Hi. In this lecture we're gonna do a little sort of bonus. I want to talk about

the normal distribution again and I want to talk about it in the context of a

business practice that has to do with quality control that's known as six Sigma.

Six Sigma was a process evolved by Motorola, you know, quite a while or

couple of decades ago. In an effort to sort of making production processes more

predictable so that we have fewer quality errors. So to understand our works, let us

go back and remind ourselves of what Sigma is and then we can understand what six

Sigma is. [inaudible] we had a normal distribution, right, we had a mean. You

know, we have these Standard Deviations, these Sigmas, one Standard Deviation, two

Standard Deviations and so on, right? And then we had a 68 percent of the time.

Right that outcome will lie within one stimulation in 95 percent of the time. It

will lie within it two standard aviations. So what would lie, how often would we lie

within six standard deviations? If I went out here, way out here to six standard

deviations. I guess that's even further out. How often would I be inside that?

Well the answer's, the only time I would fall outside of it would be 3.4 in a

million. Okay? So that means that there's almost no way that I'm gonna be way over

here outside of Six, you know, Six Sigma too big, or Six Sigma too small. And so

that's gonna be the core idea. Let me explain the idea in the context of an

example, and then take it to the production, how it's used in production.

So here's an example. Let's go back to the grocery store. So suppose I own a grocery

store and I sell bananas. And, on average, I sell 500 bananas a day. You know, I

keep, I've kept track of my data, it's a normal distribution, and the standard

deviation's ten. So what I wanted to be the case is that if I have any sort of,

you know, data within Six Sigma. I'm not gonna run out of bananas. Well, this is

easy to solve, all right? Because sigma is equal to ten, right? So that means that

Six Sigma. Is gonna be 60. So, if I wanna be within any event within six sigma, I'm

still gonna be okay. All I need to do, right, is have 560 bananas on hand, pounds

of bananas on hand. And then even if I get a four sigma event, a five sigma event, a

5.8 sigma event, I'm gonna be fine. I'm not gonna run out of bananas. So that the,

the idea, right? You want it to be that, even if you get a six sigma event, things

are gonna be okay. Okay? So let's see how this works. For production, so suppose I'm

making some metal part and this metal part has to be between 500 and 560 mm so this

is the range, anything in this range is okay but if I'm outside this range then

the part's not going to work. I could be making phones, I could be making car

doors, whatever. Now suppose it's the case that what causes the door to be a little

thicker or a little thinner than we want is just a bunch of random things being

added up so I've got. A normal distribution. Well I should be able to

make my production process so I get the mean right in the center of that, right.

So we've got 530 which is right in the center. And now I want it to be the case

that if I have a six sigma standard deviation, I'm still going to be okay.

Well, this isn't very hard to figure out, right. So we can just say here's my

distribution, 530s the mean. And I'm gonna have a bell curve. It's not a very good

bell curve. [laugh] But I want it to be the case that anything within six sigmas

is okay. So, 560 to 500 have to be that's gotta be my six sigma range. So this is

gonna be plus six and this is gonna be minus six. Okay. So six sigma is 30 above

the mean. Right. This is 560. Minus 530. Equals 30. That means I just want Six

Sigma to equal 30. So, if Six Sigma equals 30. That means sigma equals five. So what

does that mean? That means if I'm running this company, if I'm sort of making these

metal parts, I want it to be the case that my standard deviation. When I, you know,

keep track of the standard deviation of my parts, I wanna get that all the way down

to five. And if I get that down to five, then if I have any event less than six

sigma, the part's still gonna work. Now how do I get it down to five? That's not

easy, right, you've got to do continuous quality improvement. So the real

management practice was not just computing standard deviations and figuring out what

the six is, it was doing all that really hard work that makes it so that sigma

falls down to five. So it could be that initially your sigma might have been 30 or

twenty or something like that and the idea through continuous improvement as you

drive your sigma down so that sigma gets small enough so that even if something

really bad happens the process still works and the part still functions and you don't

have to do some sort of massive recall. Okay, so that's six Sigma thinking. What

six Sigma basically tells us is we can use this idea, right, this model of sort of

normal distributions with standard aviations to inform how we, you know, run

our production processes so we can figure out, like you know what. We're just making

too many mistakes. And if we make mistakes at this level, we're constantly gonna have

parts not work. Where as if we can reduce our variation. By reducing our variation,

the process is almost always going to work. Our parts will fit in whatever part

they've got to fit into. Alright, so that's at least another example how we can

use this aggregation things, these techniques, these tools we're using in

ways we might never have expected when we first came up with them. Okay. Thank you.