Let's, let's rotate, let's rotate the, you know, bell shaped normal distribution to the left. Like this, okay? So actually this is the normal distribution right? And then, we will just say that there is two points here. Upper control limit. We call that upper control. [BLANK_AUDIO] Upper control limit. And this is the lower control limit. But actually, this actually somehow we say this is tolerance range. Okay. [BLANK_AUDIO] And we said there is epsilon. So, we, we say that, we, we say that you know, if the process is in control, in other words if there are only common causes without any assignable causes, then the process were produced things following this distribution. And we say that if our product or if our service performance is within this optical image and hour control image, you would just sat it's okay, it's good. We will tolerated this much of deviation. That's the meaning of this statistical process control chart. So whenever we produce one product, one unit or whenever we finish one service. We plot that outcome here. So the first unit performs like this and the second unit, and third unit, and fourth unit, and fifth unit, and so on and so forth. So we plot, as we, as we produce additional unit, okay? And then what happens is sometimes we can see some outcomes actually outside, outside our upper control limit who is sometimes outside our lower control limit, right? And then we believe that you know, if our performance is within this strange view to say that this is in control. In other words, everything is normal, everything is okay. The deviation is just to do due the dividend causes. But if it something happens, I'll say that our tolerance range. We have to think this as very serious issues because there is a really small probability that these things occur if the process is in control. In other words, if the process is normal, if the process is okay, then the probability that these kind of things occur, the probability's very small. And therefore, we will suspect, we will guess that, okay, if that actually happens, is it implying that the process is out of control? In other words, probably, some percent of the cost is shift to process. Okay. So, let's think about what happens when actually an assignable cause hits the process. And therefore, the process becomes out of control. We can see this way, this is a normal process, right? This is normal process. But now, the mean values here and we set up our target value at the mean value of the distribution. Or because we already know our goal, we probably set up our current process at the target value. Whatever it is, I say this is our normal process. And now along the way when an assignable cause hits the process, and therefore the process mean shifts like this, and this is the normal. This is actually out of control because we know that this process is affected. This process is affected. [BLANK_AUDIO] This process is affected by assignable, assignable cause. So, this is out of control. This is in control. And now let's talk about what kind of mistakes the manager can make. Or what kind of mistakes the company can make when it uses this concept of Statistical Process Control. We think that there are two different errors. One is Type I error and Type II error. And think about this case. In other words, this is normal. Or this is normal and this is actually in-control. In-control. If we have this normal process and, if operate this normal process, then if our outcome is within this tolerance range, we call that as okay. Then we know that even if the process is normal, there is, although very small, there is a still chance for the outcomes is outside. The outcomes is [UNKNOWN] our performance is outside this range, outside this talented range. We still have very small possibility here. So, even if when the process is in control. Even if the process [COUGH] is normal, but sometimes we can see that the, some unit outside of this range, and when it happens we say that okay. There might some assignable cause, assignable causes occur by observing this one. But when the process is actually normal in control when we observe this outcomes outside the range, if we say that okay, there an external cause. If we say that, it's our mistake, right? And that's called Type I error, which is actually the probability. Probability, we say that, okay it is out of control. Lure me. When in fact it is in control, okay? So this is small probabilities, that's Type I error. On the other hand, let's say, indeed an assignable cause hits the process, and therefore the mean value shifts. That is the case. But even if the process is now out of control, but there is a still probability that we say that everything's okay. And because even if the process shift like this, we still have some probabilities like this, right? That the outcome is within this tolerance range. And, where we observe these outcomes are where we begin our tolerance range. We say that okay. Average is okay. But, in fact, it is not okay. We make a mistake. We make a mistake, right? So, that's the Type II error. This is the probability that we say the process is okay. The process is in-control, but it's wrong. Because when, in fact, the process is out of control, in other words when in fact the process is affected by the assignable cause. So, if we use this, you know, mechanism, these tools that this the process control chart. There are two types of mistakes, two types of errors, and therefore, how we can determine, maybe, you know, some size. How we determine this absolute, in other words, tolerance range and maybe sometimes some people have to decide is a sample size, how many units we have to, you know, measure. Or, you know, if you want to do it, you do this whole. Your time basis or 100% inspection policy or whatever. So there are some you know, factors you needed to have to design. You needed to have to design this you know, Statistical Process Control. And, how we can decide this one, how we can decide this tolerance level and some size, and all those things. We determine this parameters, we determine parameters so as to minimize both, okay? Not just one type of address on it. But, we want to minimize, we want to minimize, we want to minimize, these two types of address at the same time. Why we decided this design factors, all right. So, if you have some difficulty in understanding this discussion, I would just say, you want to, you know, defer to some other materials. But the one, you know, point you, I want you to learn from this discussion is that, okay, there are two types of mistakes we can make. And how I can design this whole thing in a most effective manner. When you design this statistical Process Control Chart, make sure that you know there are two different types of errors. And you want to minimize, not just one type of errors, but you want to minimize these two types of errors at the same time. So, as early as you understand the conceptual importance of these different types of errors, different types of mistakes. And, I think that it'd be pretty, pretty good. And you achieve your educational goal. Remember that the oldest discussion, sometimes even if, sometimes, due to a technical. I do not intended to teach you some highly technical, a, analogy for schemes, but my goal throughout this course is to give you some strategic insight, insight to understand this whole thing. And I hope that you look at this topic from that perspective as well. [BLANK_AUDIO]
