Measurement Systems Analysis for Curve Data (2020-US-30MP-573)
Astrid Ruck, Senior Specialist in Statistics, Autoliv
Chris Gotwalt, JMP Director of Statistical Research and Development, SAS
Laura Lancaster, JMP Principal Research Statistician Developer, SAS
Measurement Systems Analysis (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 conducting the measurements. Automotive industry guidelines such as AIAG [1] or VDA [4], investigate a one-dimensional output per test, but they do not describe how to deal with data curves as output. In this presentation, we take a first step by showing how to perform a gauge repeatability and reproducibility (GRR) study using force versus distance output curves. The Functional Data Explorer (FDE) in JMP Pro is designed to analyze data that are functions such as measurement curves, as those which were used to perform this GRR study.
Auto-generated transcript...
Speaker | Transcript |
| Astrid Ruck | So my name is Astrid Ruck. I'm working for Autoliv |
| since 15 years and Autoliv is a worldwide leading manufacturer for | |
| automotive safety components such as seatbelts, air bags and active safety systems. So today we would like to talk about measurement system analysis for curve data. | |
| And Laura, Chris, and me have also written a white paper and it has the same type of title because we think it's a very urgent topic | |
| because | |
| there is nothing else in our own knowledge for for MSA for curve data available for dynamic test machines. | |
| So first we will start with a short introduction for MSA and functional data analysis, and then we will motivate our objective of a so called spring guideline which investigates | |
| fastening behavior or comfort behavior fastening seatbelts and then Laura will | |
| explain our methodology of the Gage R&R via JMP Pro. | |
| So usually measurement system analysis is an astute is a Type 2 study. | |
| So, | |
| MSA is a process. Here in this flow chart, you can see that it starts with Type 1 and linearity study and they are done with reference parts. Reference parts are needed, because we need a reference way you to calculate the bias of the measurement system. | |
| And if it fits, if the bias is good enough, then we check if we have an operator influence or not. | |
| If and only if we have an operator influence, then we can calculate the reproducibility. Otherwise, in all other steps, repeatability is is the only | |
| variation which can be calculated. So, in this area, Type 2 and Type 3 study, production parts are used. The AIAG, | |
| automotive industry guidelines, investigate a one dimensional output per test, but they do not describe how to deal with data curves as output and we will give you an insight how to | |
| how to do it. So if one has good accuracy then the uncertainty will be low. And this can be seen in this graph. And you see the | |
| influence of the increasing uncertainty on the decision of whether good or bad parts are near the tolerance. So here we have a lower specification limit, at the right we have an upper specification limit. | |
| And so the better my accuracy is the better my decision will be. And here we have a very big gray area and it will be very hard to make a right decision. | |
| Obviously parts in the middle of the tolerance will always be classified in the correct way. | |
| And in contrast to statistical process control parts at a specification limits are very valuable. | |
| So the best thing that you can ever do for an MSA is to take parts at the lower specification limit, all the upper specification limit, | |
| plus/minus 10% of the reference figure, and in this case the reference figure is a tolerance. If you have only one specific specification limit, like an upper or lower specification limit, | |
| then you can use your process capability index, Ppk, to calculate the corresponding process variation, 6s, and that is your new reference figure. | |
| And this idea how to select your parts for an MSA can also be used for output curves and their specifications bounds instead of specification limits. | |
| So data often comes as a function, curve, or profile referred to functional data. Functional data analysis available in JMP Pro in the functional data explorer platform. | |
| We will use P splines to model our extraction of false versus distant curves and later on we will use mixed models to analyze them. | |
| So seatbelts significantly contribute to preventing fatalities, and consequently functionality and comfort of seatbelts have to be ensured. | |
| And here on the right hand side, you see a picture from extraction forces of the seatbelt, given in blue, and retraction forces over distance, given in red. | |
| And both forces are important factors that affect both safety and comfort. | |
| And to test these forces and extraction/retraction force test setup is used and this simulates the seatbelt behavior in a vehicle. | |
| So let us have a closer look at this. So here you see a test set up and here you see the seatbelt. And here's a little moving trolley which drives on a trolley arm and now you see the seatbelt is | |
| retracted. And now the extraction started and here at the right hand side you see the seatbelt, which is fixed, according to its car position. | |
| Yeah. | |
| Whoops. | |
| So, | |
| When you look at these little curves and you see that inside my extraction force curve, | |
| there are some little waves and they have a semi-periodic structure. And if you would fit this semi-periodic structure with | |
| a polynomial, for example, then you will really overfit the repeatability. That's the reason why we need | |
| some flexible models. And where do these little waves come from? This will be more clearer when we have a look inside my seatbelt. And there is a spindle and there is a spring. And how's this behaves | |
| can be seen in this video. Here inside is my is my spindle and here at the right hand side there is my spring. And the cover of the spring is open so that we can have a look inside | |
| the cover, how the spring behaves. And in the beginning when the total webbing is on the spinner, then my spring is totally relaxed. And now my webbing is extracted and at the same time the spring is wounded up. So now we have the retraction and my spring becomes relaxed again. | |
| And these little movements result into this wavy structure and that is the reason why we really need flexible models based on FDE. | |
| So the creation of the spring guideline is our objective, who require a specific fastening behavior. | |
| So the fastening behavior is given by my extraction force curves. And here you see in this picture, different groups of five different | |
| seatbelt types and the corresponding spring thicknesses. If my spring thickness is small, then you can see that my extraction force is also small and if my spring | |
| thickness is large than my extraction force over distance will also be large. And then you see we have here different colors and we have a dark color. And the dark color results from real life measurements from three operators with each... | |
| every operator made five replications per seatbelt and and you can see that they have really made a great job. And the light color, that is our model from the p splines given by by FDE. So, as a spring guideline is our target, we would like to know, for which spring we will get | |
| the corresponding fastening behavior of the seatbelt, but before you start with the project, please always start with an MSA | |
| So, | |
| according to Autoliv's procedure, we use five different seatbelts, three experienced operators and five replications as you have seen in the | |
| previous graph. And our observation y is given by the actual values plus some random noise, so noise from the operators, the part, the interaction of operator and part and the corresponding | |
| repeatability. And then my Gage R&R is defined by six times the | |
| process variation of the measurement error, which is given by my reproducibility and the repeatability. | |
| And now we would like to know what is my minimum tolerance, such that my Gage R&R is acceptable, and acceptable means that the percentage Gage R&R is smaller than 20%. If my Gage R&R is | |
| 0.2 times my minimum tolerance, then we will also get a bound for my curves which you have seen, and this plus/minus 3s error bound | |
| will help us a lot to find the correct spring for a specific fastening behavior. So | |
| our methodology will | |
| be shown by Laura Langcaster. So, we will start to estimate a mean extraction force curve and we will use flexible models by FDE. | |
| Then the residual extraction forces will be calculated and after that, random effect models will be estimated via the platform mix models and finally the Gage R&R will be calculated. So, Laura, will you start? | |
| Laura | Yes, let me share my screen. Yeah. |
| Great. | |
| Laura | Okay. |
| So yes, thank you, Astrid. So I wanted to demonstrate how we use JMP Pro 15 | |
| to perform this measurement systems analysis with curve data. So first I want to show you the data that we have. And it looks a lot like regular MSA data, except instead of just | |
| regular measurements, we actually have curves. So we have this function of force in terms of distance. So the first thing that we want to do is to to | |
| use the functional data explorer to create the part force extraction curves. So I'm going to open up functional data | |
| explorer, I'm going to go to the analyze menu, then specialized modeling, functional data explorer. So force would be my output, distance is my input, and I want to fit one for each part or seatbelt type. And so that's going to be my ID and I click OK. | |
| And I get a bunch of summary information, summary graphs, and I'm going to enlarge this one. These are my curves and you can see that I have very distinct curves for each part, which are different colors. | |
| And I can also see that semi-periodic behavior that Astrid was talking about. Now I've already | |
| fit this data, so I know that a 300 node linear p spline fits really well. So I'm going to just go ahead and fit that particular model. So I go to models, model controls, p spline model controls, and | |
| remove all of these nodes. | |
| Add 300 because I know that's the node structure that works well. I'm only going to do a linear fits. I click go, and it doesn't take too long to fit this 300 node linear p spline to this data. | |
| And I just wanted to quickly mention that I'm only going to show a little bit of the functionality from this this FDE platform. It is, it does a lot of things a lot more than I have time to show you, or that we used for this measurement systems analysis. | |
| But, I highly recommend you check it out. We added a lot for JMP 15. | |
| And so I highly recommend you check out other talks about it as well. Okay, so this is our fit. And once again, we get a nice graph of our curves and the fit. | |
| And I want to check and make sure that this is a good fit. So I'm going to go to the diagnostic plots and I'm gonna look at the actual by predicted plot, I see it looks really great. Nice linear and the residuals are really small. So I'm very happy with this fit. | |
| Now, when we did this fit, we had to combined together the operator and the replication error. And so these curves have that that variation average out, but we need | |
| that variation to actually do the Gage R&R study. So what we're going to do is actually create a force residual and once we do that by subtracting off these part force functions from the original force function, | |
| we will have residual that will contain the operator and their replication error. So I'm going to go back to data table. | |
| And I've already created scripts to make this easy. So I've created a script to add my prediction formula to the data table. And I'll just show it to you really quick. This just come straight from the functional data explorer. This is my formula for the p spline fits for each part. | |
| And then I also have a script to create my residual column and so | |
| the formula for that is simply the difference between the force and those part force extraction functions. | |
| Right. And so now that I have this residual | |
| formula that contains the operator and replication error, I can fit a random effects model and estimate my operator...operator by part and my replication error. | |
| And to do that, I'm actually going to use the mixed model platform because we're not going to be fitting part variance, because we've already | |
| factored that out by creating the residual and subtracting off the part force function. | |
| So I've already created a script to launch the mixed model platform. And you can see that I have residual extraction force as my response. | |
| And I have operator and operator by part as my random effects. I'm going to run this. | |
| operator, operator by part (which is zero), and the residual. | |
| And to calculate the Gage R&R, I find it easy just to use a JMP data table like a spreadsheet. | |
| Makes it easy. I can just use a column formula. So I've entered my variance components in the table. | |
| And I just create a formula to calculate the Gage R&R, which is just 6 times the square root of the total variation without the part. And then I see that my Gage R&R is .4385 and I can take that and apply it to my spring guidelines | |
| in my specification bounds. And I can also back solve for the minimum tolerance. | |
| And so now I'm going to hand this back over to Astrid to continue with talking about how this got applied. | |
| Astrid Ruck | Yes, thank you, Laura. It's, it's great. But for the audience, of course, this are not the original of data. |
| So, | |
| Yes. | |
| Now as as Laura explained, now we know | |
| the Gage R&R and we also know my minimum tolerance, such that my measurement system is capable. So here you see the part extraction force function. | |
| And you also see the plus/minus 3s error bound and you see that the parts are very good selected because of the bounds are non overlapping and therefore | |
| they are significant different. And we can use it to find the right | |
| spring. And here you see in black, the minimum tolerance which is... | |
| we use the green line to center it around it. | |
| So now we have our Gage R&R but on the other hand, we can use FDE | |
| to load a golden curve as a target function. So I already told you, yes, we are interested in a spring guideline, but what kind of spring shall we use? So we also can use FDE to | |
| load this golden function and then the corresponding spring's thickness is calculated to obtain a specific behavior. | |
| So FDE is a great tool. And we used it also for a Type 3 study which is independent from operators and it is used for camera. | |
| And it measures the distance between seam and cutting edge of inflatable seatbelts and cutting process and that was also a great success story of using FDE. | |
| So to come to an end, I would like to say that most of our processes and tests have curves as output. | |
| And until now it has been impossible to standardize an MSA procedure using complete curve data and therefore, we had to restrict ourselves on | |
| a maximum from the extraction force curve, all the area between extract and retraction and therefore we reduced ourselves and lost a lot of a lot of | |
| considerable amount of information. So I'm really happy that we can make MSA for curve data. And 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. And at the end, I would like to show you that the corresponding paper is also available in the in the internet. So thank you for the attention. |
