ASQ CQE Certified Quality Engineer – Section II – The Quality System (16 Questions) Part 6

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- January 18, 2023

**21. 2E-4 Cost of Quality Taguchi Loss Function**

Previously we talked about cost of quality and in that we looked at the classification of that in terms of appraisal prevention and the failure cost. Now let’s look at this aspect of the cost of quality from a totally different perspective. And this perspective was provided by Taguchi. So conventional only what we were thinking was or maybe still we are thinking that if we have a component and that component is within the tolerance, then we are fine. If that component goes beyond the tolerance, then it fails and that needs to be repaired or replaced. Let’s take a simple example that we are making a piece or a rod or something of 100 millimeter size.

So let me draw that. Let’s say this is what we are making, a piece which has a length of 100. We have a tolerance of plus and -3, mm on that. So plus minus three. So what we think is that anything between 97 which is that minus tolerance and 10 three, that is fine. So if I make a piece which is anywhere between 97 and 10 three, if I measure the piece, if it falls within this range, then we are good. If it is falls outside this range, then this piece gets rejected and then there is a cost associated with that. This is called as goal post mentality. So let me draw that goal post here. So goal post will be something like this.

So here I have 100 Mm, this is my 97 and this is 10 three. So what does this mean here is that anything which is between 97 and 10 three, the cost of that is zero. The cost of poor quality is zero. But if it goes less than 97 or more than 10 three, then there is a cost associated with this. So that’s the cost here. This is a goalpost mentality. Taguchi had a different view on this. His view was that any time you deviate from the value, the exact value, exact value is 10, zero, 100. So anywhere if you deviate from this side or that side, you are losing money. This is the loss to the society. So Taguchi view was that quality is not defined by the specification limit which we were talking earlier in terms of 97 and 10 three between that. So quality is not defined by the specification limit, but rather on whether or not it creates financial loss to the society.

So anything which deviates from the spec value basically leads to the loss to the society. These pieces might not fit together even though this might work, but this might fail in a long run. So if you have exactly 100 millimeter rod which we were making, that would have been the best thing we could have still accepted between 97 and 10 three. But in the long run that would have created some damage to the piece, some damage to other components.

So what our target should be to focus on 100, which was the target value which we wanted to produce rather than just being within the specification. Now, there are three ways to look at the loss. Three ways are that nominal is better. Nominal means that 100 is better. Like the example which we took. Rather than being between 97 and 10 three, the nominal value was 100. So that’s the best value. Then there could be another sort of tolerance where smaller is better. Smaller is better. In case of wear and tear, in case of loss, in case of erosion, smaller is better. And then in some cases larger is better.

Larger is better in terms of, let’s say, profits, largers are better. In terms of the life of the peace, larger is better. So earlier we talked about three types of losses. When nominal is better, smaller is better, or larger is better. Here let’s take a simple example of nominal is better. Nominal is better means you are trying to focus on the target value. Let’s say the rod which you are making, let’s say that is for 100 mm or 150 mm, whatever length you are making, if you get that rod made exactly to that size, your loss is zero. But as your value, the actual value deviates from the target value, there is a loss associated with that. Let me put that graph once again.

So this is what Taguchi was telling. Like instead of goal post mentality which is here, which tells that let’s say this is 100 mm, this is 97, this is 10 three. So the piece was supposed to be 100 mm plus minus three. So this was the goalpost mentality that if you make a piece within 97 and 10 three, everything is fine, you don’t lose anything. But if your piece goes less than 97 or more than 10 three, that means there is a loss. But against that what Taguji was suggesting that any deviation from the target value is a loss. And that is given by this formula, which is l is equal to k y minus m square l is the loss. In this particular case, let’s say the loss would be to replace that piece. To replace that piece means that if you have not made a piece within this range, 97 to 10 three, then there will be cost associated with repair or replacing whatever that cost might be. Let’s say if that cost is $20. So $20 would be the loss and m is the target value. In this particular example, the target value is 100 mm. So that’s your target value, actual value is the value which you measure, the piece which you measure, and the k is the constant, which is also called as loss function.

So if you want to calculate the loss function and you might get an example, you can do that. Let’s say, hypothetically, let’s say that there is a loss of $10 if your piece is not made exactly within this range 97 to 10 three. So loss will be $10 let’s put it here the target value is 100. Actual value is let’s put that tolerance here to calculate the loss function. Tolerance here is 3 mm on one side. So actual value will be 10 three constant we want to find out. So L is equal to let’s say $10. L is equal to K and y minus m y minus m is 10 three -100 and this we are calculating in case of just reaching to the tolerance reaching 103 or you could put 97 also in both the cases it’s going to give 3 mm in this bracket.

So square of that. So ten is equal to K and this is three to the power two which is nine K into nine so K will be ten divided by nine. This will be one point eleven. That’s the loss function. This is how you calculate the loss function. And based on this K value you can find the actual loss for any dimension which you produce. So let’s understand that in the next video. Looking at a different example there. We will take an example of let’s say 150 mm instead of 100. Do the same calculation.

**22. 2E-5 Cost of Quality Example of Taguchi Loss Function **

So previously we looked at an example where we were looking at a rod being manufactured which has a length of 100 tolerance of plus -3. We calculated the value of K. Let’s take a different example. Change the values slightly. So instead of 100 mm, so now our target value is 150 mm. Earlier we talked about a loss of $10 loss. Now, let’s say this is a very precious rod we are making. And the loss here is $200. So based on that, we can calculate the value of K exactly like we did earlier.

So here is an example or a question which says that the tolerance on the length of an item is 150 plus minus three. So previously also we had plus minus three as a tolerance. The cost of repairing or replacing this piece is $200. Find the loss function. You might get this sort of a question in your CQE exam. So L is equal to k y minus M square. So loss is equal to $200. So let’s put it here. $200 is equal to the value is k and y minus M square. So y minus M square is 3 mm. So that’s the one side tolerance which could be, let’s say 153 -150, in this case and square of this. So this gives $200 is equal to k and this is three to the power two. So the value of K comes out to be 22. 22.

Now, that’s a K value. Now, with this as a basic information, now, let’s say if we produce an item which has a length of 150 mm, what will be the loss in that case exactly? You are right, the loss in that case will be zero because 150 is the target value. If 150 is the target value, then there is no loss in that. But let’s say instead of 150, the piece which we produce was 152 mm. Even though this is within tolerance, even though this is still acceptable, but still there is a loss to the society in terms of the long term functioning of this piece or whatever it is.

So that loss we can calculate using this formula once again. So loss is equal to that’s what we have done loss is equal to k y minus M square k. We have already calculated earlier 22. 22. So we put that value here. Let’s put this value here. And now the piece which we produce has a length of 152, which is the actual value. The target value is 150 square of that. So this will become two to the power two, which is four. So four times of 22. 22 will give you $88. 88. So that is the loss to the society because the component which you produce was not exactly 150 mm.

**23. 2E-6 Taguchi Loss Function three models **

So earlier when we started talking about Taguchi loss function, we said that there are three cases where there could be loss case where the nominal value is the best. And we looked at example of that using the rod which we were making. And the nominal value was 100 in one case. And the second example was where we took the nominal value as 150 mm. So that was the case where the nominal is better. Then there could be other two cases where smaller is better or the larger is better. We did touch upon these two cases. Let’s once again look at that.

There could be a case when smaller is better. Smaller is better just in case when you are looking at the exhaust, toxic exhaust, how much exhaust your system is producing. In that case, what you will be looking for, not the nominal value, what you will be looking at is the smaller is better. So if there’s a less exhaust, less waste going out, less toxic exhaust going out, then that’s the best case or dead pixels on the screen.

So if you have a computer screen, there are dead pixels. So there might be a value of three pixel, five pixel as acceptable, but there is always the lower is better. So even though your acceptable value might be six pixels on the screen, dead pixels are okay, but you will still prefer to have zero pixels rather than having six pixels. So that is the case where smaller is better. There could be another case where larger is better. Larger is better in case of yield. So if you are producing something, how much yield, how much production output is there? There you are looking at larger is better case, customer satisfaction, employee morale, and many other cases where the larger value will give a better result or the better return. So we are not going into the formulas for these. We did look at the formula for calculating where the nominal value was better. So with this, we complete our discussion on the quality loss function proposed by Taguchi. You.

**24. 2F-1 Quality Training ADDIE Model **

Section two of the body of knowledge for CQE exam was the quality system. And we have looked at number of items in this section. The last part of this is section two F, which is quality training. In this we will be looking at two models, adi model and Kirkpatrick model. What are these? Let’s understand those starting with the adding model. Adding model is that when you have a training, you need to analyze, design, develop, implement and evaluate. So there are five stages in the training process. What are these stages? Let’s look at a little bit more detail on the next slide.

So, the first thing when you are preparing or delivering a training or planning to deliver a training is to analyze, analyze the learning environment, what sort of environment you have, what is the existing knowledge of the learners. And you do the need analysis. So what they do, what they know, and what is the gap between that. So that analysis is done. That’s the first part of training, analyzing the need. Where is the gap? Then comes the design. In training design, you are looking at the learning objective. What are the objectives of learning, what are the exercises to be given, what are the contents of that, what’s the lesson plan? What’s the media selection? All these things are covered in the design phase of the training. Once you have designed the training, so now you know that what sort of things you will be delivering design has been done. Then you go to the actual development process where you create and assemble the content. Just like I am doing right now when I’m talking to you. I’m developing my training. So step by step, lesson by lesson, I have to create these videos.

That’s a development phase. So once development is done, then comes the implementation phase. So in implementation, you teach, you cover the sale, you cover the curriculum which you made. Once the training is implemented, then comes the evaluation phase or the feedback phase of the training. So in this training also, there will be feedback which I will be looking for. So this is the Adi model for training, starting from analyzing the need to evaluating the training. So any training has to go through these stages. So this was one model which we wanted to cover. Then there’s another model, which is Kirkpatrick’s model. Let’s talk about that in the next video.

**25. 2F-2 Quality Training Kirkpatrick Model **

Training. Previously we talked about the Adi model for training, where we analyzed the need and we evaluated the training. So there were five steps in the training development process. Now coming to the training effectiveness, did training achieve the objective which it was supposed to? Let’s take a simple example that you have a high defect rate in one of your processes and you want to design in and develop a training for that so that the defect rate could be reduced. Teaching people, that what needs to be done, teaching them to use seven quality tools. So that’s your plan. So once you have implemented that training, this is where Kate Patrick’s model of training effectiveness comes into picture. So how do you evaluate? So there are four levels of training effectiveness. Let’s start with level number one. Level number one is reaction, the degree to which participants find the training favorable, engaging and relevant to their job.

This is the first level of effectiveness, whether people who are being trained, how did they react to this training? And remember that in this example, our goal is to reduce the level of defect in the process which we are having. So for that we developed the training. So you trained, let’s say, ten operators in a room. How did they react to that? Did they feel that training is relevant, training is engaging, they like the training, everything is fine.

So how did people react to that? That’s one level of training effectiveness. The second level of that is learning. How much did these people learn? So the level two is the degree to which participants acquire the intended knowledge, skill, attitude, confidence and commitment based on their participation in that training. How much did they learn? That’s level two. Level three effectiveness of training is behavior. Did this training made any behavioral change in those people finding interesting was level one. Learning was level two. But then did that learning made any change to their behavior?

That was level three effectiveness of the training. And the level four of this is a result whether that led to reduction in the defect rate or not. So let’s say in level three we would be seeing that, okay, after doing this training, people started using seven tools for quality. They started making histogram, they started making control chart. That’s a behavioral change. That now whatever they learn, they put that in their behavior. But then did that actually result in the reduction in the defect rate?

That will be the level four effectiveness of the training, where the outcome is being achieved because of the training. Let’s say after training, after using all these tools, now the defect rate has gone down from 2% to let’s say zero 2%. That is where you look at the level four effectiveness of the training. So training you need to look at from these four levels, what is the effectiveness of training level one, level two, level three, level four. One is reaction. Two is learning. Three is behavior, and four is the result which you achieve because of this training. So congratulations on completing the second section of the CQE body of knowledge. Section one, there will be 18 questions from that. From section two, there will be 16 questions. So if you have completed section one and two by now, so 18 plus 16 is 34. So you have covered 34 questions, which will be coming out of 175 questions.

So great achievement. And what you would have seen in these two sections are these two sections were a little bit soft skills. Many of these things you would already be aware of and there is no need of remembering. Formulas, equations, statistics, those things are yet to come. But these soft skills you have learned and you have covered 34 questions by now. So now let’s move on to section three, which will be basically covering the design part. So you are a quality engineer and design is an important part of that. That will be covered in section three. So let’s start that.

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