Now, so far, what we've been doing is we've been looking at processes that have a mean of Mu and the standard deviation of Sigma. We've been assuming that that process is constant. What do we mean by that? Suppose we are looking at a process that makes a particular component and we look at the measurement of one of the dimensions of that component, and suppose that dimension happens to have a mean, Mu, and a standard deviation, Sigma. We are assuming that as this process keeps running, the mean is not going to change. However, if you think in terms of how machines work, machines tend to deteriorate with time and they have to be readjusted or re-calibrated every now and then. As humans, as we continue doing something, even the best trained of us will start getting tired, and as we get tired, our average values will drift. They'll become larger for doing the same task. So all processes have a drift. They tend to sort of change from what is called the nominal of that particular process. Now, because this is so common, it kind of makes no sense to look at the process and say that the nominal of the process is what we should use to look at how many defects per million opportunities there are. In fact, at Motorola where Six Sigma was first developed, observed that it's very common for the mean to shift by up to 1.5 Sigma. Now, what is the importance of this? So, let's look at the figure on the side where we show two normal distributions. The first normal distribution we show is the nominal distribution with a mean of Mu. Now, if we have limits at three Sigma for what is acceptable, we have a very tiny area of rejection; the famous number by now of 0.001349. But notice what happens as the mean drifts and if the mean drifts from a mean of Mu to a mean of Mu plus 1.5 Sigma, then suddenly we find that the number of defects becomes significantly large. So one of the things that Six Sigma methodology looks at is this process drift. This process drift of 1.5 Sigma is called the Motorola shift because of the fact that it was suggested by Motorola. So a process drift of 1.5 Sigma means more defects are created than we expect. So let's see how the DPMO changes as we look at that. If we select a limit of k Sigma, then because of the Motorola shift, we have to calculate using k minus 1.5 times Sigma. Then that gives us a DPMO value which we have a formula, using Microsoft Excel, that we can use to calculate that. So if we have an actual Sigma value of three Sigma, then because of the Motorola shift, we get 1.5 Sigma and at 1.5 Sigma, the DPMO is 66,807, noticeably larger than what we were anticipating when we had 0.001349 as our probability of getting a defective. If we have four Sigma, then with the Motorola shift, we get 2.5 Sigma and we get a DPMO of 6,210. If you had an actual of five Sigma, then the Motorola shift we get 3.5 Sigma and defects per million opportunities of 233. If you have six Sigma, which is the title of our lesson, then with the Motorola shift, we get 4.5 Sigma which gives us a defects per million opportunity of 3.4. So, what we notice is that the number of defects are much larger than if you had used the same formula that we, for DPMO, using the actual Sigma. Now, there's something else to notice here. When we go from a three Sigma process in to a four Sigma process, we have a ten-fold reduction in the number of defectives, from 66,807 to 6,210. When we go from four to five Sigma, it's the same difference. So we are adding one more Sigma, but now we go from 6,210 to 233 which is roughly 26-fold improvement. When we go from five Sigma to six Sigma, we go from 233 to 3.4 which is a 68-fold improvement. So having our process being a three Sigma process and improving it to a four Sigma process gives us a 10-fold improvement in terms of the number of defects produced. And from four to five, we get a 26-fold, and from five to six we get 68-fold. So you can see that we have an exponentially increasing number in terms of improvement as we go from three Sigma to four Sigma to five Sigma to six Sigma. Because of this, it is important to sort of take that next step because we see dramatic improvements in the quality that we are observing. So, now, going from three Sigma to six Sigma, we are looking at a massive improvement in the quality that we are producing