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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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