In this lesson, we are going to learn about Six-Sigma methodology. We're going to learn about the DMAIC process and we're going to talk about why it is important to have measurable results when we look at Six-Sigma projects. So, as we mentioned in our earlier lesson, the Six-Sigma methodology originated in Motorola, and there was a time in the '70s when Motorola had terrible quality. Motorola used to own a television manufacturing plant. That television manufacturing plant used to produce lots of defectives. So, televisions that when they went out in service will fade. Motorola decided to get out of making televisions and sold it to a Japanese firm. The Japanese company took over this manufacturing plant, did not change the equipment, did not change the process, did not change the people working in the plant, but they were able to produce televisions with less than five percent of the defectives that Motorola was producing. When Motorola learned about this, that was a big wake-up call for them. How is it possible that a different company can come in and gets such phenomenal results using exactly the same resources? Now, around the same time, one of the Motorola engineers did a study and found that when Motorola, in their plan, when they found defective, they fix defective product and put it back in on the production line and he found that most of the products that were fixed in this manner when they went out to the customers, those were the products that used to fail. So, you have this defect your product, you spend a certain amount of resources in trying and fixing it, and then you send it out, and then when it gets to the customer it fails. So, you've added unnecessary cost in trying to fix this particular product and the customer is still going to be unhappy because the product fail. So, this suggested that what was more important in making a product was not to have a defect in the product in the first place, rather than having a defect and then trying to fix. The ability or the method by which we go and fix defective products so that we can sell them allows us to be complacent. It allows us to be complacent because we think, okay, so, what if we produce some defectors? We can fix them. This complacency is what is the cause of terrible product quality in many companies and so, one of the things that Bill Smith realized is that what needs to be done is to tighten the processes that produce these products, so that the processes are as stringent or as strict as possible so that the products coming out will be not defective. If they are not defective, then they're not likely to fail once they go out in the hands of customer. This is the insight on which Six-Sigma is paced. Now, for many people, when they think of Six-Sigma, the first thing that comes to mind, especially if you've had any kind of statistics, is this notion that we have a confidence interval that is often created in statistic in which you take the mean plus or minus Three-Sigma. So, people assume that plus or minus Three-Sigma, Three-Sigma on each side is actually Six-Sigma. However, that's not what we are going to be looking at here. When we talk about Six-Sigma in this case, we are actually going to be looking at plus or minus a Six-Sigma. So, the question is, why is Three-Sigma not enough? When we learn statistics, we are often told that for a normal distribution, anything beyond the Three-Sigma limits is very little probability. In fact, if you take a normal distribution with a mean of Mu and standard deviation of Sigma, a value greater than Mu plus Three-Sigma has a very small probability of occurring and that probability is 0.001349 or 0.13 percent. You can find this probability using Microsoft Excel and using the built-in functions in Microsoft Excel. So, to find the probability that x happens to be greater than Mu plus Three-Sigma, we can simply calculate 1 minus the probability and that x is less than or equal to Mu plus Three-Sigma. The way we do this, is calculate 1 minus and we use the Microsoft Excel function norm.S.Dist and because we want Three-Sigma, we use 3 and the second parameter, 1, tells us that we are looking at the cumulative distribution. So, if you enter this formula in Excel, you will get the value 0.001349. Now, that seems like a fairly small probability, 0.001349. All right. So, let's see what that means in some typical situations. Let's take the example of out-of-hospital cardiac arrests. Now, I found the statistic which said that there were 295,000 out-of-hospital cardiac arrests in the United States in the year 2008. Suppose we assume that the probability of debt in an out-of-hospital cardiac arrest happens to be that small probability of 0.001349. Then, if you calculate the number of deaths that would occur from out-of-hospital cardiac arrest, that would be 295,000 multiplied by that small probability of 0.001349 and that's 398 deaths. Now, 398 deaths is a significant event and one of the things that people suggest is that to prevent this approximately 400 deaths, what should be done is we should have what are called defibrillators available in all kinds of public locations, so that if such incidents occurs, then we can prevent that. So, the tiny probability because of the large number of incidents that occur, gets magnified into a large number of fatalities, 398 in this case. Let's look at a different example. Suppose we have a circuit board which has 100 components. Now, 100 components seems large, but it's easy to find circuit boards with 3, 4, 500 components, it's easy to find machinery which has thousands of little components. Think of your car for example, which has thousands and thousands of components. Now, each component let's say has a defect probability of 0.001349, the same probability that we've been talking about, the three sigma probability. Now suppose the defect in any one component leads to the failure of the entire circuit board, so what is the probability that the circuit board will not fail? So right now, if you look at an individual component it has a probability of failure of 0.001349, therefore the probability that it is not defective is going to be one minus that probability or 0.99865. To find out the probability that the board does not fail, we want to make sure that every component does not fail. So component one does not fail and component two does not fail and three does not fail, so on, so forth, up to and component 100 does not fail. The way we find that is take that probability of 0.99865 and raise it to the power 100 because we have 100 components, and that turns out to be 0.874, which says that the circuit board will fail with a probability of 12.6 percent. That's a significant percent of failure and any company that puts out a product with 12.6 percent of failures is likely not to be in business for too long. A third example, we can look at a resort hotel which on average has 300 guests on any given day. Now, each guest on average interacts with the hotel staff about 10 times per day. Now suppose we have a wonderful staff and that staff does a great job with it's guests, but there can still be occasional unsatisfactory interactions and suppose that on satisfactory interaction has a probability which is relatively small, again, that same number, 0.001349. Then the number of unsatisfactory interactions in the year we can calculate as saying, we have 365 days times 300 guests per day times 10 interactions per day, times the probability of an unsatisfactory interaction and that gives us 1,478 unsatisfactory interactions. Or in a year we will have complaints from our guess 1,478 times. Again notice, what's happening is that we have a very large number of interactions, and so, we have a lot of opportunity for things to go wrong. With the 100 components on the circuit board we had 100 things that could go wrong. With our resort hotel, we have 365 times 300 times 10 opportunities for things to go wrong, and this is why we end up with this large numbers. So in Six Sigma, we define two quantities. We define what we'll call the defects per opportunity or DPO, and the DPO is simply the fraction obtained by looking at the number of defects that were observed, divided by the number of defect opportunities. Now once we have the DPO, we can convert it into what we call the defects per million opportunities or DPMO, and DPMO is simply the DPO multiplied by one million. So that DPO is the fraction of times that we have a defect and DPMO is if you take that fraction and multiply by a million opportunities to have a defect, how many defects do we actually see? So that's a DPMO. Let's take a quick example. Many of you have seen this thing called capture which is something that's used to authenticate whether you're not a robot, and so, there's a computer site which uses capture to authenticate that the login attempts that it's observing are non-robotic. Now each capture figure, this tends to be a grid of figures and you're asked to look and identify some element in that trigger, so it might say, "Identify all pictures with a store front, or identify all pictures with a road sign", and so, you have nine such pictures and you have to click on each picture that has that particular thing that you are being asked to look for. Now for this particular website, the daily average of login attempts are 33,700, and what it's found is that when it looks at the number of pictures, not the number of times the entire nine picture grid, but individual pictures, the number of times it's incorrectly identified happens to be 1,600. So, now what's the defects per million opportunities here? So if we assume that an incorrect identification of a picture is a defect, then the number of defects that have been identified in this particular case is 1,600. How many defect opportunities were there? Now each login attempt has nine pictures, so there are nine opportunities per login attempt. So therefore the total number of defect opportunities is 33,700 multiplied by nine or 303,300 defect opportunities. So now we can calculate the DPO, which is number of defects divided by number of defect opportunities, so that's 1,600 divided by 303,300 or 0.005273. Now, the DPMO is simply multiplying the DPO by a million and so that gives us 5,273 opportunities. So we have a DPMO of 5,273 for this capture exercise for this particular website.