Lean Six Sigma Green Belt – Six Sigma Measure Phase

5. Case study on Attribute Agreement Analysis_Part 2

What does this mean? Let us understand this for a while. There are 20 custom application forms which were inspected and twelve matched twelve by 20 multiplied by 116. But where am I getting this twelve from? Let us go back to the worksheet and understand. Click on this icon show worksheets older to build worksheet here’s the worksheet between appraises means between all of them if they are greater than two, probably it should be among appraisers grammatically that’s fine.

False representative one, trial one, trial two faulty representative two in trial one and two quality representative three in trial one and two everyone says customer application form one is incomplete fine. Here also everyone says customer application form is incomplete fine. Look at this third one. All except your quality representative in his trial two does not agree. Quality representative in his trial two says customer application form is complete, in all the rest of the cases it is incomplete.

So there is a mismatch. Look at this fourth customer application form. Everyone says it is incomplete except for quality representative two in his trial one. One only in this trial one is saying it is complete, in rest of the places it is incomplete, right? There is a second mismanage here we have a third mismanage, right? Quality representative two in trial two says customer application form is complete but in the rest of the places trial is performed by quality representative one and two says it is incomplete.

So another mismatch here we have another mismatch right here also there is a mismatch here also there is a mismatch. Custom application form twelve, customer form 14 this also has a mismatch. Custom application form 17 also has a mismatch. So if you count the number of mismatches there would be eight mismatches. So if there are eight mismatches out of 20 custom application form, how many matches it’s? Twelve. And that is a twelve number which you see here and between appraisers is called as reproducing between or among the various appraisers.

Now let us look into each appraiser was a standard first quality representative. One has inspected 20 customer application forms and you have found that 16 have matched. 16 by 20 multiplied by 100 would give me a percentage of 85. Sorry, 80 quality representative two out of 20 customer application form 17 of match 17 by 20 multiplied by 100 would give me 85 on similar lens.

We can also calculate the percentage of agreement for quality representative fee. But where am I getting the 16 from? Let me go back to the worksheet and explain this. So we have quality representative one who has conducted trial one and trial two and he has also looked into 20 customer application forms.

Now these values are compared with the standard which is your team leader and zero for the first customer application form that means customer application form one is incomplete. Two is also there is a match zero zero and here we have zero for the standard. Three, also we have zero, zero and then we have zero for the standard. Zero means customer application form is income here, also it’s matching.

But when you go to this customer application form nine, customer quality representative one says customer application form is complete in trial one, he says it is incomplete in trial two, also the standard says it is incomplete. First, mismatch here. Looking to customer application form twelve, quality representative in his trial one says it is incomplete in his trial one. Trial two says it is complete. Standard also says it is complete. However, there’s a mismatch. All numbers are not the same. Look into customer application from 14, 10 and one, right? It has to be the same for it to be qualified as matching. Look into customer application form 17, 10 and zero, not matching.

Quality representative one in trial one says application form is complete. In trial two he says it is incomplete and also the standard says it is incomplete. So there is a mismatch, right? So that is what is coming here. Each uprising was a standard 1616 times matched with the standard. And this is called as individual accuracy or appraiser accuracy.

Once again, remember that greater than 90%, my measurement system is acceptable. In between 70 and 90, it is cautiously acceptable. Less than 70, it is unacceptable. There’s one last thing which we’ll have to look into now, which is all appraises was a standard. Out of 20 customer application forms there was a match of twelve and the total percentage is coming to 6012 by 20 multiplied by 160, right? So let us go back to the worksheet and understand where this flow is coming from. So click on this icon, go back.

And now I need to look into each and every appraiser, what is the standard? Each and every appraiser reading what is the standard? Even if one number is different, that is a mismatch. Look at this, customer application form three. Everyone says customer application form is incomplete including your standard which is routinely. However, quality representative three in trial two says application form is complete. So there’s one mismatch for this. Also there is a mismatch here. Quality representative two in his trial one says custom application form four is complete.

No one else agree with that. Eight has a mismatch, there’s a one here, nine has a mismatch, there is a one here, eleven has a mismatch. Quality representative two in both of his trials it is incomplete. Here, also there is a mismatch here, also there is a mismatch.

So if you count these number of mismatches, there will be eight mismatches out of 20. That leaves us with the count of twelve which are matching consistent across including the standard. Hence you see that twelve here and this person. Now while appraisals was a standard, is called as team accuracy. Greater than 90% acts of the measurement system in between 70 and 90%, cautiously acts of the measurement system. Less than 70% unacceptable. Reject your measurement system. That is what it seems.

6. Sigma Level (Z) – Continuous Data

All right, now let us look into current performance measurement. Assuming that the measurement system is accurate, assuming that the measurement system is reliable, we move on to look into current performance measurement we need to evaluate current performance of my output and baseline it for comparison. In the improved phase postimprovement the values are going to increase. I need to compare my current performance with the improved performance. That is my objective because I need to know whether there has been an improvement or not. All right? We may choose to compute sigma level or any other process capability in this system. So this is how we do that. This is how we do that. Let me erase everything, okay? Sigma level sigma level can be computed for the following situations if you have a continuous data and if you have specification limits, mean and standard deviation this is how you calculate if you have attribute data.

There are three different scenarios. Scenario one is I know the defects, I know the sample size, I know the opportunities for error. Scenario two I know the defects, I know the sample size, I know the opportunities for error are unknown. I know that the opportunities for error is not known. Right?

Scenario two scenario three you know the defects, you know the sample size, calculate your signal. You can also use yield. You can either calculate first time yield or roll the throughput yield. We’ll discuss about that as well. Then we have Cpcpk. We calculate this for continuous data and remember one thing, data should be normally distributed. This goes back to the central limit theorem explanation, right? Remember that and then we have specification limits, mean and standard deviation.

St is short term, we’ll discuss about that in a while. Sigma level, basically, right? Sigma level is number of punches a boxer can take and still withstand without getting knocked out. It seems like you have ten size strength, right? How much maximum stress that a material can undergo, right, without failing or breaking that is your sigma level. You are assessing the strength of your process, basically.

So let us quickly get into the case studies and understand by calculating these values. First thing is sigma level for continuous data. If we know the specification limits, if we know the mean and the standard deviation, we need to first check whether data are normally distributed or not. We need to compute the mean and standard deviation.

We need to input these values in a spreadsheet calculator. I’ll show you the spreadsheet calculator in a wide map and based on which you’ll calculate z Lt and Z-S-T right? So let me tell you this. Let us understand the case that you XLR has specified to the hotel that temperature in the training room should be 21 plus or minus three degrees. The average room temperature is 22 degrees and the standard deviation is two. What is a sigma level? First try to write down the information which is provided to US inputs USL is 24.

Where am I getting this 24 from? 21 plus three is 24. Lower specification limit is 18. Where am I getting this from? 21 minus what is my target is 21. Where am I getting 21 from? Here. That’s my target. Mean is 22, which is given. Standard deviation is two, which is also given. Right. What is ZLT and what is ZST? Z. LTE is long term. ZT is short term. Think about you have made an improvement in a month of jan and you claim that post improvement, your process operates at six sigma. Fine. Six months down the lane, probably you’ll still be operating at six sigma.

One year down the lane, you’ll still be operating at six sigma. Maybe. Right. But can you guarantee that you would be operating at six sigma throughout the journey for the next ten years, 20 years? Is it possible? No. Right. So according to various experiments conducted statisticians, mathematicians say that if your process is at six sigma, which is short term, right. If you say that you have made an improvement and your process is operating at six sigma, then in the short term, for the next three months or for the next six months, you can claim that your process would be at six sigma only. But when you look into the long term, your process tends to drift.

And how much will it drift to? People say there will be a drift of 1. 5 sigma. So if it is six sigma in the long term, it would be 4. 5 sigma. It keeps drifting in the long term, and this sigma shift is 1. 5 sigma. All right. Okay. So with that context, let us go ahead and look into our SIG spreadsheet calculator. Let me show you that. Here’s the sigma level calculator.

We are given the values as 20, 418, 21, 22. Standard deviation is given as two. Upper specification limit is 24 and the lower specification limit is 18. If I keen those values, I get my ZST. Sigma level short term and sigma level long term. Look at this. Sigma level long term is zero point 91. If I add 1. 5 sigma to that, I would get z short term. Let me highlight this. Here is the formula. Here is a formula on how to calculate VPN mode and how the values of z are getting calculated. Just in case you’re interested of look at this formula. Okay? So these are the values. This is how my back this is how you can get.

7. Exersice – Sigma Level Calculation

Case study one. What does this say? A shoe manufacturer wants to assess the performance of shoe sole. Cutting machine auditor has audited 108 inch shoe soles. Right? And the shoes accepted specification is eight plus or minus half. So your upper specification limit would become 8. 5 and the lower specification limit would become 7. 5. And what is z value? That is what people are asking. Let me go back to the previous slide. Look at this.

What are we first supposed to do? We need to check whether data are normally distributed or not. Step one, compute the mean and standard deviation. Right. Step three, input the specification limits mean and standard deviation in the spreadsheet. Okay, here we go. Let us look into those case studies. This is the shoe sole measurement in inches, right? And these are the various values we have data for under shoes. That is what a question says. Case study. The first step is I need to check whether data are normally distributed or not.

What do I need to do for that? Go to stat basic statistics. And I do graphical summary. This window pops up. Just select the particular column. I select shoe sole measurement. I highlight that. I click on selected. Now I click on OK. And this is going to give me a graphical representation. This is a histogram. This is the probability distribution curve. And here is the box plot.

We discussed about all these things in our introduction. This data seems to be following normal distribution. If I look into the graph because it’s beautifully shaped symmetrically, that is what I think. But I do not want to base my decisions by looking at the images. So let us base our decisions based on few numbers. Look at this. Anderson, darling. Normality test. If the p value is greater than 0. 5, that means data are normal.

Now, how are we getting 0. 5? Why are we taking p value as 0. 5? Things will become clear in analyze fees. For now, just think about this as a thumb rule. If the p value for ad normality test anderson Darling normality test. If the p value is greater than 0. 5, that means data are normal. So in this case, data are normal. Fine. We also have a mean and the standard deviation which is given. What is the mean here? Average 8. 58. 5. That’s my mean. What is my standard deviation? Zero point. It is zero point 29. 56. All right. So now I know mean. I know the standard deviation. I know that the data are normally distributed and also from the case study. Let me go to the worksheet and let me go here. Where is the case study? Let me go to the keystart. Right? And we also know the specification limits from the case study. So now you have all the values key in your numbers in a spreadsheet calculator.

Here’s a spreadsheet calculator. What is the mean? Mean we calculated and it came up to 8. 0215 what was the standard deviation? It was 0. 2956. What was upper specification limits from the case study? It was eight plus half, which is 8. 5. What was the lower specification limit? It was eight minus half, which is 7. 55. Now, once I keying these values, I get my z values. Z long term is 1. 3 C. If I add 1. 5 to this, I would get the short term, which is 2. 85. Right. Let us go back to the worksheet. Or not the worksheet