0:15

So let's take this idea of defects per million opportunities and

sigma levels and apply it to a very simple situation.

So here we have a medical center pharmacy that is concerned about the amount of time

pharmacists are spending calling doctors to confirm prescription information.

So what is happening here?

The pharmacy gets a prescription, and what they're finding is there's a problem with

the prescription, they have to call and they have to get some things clarified.

The number one reason for such cases is illegible handwriting.

The pharmacist keeps a prescription log for two weeks, records for

each prescription whether there was illegible handwriting-related to the drug,

the dosage, the number of refills, and the doctor name.

So we have four pieces of information, four what we call critical to quality

characteristics from this process, four things that are critical to performing

this process correctly that are being looked at.

So those become the four opportunities that we're focusing on in

this particular example.

Now, we have a 1,200 prescriptions,

the sample that was taken was 1,200 prescriptions, and

there were 605 defects that were found in these 1,200 prescriptions.

Now, what you want to have clear in your mind is that these 605 defects

could mean that there where 605 prescriptions each with 1 defect each,

or there were many prescriptions that have several defects.

So the, actually, number of prescriptions that had defects was much less than 605

because there were prescriptions that had multiple defects.

So you can have almost as low as, in this particular case, we're going to be

talking about 151, 152 prescriptions that might have 4 defects each,

in which case you would get 605 defects, but

we don't know that just from looking at this information.

All right, so now that we have the data clear, we have 1,200 prescriptions,

we have 605 defects, what is the total number of opportunities?

Well, each prescription has 4 opportunities, so therefore our total

number of opportunities are going to be based on 1,200 multiplied by 4.

So to calculate your defects per million opportunities,

we're going to take 605 divide by 1,200 times 4, which is 4,800.

And, in order to scale it up to defects per million opportunities,

you're going to multiply by 1 million.

That gives you 126,042 defects per million opportunities,

so that's 126,042 defects per million opportunities.

Now, you can use the Excel formula to get the sigma level,

the Excel formula that you use for the standard normal distribution.

And what you're doing there essentially is you're saying give me the z-score for

when I have 126,042 defects per million opportunities in the right-tail.

So you're putting that in the tail of standard normal distribution,

and then you are trying to get to the z-score for it.

So, going through that in Excel you can see that 126,042 defects per million

opportunities translates into a sigma level of 1.15, so what this is telling us?

It's telling us that this is way far off from a six sigma level of performance,

and it's also telling us the current sigma level is 1.15.

So, you can have a target of two or

three sigma level as a first cycle of improvement,

trying to get better from this baseline that you have in this particular process.

Now, we talked earlier about Six Sigma not exactly resulting

in 3.4 defects per million opportunities.

We said that 3.4 defects per million opportunities does not exactly translate

to a Six Sigma level of performance, and why is that the case?

And then, again, you can trace this back to something that Motorola did, just as

you can trace the idea of six standard deviations, Six Sigma to Motorola.

There's also this adjustment that Motorola did

in order to compute their sigma levels.

So what they said was, well,

any process is going to have some natural drift over time, and

we are going to cut some slack to the process in order to calculate z-scores.

So what we're saying is that we're going to take a smaller

level of sigma and we're going to call it 3.4 defects per million opportunities.

We're not going to quite have it all the way to Six Sigma.

So what was the adjustment?

They gave it an adjustment of 1.5 sigma.

So when we say 3.4 defects per million opportunities, what we are actually

saying is that the process is at 4.5 sigma when

you're talking about it from the point of view of pure statistics, all right?

When you're talking about it from looking at a z-score, and

we're talking about it from looking at it from putting the formula into Excel and

trying to get a sigma level.

When you're talking about 3.4 defects per million opportunities,

it'll translate into a sigma level of 4.5.

So put this in the form of a picture, what you can see here is.

What you have on top is the actual distribution and

the level of defects if you're basing it on Six Sigma.

And what you have on the bottom is that you have a shifted distribution,

shifted by 1.5 sigma or 1.5 standard deviations.

And so you're using the one at the bottom, which is at actually 4.5,

but you're calling it 6 based on the picture on top because you're

saying that if it's at 4.5, we're going to call it Six Sigma.

So how do we do this calculation?

It's nothing more than simply taking what you get from Excel, taking what you get

from a purely statistical perspective and adding 1.5 to it.

So, you get your sigma level, it's 1.15.

If you remember from our example for that pharmacy and

the errors in prescriptions, we had a sigma level of 1.15,

you add 1.5 to that and you have a sigma level of 2.65.

So in other words, whenever you have a sigma level,

you just have to have this question of was this adjusted for the Motorola shift?

We even call it the Motorola shift because that's the company that made

this something that has become popular since then.

So, has it included the Motorola shift or

not is the question that you should be asking when you see a sigma level.

Now, just to make comparison, just to clarify this a bit more.

Here's a comparison of computing sigma levels with the shift and

computing sigma levels without the shift.

So with a shift of 1.5

Six Sigma translates to 3.4 defects per million opportunities.

But when you're talking about without the shift, what you can see it

is at 4.5 sigma, you have 3.4 defects per million opportunities.

In fact, without the shift, if you're talking about a Six Sigma process here,

it is going to be closer to 0 defects per million opportunities.

It's going to be, even if you go to two decimal points,

you're not going to get a number.

So you have to go to four decimal points to find a defects per million

opportunities number when you're talking about it without the shift.

7:37

Now, all this is about the metric of Six Sigma, right?

We're talking about this from the point of where did 3.4 defects per million

opportunities come from and where did the idea of 6 come from.

But Six Sigma as a process improvement initiative, Six Sigma as a continuous

improvement initiative is much more than simply the metric.

It's a methodology, it's a methodology that is used by companies to implement

continuous improvements.

So here you have a definition of Six Sigma which takes all of that into account.

So going partially into this definition,

Six Sigma is uniquely driven by understanding of customer needs,

disciplined user facts, data and statistical analysis.

So what are we talking about here?

We're talking about taking some problem, taking some improvement

opportunity based on customer needs, and that could be a process customer.

Using facts, using metrics as much as possible, using numbers,

and trying to use statistical analysis to improving that process.

Going back to the first line in the definition, it's a comprehensive and

flexible system for achieving, sustaining, and maximizing business success.

So it's a system for putting continuous improvement in place, it's a system for

having the idea of continuous improvement in place.

So what is it beyond 3.4 defects per million opportunities,

what is it beyond the metric?

So, Six Sigma is not only about reducing defects,

it's also about reducing cycle times.

We could be talking about a project that not only focuses on defects in

the conventional sense, in terms of a product not working, or

a service having a defect, but in terms of saying we want to reduce the cycle times.

We have certain cycle time in mind, we want to reduce the cycle time, we want to

reduce the lead time for when somebody places an order and receives a product.

We want to target higher levels of customer satisfaction or

even employee satisfaction, we want to target higher levels of that.

So that could be an objective.

So it's not just about looking at defects in

the very common sense of looking at defects in a product.

It could be about reducing work-in-progress inventory, or

it could be a longer process in talking about decreasing time to market from

conceptualization of a product idea to actual production and

bringing it into the market for customers.

So it could be any of these things.

Different elements of Six Sigma that go beyond the metric, different

aspects of Six Sigma that go beyond the metric are cross-functional teams.

So we're talking about teams that are made up of people from

different parts of the process.

You have people that are related to the actual process that is being improved or

they could be support staff or support employees.

So if you're talking about a process for reducing cycle time, you

may have somebody from information systems because if there's an IT solution to that,

you want them involved.

Although they're not directly in the process, they're somebody that can help

with the improvements, so it's cross-functional teams.

Six Sigma relies a lot on the idea of project leaders,

it has this concept of black belts and green belts.

And these are some full-time project leaders, some part-time project leaders

that lead continuous improvement projects, that are trained in the methodology for

conducting a process improvement project using Six Sigma methodology.

So there's a specific methodology for using Six Sigma in a project.

Systematic project selection, it's about getting projects that are going

after organizational objectives and making sure that we prioritize projects

based on how much they're going towards particular organizational objectives.

So which ones should we be focusing our attention on more, and how

does that translate into something that the organization will be able to achieve?

Six Sigma has this idea of having very specified project goals, so

the notion that even before you start a project there should be specific goals

and, to the extent possible, enumerated in terms of money,

in terms of dollars, euros, rupees, whatever the case may be.

But in terms of what is this project going to get us in terms of top line and

bottom line, that's what there should be some specification of that before you

start the project.

It's about structure, project execution,

using the DMAIC way of executing a project, define, measure,

analyze, improve, control, that's the most popular framework under Six Sigma.

It has emphasis on data and measurement and

the idea of we're focusing on making improvements based on root cause analysis.

We're trying to find the causes for the effect.

We're trying to find the ys,

we're trying to find the xs that have an impact on the y.

If y is the outcome, we should be looking at what are the different xs

that are affecting that why and focusing on those to make improvements.

So here we can see that Six Sigma is much more than simply the idea

of 3.4 defects per million opportunities.