Solving an Industrial Problem Using Advanced Statistical Tools (2021-US-45MP-854)
Matheus Sguissardi, Lean Six Sigma Consultant, Plana Consultoria e Treinamentos
The worst problem that a company can have is customer dissatisfaction. This talk examines a problem that happened on the customer's assembly line when disassembling and assembling the cover of an electric motor connection box. The disassembly and assembly concept was specified for at least 10 cycles, but the customer had problems in the first cycle when connecting cables to the purchased electric motor.
To solve the problem, some statistical tools and methods of the Six Sigma methodology were used, in a sequential and structured way to validate and invalidate the main hypotheses of the problem and then make all decisions in the process and product in an appropriate way, all based on facts and data analysis.
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| Nicholas Shelton | Okay, and i'm going to go on mute and once I go on mute, then you can begin when you're ready and like I mentioned don't worry if you make a mistake or anything just keep continuing and and then, when we're done, I will I will stop the recording and unmute myself. |
| Okay okay all right when you can go ahead and start when you're ready. | |
| Hello everyone i'm here to i'm here today to explain to you to talk about. | |
| An industrial problem that was solved using some advanced statistical tools and JMP, so this is a real problem that I faced when I when I was working in an electrical modern manufacturer. | |
| So what what was the problem that we face at the time right we had this electromotors, and so the customer, he buys the distillate from water. | |
| And he has to connect these electrical model to his own machine, so he has to open this box here. | |
| This box has four different screws here and four holes, so he has to open this cover he has to connect the the electrical cables to his own machine and he has to fix it again to close it against so. | |
| When the customer tries to do this and, at the moment that he has to fix the to close the box with this cover and these four different. | |
| screws sometimes he has this problem when the screw is [turned false?]. In other words we don't have the grip anymore between the screw and the aluminum hole so. | |
| By specification, this screw this this process of assembling, and these are assembling has to withstand at least 10 times. | |
| And the customer do this without any problems for for for a long, long time or different times, or if he has to. | |
| change the position change the machine of where these these electric motor is being used, he should just open and close the box, without any problem So here we have a little. | |
| Short video just a nice illustration about what is the problem, so this crew is lost here, there is no grip at all. | |
| When these happen is not a common problem that we face every day, but sometimes it can happen when it happened, the director received. | |
| a complaint, the director, called the quality manager and the quality manager called me so Matheus, we have to solve this problem so put people together and start this investigation. | |
| And that was what happened that was what we started doing so. | |
| As other situations other problem that we have to investigate. | |
| We will always start with some hypotheses so will least some hypotheses what can be affecting this problem, how can we explain this this failure, so we put together some people from different areas, for example, product engineering. | |
| What can we be doing wrong here, it can be any problem and in the product engineering department, causing the these problems, some design errors or can we have assembly line errors problems variation maybe the this the the screwing machine. | |
| is working with a high torque and generating generating these this problem or this screw that we are buying right this supplier, that is providing us this screws maybe they have. | |
| Reduced diameter and we cannot have this grip or the the last hypothesis that we listed at the time was the injection process, so this fitting aluminum box here. | |
| This diameter could be opened so, even if we had a bad screen or a good screw diameter, we could have a very big diameter and the screw cannot have this grip with this. | |
| Whole so we could have a problem. | |
| Once we had these meetings these these hypotheses listed we started validating or invalidated them. | |
| With some studies some with some data and we started here talking about the product engineering and assembly line so both of them were invalidated. | |
| We check it all the designs we check it all the specifications all the standards that we had when we are designing these assembly this combination between screw and hole the different materials, everything was Okay, so we didn't need to do anything here. | |
| The screwing machine that we were using at the assembly line we just got this. | |
| came to the laboratories, the metrology and we checked the park we check the machines and everything was Okay, so we didn't have problems here, so what can be affecting this problem now we. | |
| Only had the screw and the fitting hole this aluminum part this box here that we could check okay let's do this let's talk about the Israel diameter, one of the main hypothesis of this problem. | |
| And here we started using JMP, but how so before before we start measuring the screws in the factory, we always need to be sure that the measurement system is approved so. | |
| Here is a simple variability chart where we have here the diameter, the screw diameter, we have five parts each part was measured by two different operator three times each one. | |
| We have our various components here, where we can see these 93.8% of the variation of variation was caused by parts, so this is one of the things that we can be sure that our measurement system is good, we can differentiate. | |
| parts in the process, so the measurement system was approved, and now we can move on, we can go to the process Aaron we can is 30 evaluate this is screws so let's do it, how is the voice of the process right and we had a sample strategy every every step that I am presenting here to you. | |
| We used the six Sigma methodology, so we follow it some. | |
| Very structured approach is starting with the measurement system evaluations and go into the process and understanding the voice of the process and, at the end. | |
| doing some combinations and trying to validate or validating those hypotheses that I just presented so the sampling is strategy here. | |
| Was we had a box, full of screws inside, so we knew the only information that we had was that we received these screws in some different batches so each batch had their on it's on. | |
| They manufacturing date or a manufacturing moment, so we just separated it in three different batches each batch we called. | |
| 20 parts and each part we measured in two different positions on the square of like zero degrees and 90 degrees. | |
| Why this? To see, to understand if we could have some circularity problems in this diameter right so with this sampling strategy we started to collecting data and we had 120 points to be analyzed in JMP. So again. | |
| In a very practical analysis running a variability chart here just putting all the 120 points, we can see that everything was inside of the specification limits. | |
| Each dot here is one measure in the the screws. These blue line | |
| it is connecting the position one and two of this screw so if we have a very big blue line here, it means that we have a very big circularity error. | |
| It means that these two different position of the diameter, they are very different so. | |
| The diameter, in the mean can be good, but the difference between these and these diameter could be wrong, and this could affect our problem at the moment of screwing it in the aluminum box okay so. | |
| This is a very practical analysis about this screw everything seemed to be good in a graphical analysis comparing these two different position of the the the screws, we can see, we can invalidate the hypothesis that the the circularity errors. | |
| Were could be affecting so the mean of the position one and the position two was almost the same. The size of these bars here, there is nothing that Okay, the position two or one is very different so. | |
| This graph analysis here we with variability chart just comparing the position against diameter, we can see anything that. | |
| We should pay attention so okay now in a quantitative analysis using these process capability in JMP, we can see how is the voice of the process of the supplier right the supplier, that is delivering us these screws. How is the process? Right. | |
| We we have here a CPK about 1.47, a PPK about 1.014. We have instability takes about 1.45 so is not the best process that we we have. | |
| Seen but. | |
| Considering and ideal PPK 1.33. And thinking about a critical to quality characteristic or dimension here. | |
| We could assume that this screws could affect the problem in our long term basis, right now, they are all inside of this specification but based on the statistics, based on the PPK value. | |
| Less than 1.33 maybe it can be a problem in the future right. | |
| But before blame the suppliers, we need to understand the the injection process, our process. If we can be robust against this variation of the screw, better for us because we don't need to. | |
| start doing anything in the supplier and okay. | |
| So this hypothesis. | |
| It was on hold. Let's put this aside and let's wait, the studies about our injection process. | |
| let's let's see how we did this so. | |
| to inject these these box, we have a mold. | |
| This mold has four different cavities. So every time that we inject | |
| this process we get four different parts, right? Each part has four different holes, the holes that the the customer use to fix the cover. And each part, we will also measure in different positions. Position one and position two. | |
| So again, before we start measuring this process and see what is happening in orignal, actual process, we have to be sure that our measurement system is is good is approved. | |
| We have to be sure that we are, we know how to event five bad parts and good parts. So with one part, one box we we ran this. | |
| These measurement system of variation in those four different holes. Each hole measured by two different operators three times each one. So, we had the the biggest variation of this measurement system being caused by hole 95%. | |
| I have to say here that it, it was very difficult to approve. | |
| It was like the third MSA that we ran. We have to buy a new guard here to to measure this internal diameter. The specification was very tight and the the resolution about the | |
| about the gauges not appropriated at the beginning, so we had this third MSA approved. So once it's approved | |
| now we can move on, we can measure the parts in the process, we can understand how is our injection process variating. And how can it affect our our problem. So we went to the process we we got that mode with four different cavities. | |
| Five parts from each cavity. | |
| So we just injected five times in the process, each cavity gave us five parts. Each part had | |
| four different holes and each hole we measure into different position, so this is a sample strategy for a six Sigma tool that we call | |
| components of variation with these components of variation we can understand how is the voice of the process, we can compare the voice of the process with the voice of the customer and using the process capability in JMP and we can understand how big is the problem. So, | |
| here we have COV practical analysis. And, all the data that we collected are here. | |
| So we have four different cavities in this variability chart. The first cavity here, the second cavity here the third one here and the fourth one here. So we can see a lot, a lot of different situations here a lot of | |
| information that is very important to us. For example, what is the the worst cavity that we can see in this variability chart is the cavity number two. | |
| Because we can for example let's get the part number six here we have the first hole inside of this specification, the second hole. | |
| outside of this specification that third hole inside of the specification and the fourth hold one of the position outside and one of the position inside. So, this is not good. | |
| This is causing...it's causing a lot of variation in this data and maybe, here we have the root cause of our problem, right? | |
| And why this mold, this is the same old four different cavities and why the cavity number three is so good, and the cavity number two is so bad, and the one and four is more or less, right? | |
| There's a lot of variation between these two position on the hole. It means that the hole is not circular. We have | |
| circularity error here that can be affecting the problem. So, this is a very practical analysis, we can see a lot of things here in JMP with these variability chart. | |
| A more graphical analysis I just took off the position hole her,e and those blue lines now they are inside of this bar. So the bigger is the bar the bigger is the circularity problem. | |
| We can see again the cavity three. We don't we don't see that problem but, the cavity one, cavity four and cavity two we still can see the problem. | |
| being very, very big, right? In a quantitative analysis using now our process capability, we can see, as we put all the hundred 60 data | |
| inside of the same batch inside of the same evaluation, the same distribution, we can see a very bad process our CPK and PPK is almost equal to zero, so is a very bad process. | |
| Thinking about non conformance in a long term or short term | |
| basis, we are talking about more than 300,000 parts being non conform | |
| against our specification, it means that we if we buy 1 million we sorry if we inject 1 million of those box, | |
| aluminum box, we will have more than 300 or 30% of them being our of the specification so maybe we just found the problem. And another thing that is very interesting here that JMP provide to us, we have this 160 | |
| data here, but we know that the person that is investigating this, the person that is analyzing this, | |
| knows that we have four different cavities and we have like 40 data points for each cavity, so why not separate these analysis into different cavities? So, that what we did here. So we have process capability analysis for the cavity one. | |
| Very unstable process. Cavity two again very unstable process we have negative PPK and CPK values. | |
| It means that the measure of this, the meaning of this process is outside of the specification one of them. So, we can see here like the sample mean is 4.50075, | |
| while the upper specification limit is 4.5000. So we are out of our specification. It means that our PPK is negative. So, | |
| is very bad very bad process worse than the cavity one. The cavity three is that good one. So, we can see a very stable process. The stability index is close to one. | |
| The CPK and the PPK values are very good. The normal forms expectation is very good. So, the cavity four, we also have a bad process. | |
| CPK and PPK bad, and comparing each one year is very clear now where are where where is our problem, right? Is in the cavity 1, 2, 3 or 4? | |
| So if we had to start acting in our process, we must evaluate the dimensions, the situations, the characteristics the cavity two, and the one, and four and we don't need to do anything in the cavity three. | |
| So the hypotheses about our injection process is validated. | |
| And we still have that screw diameter hypothesis on hold. So, why did I put this on hold because we can evaluate them together. | |
| We have an interference between the screw and fitting hole. How can we evaluate how they are interacting in the in the process in the product. | |
| And how good or how bad they are once we have the information about those two process, right? We have the mean and the standard deviation of each process, so we can put this together. So let's start here running. | |
| bivariate fit of hole diameter by a screw diameter. What did I do here? | |
| I just went in JMP in these Fit Y by X, I just put hole diameter in the Y and the screw diameter in the X. Here, | |
| this blue shadow here they are the specification limits. So we have the specification limits of the screen diameter and we have the specification limit of the fitting hole diameter. All this single dots here they are combination between screw and hole diameter. So, | |
| once I measure this in the process I identified each one of the parts like this is part number one, part number five and I [unintelligible]. | |
| part number 25 part number 30, for the screws and the aluminum box. So, for example, this dot here, this point here, this is the box number six the hole number two and the screw number nine. The screw number is here, the hole diameter is here. And for each point here. | |
| I combine in a strategic way because I wanted to see | |
| what will be the behavior of these parts, these components together when I have a small screw diameter and being put together with a small hole diameter. But what can happen if I have a small screw with a big | |
| fitting whole, right? What can happen if I have a big screw diameter, with a big hole diameter? And what can I have in the process, if I have | |
| A very big is screw diameter with a very small hole diameter? And we have a lot of points in between. So we had here like 60 different combinations of this data and | |
| I got every single combination here. Trying to reproduce this failure right? Right? Because, once we reproduce the failure we can understand what is happening in the process. What | |
| can be affecting the process. What is the root cause. Is the screw?Or is the fitting hole. What dimension we should have to avoid this problem? So, | |
| for example this one here, when they put this screw number nine in the whole number two of the box number six I assemble it using that machine | |
| that we were using in the process. And, I disassemble this. And when I tried to | |
| do it again, I could not do it. So I had the problem. The number of this assembly here was equal to one, it means that I could do it only one time. | |
| Let's get another situation here. This point, right here. When I get that screw number 15 that had a screw diameter about 4.73 | |
| against the hole number two of the box number 14 with a hole diameter about 4.43, it means that the interference between a screw and the whole diameter here was about point 0.3 millimeters. So how many times | |
| I could do this, right? So, I could repeat this process of opening and closing the box, opening and closing, opening and closing, 30 times. This situation here, five times. The situation here, 21 times. So each one of these points, we ran this assembly process until we have the problem. So we could. | |
| count the number of times that we repeated this process. So as we have a column in our data table called | |
| amount or quantity of these as these assembly, we can just put a legend here and we have here, for example, points being from red to green. The red dots here they are bad. They are. | |
| between zero and 10. Remember that the the lower specification limit is 10. We have to to be able to repeat this process at least 10 times. So all the red points here they are bad. | |
| And another another tool, very interesting tool that we use here in JMP was the Prediction Profiler. In these moment I use the Fit Model, where I put their three degrees of freedom, the hole diameter, the screw diameter and the interaction between them. I had. | |
| an R square about 0.88. So, this is quite good, right? We can represent these model well. So, here we can start playing with some different situations in our with our data, right? | |
| Because we have | |
| the hole diameter here, the screw diameter here, and we have here the result, our Y, our objective, our goal. That is, the quantity of this assembly that we can have in this process. | |
| So if we fix the first the first scenario that I ran here was if we fix the screw diameter at the mean that the suppliers, providing to us | |
| today, what should be the mean of the whole diameter, to guarantee at least 11 as disassembly, right? This mean should be 4.50 millimeters, right? Oh that's nice. We have our first scenario, but what about the process variation, right? | |
| Remember that we measured | |
| 160. | |
| parts, the aluminum box. We measured 120 diameters. So, we have the standard deviation of those products, right? When we use the Simulator in the Prediction Profiler | |
| putting here, saving the lower specification limit, adding our random variation. | |
| around this hole diameter. Putting the standard deviation that we got in the process and the standard deviation of the screw that we got in the process, we can simulate. I just simulated here 10,000 | |
| different combinations and we have a failure rate about 44%, so this is very, very big so let's let's start with some different scenarios. | |
| Let's suppose that we do we we don't do anything in our injection process and ask the supplier to | |
| put their specific results in the mean of the specification limits in the nominal of the specification | |
| and reduce a little bit the variation. So, this I will change the the values here. So, I just put the mean of the screw diameters in the nominal reduce the variation. So this green | |
| curve here this green distribution was reduced. I simulate it again and we got from 44% to 32%. So, | |
| little benefit and too much effort, but because we will we will ask to the supplier to to give us a better result, but their results was already good, right? Everything was inside of the specification. So, | |
| what happened we we work in our process right let's see what happen if we just | |
| put again the screw diameter in the mean that they are delivering right now with the standard deviation. And we just reduce a little bit our variation in the process, and both, | |
| the mean of the processing the nominal this 4.45. Remember that the variation of these cavities was very, very big so let's suppose that we correct, we fix, our process. | |
| put the mean of the processing the nominal and reduce variation. How how many disassemblies we could have? Why? So, the prediction profiler just put here as a result 20 repeated disassemblies. The rate, the failure rate | |
| goes down to 0.009% This is very, very good for us. So, | |
| even with this group variation the process would work with a means of 20 disassemblies. This very good. So we just now validated the injection process problem, right? If the hypothesis. We don't have a screw diameter process but yes, we have a problem in our injection process. | |
| Once we saw this we went to an action plan. We wrote these we presented this to the managers, the quality managers, the engineering manager, the Director and | |
| the injection process manager, right? The the owner of that injection machine, the owner of that mold. So, after sharing the results and predictions to the leadership | |
| actions have been taken in the aluminum injection mold. The pin used to create the fitting hole was replaced for new ones. The modified mold delivered the following results for validation. So, | |
| once we fix the pins that we're delivering were. | |
| making these holes in the box, we ran another COV validation study. And, we had this result here. So, another 20 parts on those same four different cavities for holes, two different positions. We have now | |
| a new cavities with a very, very good results. Even better than the results that we were predicting in our prediction profiler. | |
| A very small variation. So, let's see what happens when we talk about stability right? This is a very good process capability. We have. | |
| zero non conformance to [unintelligible], so this is all. | |
| almost zero right, this is a very good new process. And, we can now compare the before and after actions here | |
| with our new process. So, the same bivariate graph that I used in the beginning of the investigation, now i'm presenting here with the new values, because what what we did, here we got these new 20 parts. | |
| We measure a new screws. And, we combinated, we put together different situations again. Different values for screws diameter and holes diameter and | |
| we went to the process, got that machine and started disassembling, and assembling, disassembling and assembling repeating this process, until to have the failure. So, | |
| as you can see here all of the dots are now inside of this specification for both of the characteristics here. And, the worst point here the red one is having 10, 11, 12, 15 disassemblies. So now we have the problem | |
| solved, right? We don't have the problem anymore. We just put in this process. | |
| some control plans in the factory, so they they have to control the the | |
| diameter of the pins now to be sure that | |
| in a specific moment, they have to replace these pins. To guarantee the hole diameter. To guarantee not having this problem in the customer, righ?T So this was the problem. The problem was solved. | |
| And that's it guys. I will use some minutes here to to show to you how I did this right in | |
| JMP. So, I have here our data table where I have the boxes that I use the holes that I use and each hole, we have the diameter. | |
| each screw will have the diameter measured here, and the number of this screws all the combinations and we have here 60 combinations and we have the quantity of disassembly for each one. So, | |
| one of the things that I did here was these Analyze -> Fit Y by X. Where I put the hole diameter in the Y and the screw diameter in the X. | |
| I have this graph here, so this is different from what I presented because there, I have the specification limits, right? So, the specification limits, I put here allow ranges. I put here | |
| this is the screw, so this is 4.617 to 4.8 I just put blue here and add. So, we have the specification about. | |
| the screw diameter and here we have the 4.4, 4.5. | |
| And, I will put here the | |
| hole specification as well. | |
| Hole specification. | |
| By so is here. | |
| I would take off. | |
| So. | |
| whoops. | |
| A range again 4.4, 4.5. | |
| So now we have that graph there. So, all the dots that we have there. | |
| And the legend I just with the right click here, Row Legend | |
| disassembly. I chose here, these green to red. | |
| I chose reverses scale here, because the green, I want to be the best. So, they are here. Okay, I could also, | |
| get bigger dots here. So, this is one of the graphs that I used. | |
| Another thing that I did let let just clear the Row States here, was the Analyze->Fit Model. So, the my Y, my goal here is the amount, the quantity of disassemblies. The whole diameter and the screw diameter I just put here. And, I put the interaction between them as well and I ran. | |
| And I have here, | |
| my Summary of Fit with our our R-square here and | |
| the profiler right here. So, | |
| here was where I put the the diameter here, where I changed this hole diameter, the simulator I I used here, so I saved the spec limits here, so I know that the 10 is the lower specification limit for the quantity of disassembly. | |
| I put here a random variation around these means. So, once I had this I just... | |
| I could choose 5000 number of runs and I simulated here and I have this failure rate here. This is different because I didn't use the same values as the presentation. So, we could run at different scenarios here. Let's suppose that we started delivering holes in 4.43. | |
| So the amount of disassemblies will be 24 with the same mean of the | |
| the screw diameter. And this is a very, very nice tool in JMP, and I use it a lot in my presentation. So, | |
| thank you for watching and that's it guys. That's the end. |
