functional data analysis is available in JMP Pro in the Functional Data Explorer (FDE) platform. § FDE fits functional models using B-splines, P-splines or Fourier basic models. § It can also reduce the dimension of the data by performing functional principal components analysis and converting the data to a form that can be analyzed by other statistical platforms in JMP. 5 October 2020 Measurement Systems Analysis for Curve Data, A. Ruck, C. Gotwalt, L. Lancaster Copyright Autoliv Inc. , All Rights Reserved Americas JMP Discovery Summit 2020

Motivation and Background Seatbelts significantly contribute to preventing fatalities. Consequently, functionality and comfort of seatbelts must be ensured. Extraction and retraction forces of seatbelts are important factors that affect both safety and comfort. To test these forces, an Extraction/Retraction Force-Test Setup is used, which simulates seatbelt behavior in a vehicle. Ex-/Retraction Force-Test Setup Discovery 2020_Test_Setup. mp 4 Spring in a Seatbelt Discovery 2020_Video_Spindle. mp 4 Force vs. Distance Curves and Spec. Bounds The enlarged section of the wavy extraction curve (right Figure) shows a fine semi-periodic structure. These waves within the curve result from spindle rotations during extraction and retraction. 6 October 2020 Measurement Systems Analysis for Curve Data, A. Ruck, C. Gotwalt, L. Lancaster Copyright Autoliv Inc. , All Rights Reserved Americas JMP Discovery Summit 2020

Objective Investigation of the comfort behavior of fastening seatbelts for § different types of seatbelts with varying spring thickness Creation of a spring guideline for our customers, who require a specific fastening behavior. § Focus on the extraction force curves, because that affect the comfort of fastening A smaller spring thickness results in a smaller extraction force. The spring guideline is our target, but before we need to understand the variation of our measurement system for these extraction force curves. Force & P-Spline Force (light colors) Functions vs. Distance 7 October 2020 Measurement Systems Analysis for Curve Data, A. Ruck, C. Gotwalt, L. Lancaster Copyright Autoliv Inc. , All Rights Reserved Americas JMP Discovery Summit 2020

GRR Study Design § 8 October 2020 Measurement Systems Analysis for Curve Data, A. Ruck, C. Gotwalt, L. Lancaster Copyright Autoliv Inc. , All Rights Reserved Americas JMP Discovery Summit 2020

Methodology § Estimate mean extraction force curves for each part by fitting flexible models with FDE, and treat these mean functions as the ideal “Part Extraction Force Functions”. § Calculate the “Residual Extraction Forces” by subtracting the “Part Extraction Force Functions” model predictions from the original extraction force data. § Fit a random effects model using the “Residual Extraction Forces” to estimate the operator, operator by part and random error variance components. § Calculate the GRR and apply this result on the spring guideline or specification bounds. 9 October 2020 Measurement Systems Analysis for Curve Data, A. Ruck, C. Gotwalt, L. Lancaster Copyright Autoliv Inc. , All Rights Reserved Americas JMP Discovery Summit 2020

Result The extraction force measurement system is acceptable, if %GRR = GRR/T*100 ≤ 20%. Þ Tmin = 5 GRR is the minimum tolerance band width for an acceptable measurement system Þ As the seatbelts parts are selected over the total tolerance width, it follows %GRR < 20%. Part Extraction Force Functions (light color) Tmin 10 October 2020 Measurement Systems Analysis for Curve Data, A. Ruck, C. Gotwalt, L. Lancaster Copyright Autoliv Inc. , All Rights Reserved Americas JMP Discovery Summit 2020

Outlook § Reduce further the measurement variation by performing separate MSA studies by seatbelt type or spindle diameter. Part 4 has a different spindle diameter § FDE will help us develop the spring guidelines by seatbelt type since it is possible to load an extraction force “golden curve” as a target function. § Recently, we applied FDE and Mixed Models successfully on a GRR Type-3 study for cameras that measure the distance between seam and cutting edge of inflatable seatbelts in a cutting process. § Since the cutting process is destructive and only repeatability is of interest in a GRR Type-3 study, each curve was fit individually with FDE. 11 October 2020 Measurement Systems Analysis for Curve Data, A. Ruck, C. Gotwalt, L. Lancaster Copyright Autoliv Inc. , All Rights Reserved Americas JMP Discovery Summit 2020

Conclusion § FDE and Mixed Models platforms are effective and important methods for generalizing MSA studies to curve data. § Most of our processes and tests have curves as output. Until now it has been impossible to standardize an MSA procedure using complete curve data. We had to restrict ourselves to using the maximum value of a curve or the area between curves as the measurement output for each test, and we lost a considerable amount of information. § As far as we are aware, there are no other publications that discuss this type of MSA generalization for curve data with other commercial software. Link to the JMP White Paper „Measurement Systems Analysis for Curve Data“ https: //www. jmp. com/en_us/whitepapers/jmp/measurement-systems-analysis-for-curve-data. html 12 October 2020 Measurement Systems Analysis for Curve Data, A. Ruck, C. Gotwalt, L. Lancaster Copyright Autoliv Inc. , All Rights Reserved Americas JMP Discovery Summit 2020