Green Belt Case study

Six Sigma Green Belt Book 5 | Module 5

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Table of Contents

Introduction ������������������������������������������������������������������������������������������������������ 4

Objectives ��������������������������������������������������������������������������������������������������������� 4

Assignment Checklist ����������������������������������������������������������������������������������������� 4

Correlation and Scatter Plots ��������������������������������������������������������������������������� 5

Performance Indicators ����������������������������������������������������������������������������������� 7

Types of Data ����������������������������������������������������������������������������������������������� 11

Levels of Measurement ��������������������������������������������������������������������������������� 16

Operational Definitions and Target Types ��������������������������������������������������������� 18

Tollgate Review: Performance Indicator Identification ���������������������������������������� 20

Gage Repeatability and Reproducibility (R&R) ������������������������������������������������ 20

Tollgate Review: Data Collection Plan ������������������������������������������������������������ 23

Data Collection �������������������������������������������������������������������������������������������� 23

Baseline Performance I �������������������������������������������������������������������������������� 25

Baseline Performance II ������������������������������������������������������������������������������� 28

Process Capability Analysis ��������������������������������������������������������������������������� 29

Tollgate Review: Baseline Performance Measurement �������������������������������������� 33

Conclusion to the Measure Phase ������������������������������������������������������������������ 33

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Module 5 Introduction Week 5 continues the discussion on the Measure phase of DMAIC, starting with more graphical data

representation tools� You will then be taught about the three major categories of collecting data, the types

of data that can be collected, and the levels of measurement used in correlation with that data� You will

be introduced to operational definitions and target types, and an overview of the performance indicator

identification and data collection tollgate review meetings will be provided� Baseline performance will

also be discussed�

Objectives • Apply a Pareto analysis�

• Define your Data Collection Plan�

• Interpret histograms�

• Describe the Motorola Shift�

• Calculate the Process Performance, Pp and Ppk, based on the current process�

Assignment Checklist � ____________________________________

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Correlation and Scatter Plots

Introduction

In order to improve a specific performance metric, we must find the upstream variables that influence

that metric� To accomplish this task, we need methods that allow us to evaluate the influence one factor

might have over a critical-to-quality variable� Correlation analysis is one of the statistical methods we

use�

Correlation analysis attempts to measure the association between numerical variables� That is, the

result of correlation analysis is a quantitative measure of the strength of association between numerical

variables� However, before we compute a correlation measure, we first check the data graphically with

a scatter plot to examine the nature (if any) of the association� A scatter plot (or scatter diagram) is a

graph that displays the relationship between two variables�

Example: suppose a professional service company is concerned the wait time (minutes) for an important

service is related to the number of complaints they receive� They were able to group the typical wait

time into several typical wait times and total the number of complaints received for that group’s wait

time� The data and scatter plot are shown below�

Wait Time Complaints

8 17

12 25

16 33

20 38

24 45

28 57

Figure 1

Figure 2

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The scatter plot clearly shows that the number of complaints increases as the wait time increases� That

is, there is a positive association between wait time and number of complaints�

The scatter plot allows us to perform an initial inspection of the data� If the variables are negatively

associated, then as one of the variables increases, the other variable decreases� If the two variables

lack much of an association, then the scatter plot will exhibit a random pattern�

Correlation Analysis

Again, correlation analysis attempts to measure the association between numerical variables� Typically,

for a suspected linear correlation, the Pearson Correlation Coefficient is used� The measure is named for

Karl Pearson (a British statistician)� The sample Pearson correlation coefficient (rxy) for two variables

x and y is computed as follows�

Note that n is the sample size, sx is the sample standard deviation for x, and sy is the sample standard

deviation for y. ∑ is the symbol for “sum.”

The Pearson sample correlation coefficient varies between -1 and +1� Values close to -1 or +1 indicate

a strong linear relationship, while values close to 0 indicate a weak linear relationship�

Example: consider our previous examples concerning wait times and the number of complaints� First,

let’s organize our data so that the calculation will be more direct�

Wait Time, x Complaints, y xy

8 17 136

12 25 300

16 33 528

20 38 760

24 45 1080

28 51 1428

Sums 108 209 4232

Std. Deviations 7.483 12.592

Figure 3

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The sample Pearson correlation coefficient is 0�998 (almost 1) which indicates a very strong positive

correlation�

Performance Indicators There are three categories of ways in which a project team can gather knowledge about customers’

needs and requirements�

Sources of VOC

• Direct – you directly involved with the customer, observe directly�

• Indirect – comes from a party internally such as sales or customer service�

• Third party – industry experts, associations, competitor data, market research�

Direct

In the direct category, you are directly in contact with the customers:

• Conduct interviews�

• Participate in focus groups�

• Survey customers�

• Direct observation�

• Become the customer�

• Various scorecards�

Indirect

In the indirect category, data comes from an internal third party:

• Complaints department�

• Service department�

• Salespeople�

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Third Party

In the third party category, data comes from outside the company:

• Industry experts that publish information about customer groups�

• Industry associations�

• Competitor data�

• Market research�

Advantages and Disadvantages

• Each category has its own advantages and disadvantages�

• Always weigh your pros and cons and mix up your approaches�

Source Advantages Disadvantages

Direct • Firsthand information

• Target groups

• Face-to-face contact

• Costs

• Groupthink

• Response rate

Indirect • Immediate resolution

• Explicitly expressed concerns

• Direct communication

• Dissatisfaction not expressed

Third-Party • Competitor data

• Research data

• Reach more people

• Cost of consultants

• Consultants’ timeline

• Too much data

Figure 4

Matching Needs and Requirements

• Customers’ needs are equivalent to a process output�

• Customer needs and requirements do not always match up�

- Requirements are supposed to identify a specific characteristic of an output�

- Clarify that the need and the requirement actually match up�

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Figure 5

Feedback Challenges

There can be challenges to receiving feedback:

• Instead of feedback, customers sometimes give solutions to issues that you are not ready to solve�

• Sometimes needs go unspoken; these are called latent needs.

- Customers may not even know their needs�

- Presumptions of your product/service may not match what the customer needs/requires�

• You may run into competing critical to quality characteristics�

- Salespeople want fast and easy while risk management needs a lot of information�

Actionable List of Measures

• What kind of data do we really need to develop the ALoM?

• What the customers want based on their true needs regardless of what your process is capable of

delivering�

• Don’t bias your data collection with your present process capability�

• Customers’ perception of your process performance compared to your competitors�

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SIPOC

• Start your search for customers with your high-level process mapping tools, such as a SIPOC�

- The “C” in SIPOC stands for “customer.”

- This will help you find a list of key internal and external customers�

- The map relates the customers to specific processes your project has targeted�

Figure 6

Leading and Lagging Indicators

• Leading and lagging indicators are types of measures�

- Leading indicators are things you can change in order to get better results in your lagging

indicators�

- Lagging indicators cannot be changed, so focus more on leading indicators�

- We tend to focus more on the lagging indicators and wonder why we can’t change the lagging

indicators�

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Twofers

• There are three areas you need data for

• Customers require quality – use two effectiveness measures

- Inputs from the suppliers – effectiveness

- Outputs – effectiveness

- Process – efficiency

• In each of these areas, there are two types of measures; that’s why they are called twofers�

- There are two measures for each data area�

Conclusion

In this section, we explored where project teams can get information, pros and cons for each approach,

challenges with feedback, alignment of requirements with customer needs, and actionable measures�

Types of Data

Qualitative vs. Quantitative Statistics

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Figure 7

Qualitative data, or the quality of something, can be described as:

• The divisions between sources or categories of data�

• A good example of these are the 6Ms�

Figure 8

When we start talking about quantitative data, now we’re starting to talk about divisions of actual

values:

• Name�

• Order�

• Interval�

• Origin�

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Figure 9

• Attribute data are things that are counted�

- This is discrete data�

- The answer to these questions are either “Yes or no,” “Go or no go,” or “Counted data.”

• Variable data include things that are measured

- Here, we are talking about continuous measurements such as distances, heights, or time�

Measurement Scale - Examples

Four types – nominal, ordinal, interval and ratio�

• Nominal scale is color�

• Ordinal scale can be days of the week since they follow a sequence�

• Interval scale is time�

- It shares the same properties as nominal or ordinal data but does not have a defined starting

point�

• Ratio data can be distance, temperature, or weight�

- It has a fixed starting point�

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Independence

• If two events are independent, the outcome of one particular event does not impact the outcome

of another�

• If they’re dependent, then the outcome of one does impact the outcome of another�

Figure 10

Mutual Exclusivity

• Means two or more events cannot coincide�

• Example – rolling a die – it cannot be two numbers at the same time�

Figure 11

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Mutually Exclusive, Complementary

Must be one outcome or the other�

Figure 12

Mutually Exclusive, Non-Complementary

Figure 13

Conclusion

In this section, we saw examples of qualitative and quantitative statistics, explored measurement

scales, and understood the meanings of mutually exclusive and independent probabilities�

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Levels of Measurement

Introduction

Understanding the nature of your data and how to represent it can affect the types of statistical tests

that you can do, and so we’re going to look at four levels of scales� These are:

• Nominal�

• Ordinal�

• Interval�

• Ratio�

Nominal Scale

• Has the least number of options�

• Consists of categories:

- Names, labels, telephone numbers, street addresses, social security numbers�

• Cannot be arranged in an ordering scheme�

• No arithmetic operations are performed for nominal data�

• Possesses no order, distance, or origin�

Ordinal Scale

With ordinal scale, data is:

• Arranged in some order, but differences between data values either cannot be determined or are

meaningless

• Ordered but with no distance or origin�

• Examples include:

- Movie ratings – PG, X, R�

- Course grades – A, B, C, D, F�

- Horse race – 1st place, 2nd place, 3rd place�

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Interval Scale

With interval scale, data can be:

• Arranged in some order and for which differences in data values are meaningful�

• Arranged in an ordering scheme and differences can be interpreted�

• Arranged by order and distance, but without origin�

• Examples include:

- Time between calendar dates�

- Average temperatures�

Ratio Scale

With ratio scale data can be:

• Ranked and serve as that which all arithmetic operations including division can be performed�

• An absolute zero, and a value of zero indicates a complete absence of the characteristic of interest�

• Arranged by order, distance, and origin�

Examples include:

• Speed of a jet�

• Crime rates�

• Production rates�

Scale Central Location Dispersion Significance Test

Nominal Mode Information Only Chi-square

Ordinal Median Percentages Sign or Run Test

Interval Arithmetic Mean Standard or Average Deviation t Test

f Test

Correlation Analysis

Ratio Geometric or Harmonic Mean Percent Variation (same as usual)

Figure 14

Conclusion

Discussed nominal, ordinal, interval and ratio measurement scalesand the different ways that the

central tendency, location, and significance can be measured for each�

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Operational Definitions and Target Types

Operational Definitions

When I’m working with teams, I stress the importance of operational definitions� Take the example of

door-to-balloon time in a hospital setting� The definition of door-to-balloon time is the amount of time

that passes between when a patient arrives at the hospital and when they get treatment� (Here, the

term “balloon” refers to, in the angioplasty process, the little balloon that rises and pushes the blockage

apart�)

Could that definition be refined in order to measure it over time and see if it is getting better or not?

For example, what door are we talking about? The word “door” could refer to many things: the door to

the emergency helicopter, the ambulance door, the front door of the hospital, or the emergency room

door. If two people are measuring this, and they have different understandings of what “door” refers

to, there could be measurement error� We need to operationally define things ahead of time in order to

avoid confusion and prevent the introduction of variation into the process� Ultimately, an operational

definition isn’t the most exact definition – it’s the definition that everyone can agree to�

Types of Targets

When we are measuring things, there are different types of targets� No matter what the target type is,

you want as little variation around that target as possible�

Larger Is Better

• The target could be infinity or 100%�

- When talking about tires on a car, the target would be infinity because we want the tires to last

for an infinite number of miles�

- When talking about attendance, the target would be 100% because we want 100% attendance�

Smaller Is Better

• Zero is the target�

- If we’re measuring contamination in a chemical bath, we would want zero contaminants�

Nominal Is Best

• The target is some middle value�

- Kicking a field goal right down the middle of the goal posts�

- Landing a plane in the middle of a runway�

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To illustrate that, imagine driving down a single-lane mountain road� There are no cars coming the

other way, but there are no guard rails on either side� You could drop off 1,000 feet on one side or you

could scrape against the wall of rock on the other side� The rework side is the rock wall – if you scrape

it, you could rework your car and fix it� The drop off is the scrap side – if you go off the edge, there’s

no coming back� Which side are you likely to favor? Most people would probably favor the rework side

over the scrap side� Instead of thinking about the lower spec and the upper spec, the most marginally

accepted product or service measurement, look down the middle of the road with as little variation

around that as possible� This should all be part of the operational definition ahead of time� What are

we measuring? Is larger better? Is smaller better? Or is some middle value best?

Real-Life Examples

You can apply these concepts in your everyday life� For example:

• At a bakery, will you choose the fresh, hot bread that just came out of the oven, or the bread

that came out of the oven an hour ago? Most people would want the bread right out of the oven,

meaning zero time has passed�

• If you’re buying milk, will you choose a carton with a pull date that is sooner or later? Even though

the label says it is good for seven days after the pull date, many people will try to find one with a

date that is as far out as possible�

• If there are 15 registers at the front of the store, which one will you pick? You will most likely pick

the one with the shortest line�

Scenarios

• Is the payment of an invoice a larger-is-best, smaller-is-best, or a nominal-is-best scenario? You

don’t want to pay it too fast or too late, so in this scenario the target is some ideal amount of time

in the middle�

• Regarding salary, is a larger, smaller, or nominal target best? If you are an employee, you would say

larger is better� If you are in top management, larger is not best because then you give up some of

your profits� Management doesn’t want to pay too little either, because then employees will leave�

So, there is this ideal salary for each position that falls somewhere in the middle�

• What about departure times in an airport? Larger is better, smaller is better, or nominal is best?

Maybe they are one or two minutes late every now and then, but typically you would want that to

be at zero with as little variation as possible�

• What is the target for playing an 18-round golf game? Many people would say par, however, the

ideal target for 18 holes of golf is a hole-in-one in every hole� A goal, however, is different, because

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people do better than par� So, par is not really a target – it’s what you’re gravitating toward� If larger

is better, for example, you’re gravitating toward 100 percent or you’re gravitating toward infinity�

Is it likely you’re going to get there? No, but that’s what you’re pulling toward� So, if you have an

average golf score of 115, next year you could have a goal of getting it down to 100, but ultimately

you’re still gravitating toward that even smaller score�

Conclusion

Often, the decision of whether larger is better, smaller is better, or nominal is best, is in the eye of the

beholder� However, we always want as little variation around that target as possible�

Tollgate Review: Performance Indicator Identification At the performance indicator identification tollgate review meeting, the sponsor will want the following

information:

• What you are going to measure�

• A clear explanation of the performance measures you chose and why they are good choices�

- Do not focus on outcome measures; instead, focus on upstream measures, leading indicators,

etc�

If data already exists for the measures that you suggest, bring some of that information with you to the

meeting� If the organization doesn’t exactly have what you are looking for but they have things that

are close to it, the sponsor may want to know why you are suggesting that the team gather new data

instead of using the information that is sort of like what you want� So, be prepared to answer that at

the meeting� If the data is not available, you will have to figure out how to get it by the next tollgate,

but try not to make promises about gathering the data until you put the data collection plan together�

Gage Repeatability and Reproducibility (R&R)

Introduction

The purpose of Gage Repeatability and Reproducibility study (Gage R&R) is to discover whether the

variation caused by the measurement system, Measurement System Analysis (MSA), is small enough

that when we measure something with it, we are seeing mostly the true variation�

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Definitions

A Gage R&R study addresses two questions about the measurement system:

1� What percentage of the variation in the measurements is due to the measurement system?

2� How precise is my measurement system?

Precision

The extent to which the measurement system is subject to spread� Precision is divided into repeatability

and reproducibility�

Reproducibility

Measurement of the variation due to differences between operators�

Repeatability

The remaining variation if all circumstances, such as measurement instrument, person, and location

are kept equal for each of those repeated measurements�

Accuracy

How close the measurement is to a standard or a true value� In order to determine the accuracy of the

measurement system, the measurement is compared to a specific value from an instrument that is

designated as the standard, or master gage�

Bias

A systematic measurement error� The difference between the average of multiple measurements on

the same object and the reference value� Bias can be corrected by calibration of the measurement

equipment�

Gage R&R

A Gage R&R checks:

• Repeatability and Reproducibility of the measurement system, not just the gage itself�

• It answers the question, “what percentage of the variation in the measurements is due to the

measurement system?”

• How precise is my measurement system?

• It does not tell you how accurate the measurement system is�

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How to Conduct a Gage R&R

Most people follow the automotive industry’s model for conducting Gage R & R studies:

Ten Parts are each measured

Three Times (Three Trials) by

Three Operators

For a total of 10x3x3 = 90 measurements

It is possible do a smaller study with only 5 parts, measured again 3 times by 3 operators, but the

results will not be as reliable or, as we say, statistically significant� Or we could include only one

operator, but if we do, we would not get any information about reproducibility�

After collecting the data for all the parts, trials, and operators, the data is analyzed usually by one of

two methods:

• Xbar and R�

• Analysis of Variance (ANOVA)�

The actual calculations for these methods are beyond the scope of this class, but it is important to

remember the main point we are trying to find out if the variation caused by the gage and operators

(Repeatability and Reproducibility) is adequate for the tolerance needed�

P/T Ratio

The P/T ratio is they key outcome from a Gage R&R� It checks the precision of the measurement

system against the total tolerance allowed from our customer for whatever the part or service is we are

providing�

A P/T ratio gives us:

• 0�10 or less, which is good

• 0�30 or greater, which is not acceptable

• In between we have to make arrangements�

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Tollgate Review: Data Collection Plan At the data collection plan tollgate review meeting, the sponsor will want the following information:

• A plan that tells the sponsor exactly what data you are going to collect, how you are going to collect

it, and how much of it you are going to need�

• An estimate of the cost and time that it will take to go get that data�

Give the actual data collection plan worksheet to the sponsor ahead of time� Be prepared to give a clear

and concise explanation of each measure at the review meeting�

If the sponsor finds anything unreasonable or not acceptable within the data collection plan, you

may need to revisit the performance indicator identification tollgate� You might want to come to the

data collection plan tollgate meeting prepared for that and have a backup recommendation ready to

go, especially if some of the data is going to be expensive, time-consuming to gather, or disruptive to

business�

Data Collection

Introduction

In Six Sigma, Y = f(X)� Good data helps us understand the potential of the X’s on the overall Y� When

we have narrowed down the X’s to a vital few, we need to be able to validate them with data�

Collecting data in a deliberate fashion helps us:

• Understand the baseline performance of our process�

• Measure the magnitude and frequency of our defects or issue�

• Ensure we can sustain the gains or quality improvements�

How Much Data to Collect

Some considerations when deciding how much data to collect include:

1� Finances can restrict how much data you can realistically collect�

2� Time may also be a factor in how much data you can collect for any given project�

3� Governmental agencies and/or regulatory groups�

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Formulas are available to help determine a good minimum sample size, and you should consult your

Black Belt, Master Black Belt, or a statistician if you have any concerns or questions regarding sample

size�

Benefits of a Data Collection Plan

Data collection plans:

• Ensure you are collecting only what data is needed�

• Prioritize the collected data�

• Determine how often to collect the data�

• Determine how much and where in the process is the data to be collected�

Two additional considerations in any data collection plan:

• Destructive and nondestructive production of a data point: is what we are measuring going to be

destroyed in the process or not?

• Return on investment: how much improvement of our output variable or project Y are we going to

get for this data point?

Granularity

There are two guidelines that help us determine how many data point we need, and which you should

use depends on what type of data we have�

• For continuous data, 30 data points�

• For discrete data, 100 data points�

Data Collection Plan

The data collection plan should be easy to read and understand� How you actually set up the data

collection plan is up to you and your team� However, every data plan should:

• Define all the columns�

• Ensure that it presents the opportunity to get the right kinds of data in the right amounts (appropriate

granularity)�

• Identify what data is already available through the document control�

• Consider whether the data is discrete or continuous�

- This will help in the Analyze phase�

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Using Images

• When possible, convert check sheet data into a picture�

• Use a Pareto chart for discrete data; it prioritizes causes for you�

• Use cycle time information as continuous data; this shows frequency or distribution patterns in the

data�

Conclusion

Use data to support your decision making. Choose substance over “gut feelings” and you will get the

information needed to improve processes�

Baseline Performance I

Introduction

Baseline quality performance focuses on ways to measure the starting (or baseline) quality performance

for your situation� There are multiple ways of looking at baseline quality performance�

1� Defects per unit (DPU) looks at total defects over total units produced� It is a simple metric for

assessing the cost of poor quality, however DPU does not account for varying complexity�

2� Rolled throughput yield (RTY) looks at the yields of a process multiplied together� RTY only accounts

for defective products or services, not if a product has multiple defects per process step�

3� Defects per million opportunities (DPMO) accounts for the opportunities for failure� DPMO allows

an organization to compare products or services of varying complexity across the same process

steps�

Defects Per Unit (DPU)

Defects per unit (DPU) is the total number of defects found within a specific period of time divided by

the number of units produced in that time�

DPU = Total Number of Defects / Number of Units Processed

Example: Mortgage Applications

How many mortgage application processing defects were there for one client in the past month? During

that time, 85 applications were processed� There were 15 W-2s with the incorrect year, 11 pay stubs

that weren’t recent enough, eight incomplete lists of debts, and four 1099 forms went missing�

DPU = (15 + 11 + 8 + 4) / 85 = 38 / 85 = 0�45

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Rolled Throughput Yield

Rolled Throughput Yield (RTY) is the probability that a product or service will go through all the steps

of the process without a defect� Rolled throughput yield is equal to the first pass yield (FPY) of the first

process step multiplied by the first pass yield of the second process step, so on and so forth for all

process steps� It accounts for both scrap and rework�

Example

RTY = FPY1 × FPY2 × ��� FPYn

Three Processes

• Process A = 20 Units / 4 Defective = 0�80 = 80% FPY

• Process B = 20 Units / 2 Defective = 0�90 = 90% FPY

• Process C = 20 Units / 1 Defective = 0�95 = 95% FPY

Therefore, RTY = 0�80 × 0�90 × 0�95 = 0�684 = 68�4%�

DPU vs. RTY

Key differences between defects per unit and rolled throughput yield include:

• DPU considers how many total defects existed in a given number of units�

• If multiple defects can exist on one unit, the calculated DPU can be greater than one�

- RTY only considers that a unit was defective, regardless of how many defects existed�

• A unit with one defect can have the same impact on RTY as a unit with 10 defects�

When to Use One vs. the Other

• Use DPU when the cost of rework is high and multiple defects per unit are possible�

• Use RTY if there are checks and yields from multiple process steps, and if multiple defects per unit

are rare and not impactful to the cost of quality�

Drawbacks to Using Defects Per Unit and Rolled Throughput Yield

• They do not consider the complexity of the product or service being analyzed�

• The more complex a product or service is, the worse its DPU or RTY will be when compared to

similar products that are less complex�

• Only considering DPU or RTY may cause an organization to choose the wrong priority when trying

to decide for which services or products to deploy resources for improvement�

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Defects Per Million Opportunities

Defects per million opportunities (DPMO) is a good metric to use for more complex products and

services�

The formula:

DPMO = Total Defects in Sample / (Total Opportunities × 1,000,000)

DPMO is something like a percent, but 1,000,000 is better for low levels of defects� To get from

percent to DPMO, multiply by 10,000� For example, 0�08%= 800 DPMO�

Benefits of Using DPMO as a Metric

DPMO:

• Provides numbers that are easy to discuss�

• Makes it easier to compare different products or industries�

Calculating DPMO

What are the steps for calculating defects per million opportunities?

1� Determine the number of defects (D).

2� Determine the number of units processed or services offered (U).

3� Determine opportunities per unit (OP).

4� Calculate the total opportunities (TOP).

5� Divide the total defects by the total opportunities (DPO).

6� Multiply that answer by one million�

Example: Gold Wedding Bands

A gold wedding band might have opportunities for defects regarding size, purity, and weight� Therefore,

each ring could have three opportunities for defects per unit�

• If we find a total of 150 defects, then D = 150�

• Assuming we have 10,000 wedding bands, then U = 10,000�

• Opportunities = OP = 3 (size, purity, weight)�

• Total opportunities = TOP = 3 × 10,000 = 30,000�

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• Defects per opportunities = DPO = 150 / 30,000 = 0�005�

• Defects per million opportunities = DPMO = 0�005 × 1,000,000 = 5,000�

Conclusion

This lecture discussed:

• Defects per unit (DPU)�

- Total defects over total units produced�

- Simple metric for assessing the cost of poor quality�

- Doesn’t account for varying complexity�

• Rolled throughput yield (RTY)�

- The yields of a process multiplied together�

- Only accounts for defective products or services, not if a product has multiple defects per

process step�

• Defects per million opportunities (DPMO)�

• Accounts for the opportunities for failure�

• Allows an organization to compare products or services of varying complexity across the

same process steps�

Baseline Performance II

Calculating Sigma

There are multiple approaches to calculating sigma:

• Using a Z-score table (which is covered in greater detail at the Black Belt level)�

• A Sigma table is provided in this course material� There are two kinds of Sigma tables:

- With a 1�5 sigma shift – Six Sigma is 3�4 defects per million (preferred)�

- Without a 1�5 sigma shift – Six Sigma is around two defects per billion�

• A Sigma calculator can be found online or in some statistics programs�

• The 1�5 sigma shift is a way to practically account for the fact our process will produce more

defects in the long run than we will probably measure over the short time of our project�

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Example: Defects Per Million Units

A call center monitors employee performance and listens to 500 calls� They are only listening for

whether or not the customer is given the correct answer, so this is a defects per unit problem� They find

75 wrong answers, or defects, over the course of 500 calls�

1� Defect rate = 75 / 500 = 0�15 = 15%�

2� DPMU = 0�15 × 1,000,000 = 150,000�

3� Use the Sigma table�

- One column shows defects per million units and the next column shows Sigma�

- Large numbers appear at the top and decrease until it reaches Six Sigma (3�4 defects per

million units)�

- Find a number slightly larger than 150,000 and a number slightly less than 150,000�

- In between those numbers, we’ll see 150,000 defects per million units equals somewhere

between 2�5 and 3 Sigma�

Example: Defects Per Million Opportunities

For the same call center, we can now look at total service� 500 calls are monitored and 75 defects are

found in the areas of answer speed, courtesy of service, and correct response�

1� Opportunities for a defect = 500 × 3 = 1,500�

2� Defect rate = 75 / 1500 opportunities = 0�05 = 5 percent�

3� DPMO = 0�05 × 1,000,000 = 50,000�

4� Use the Sigma table to find that 50,000 defects per million opportunities is somewhere between

3 and 3�5 sigma�

Process Capability Analysis

Introduction

Process capability analysis consists of a set of metrics that assess the propensity of a stable (in-control)

process to meet the stated requirements� Clearly, in the end, we want processes to meet our operational

definition of quality: that is, minimum deviation from the appropriate target� The way we establish

specifications and performance requirements for our processes (and our products and services) is a

result of our understanding of the voice of the customer� Our ongoing monitoring of the critical-to-quality

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characteristics provides actionable direction for our improvement efforts� Our objective is to match the

voice of the customer with the voice of our process so that we meet the customer’s requirements (see

the graph below)�

Figure 15

Process capability analysis provides us with a method to measure the extent to which our processes do

or do not meet our requirements (and, so, whether we do or do not meet the expectations of the voice

of the customer as we have deployed it)�

Process Capability Metrics

Over time, several metrics were developed in process capability analysis� We typically work with them

in two groups: (1) Cp and Cpk, and (2) Pp and Ppk� In general, Cp and Cpk are computed from the

results of a control chart and Pp and Ppk are computed using all the individual data values collected�

Example: Cp and Cpk. Suppose we are monitoring the time (in minutes) for the process for completing

a specific task with an Average and Range Control Chart (Control Charts are discussed in Module 6)�

Let’s assume the Average and Range Chart shows the process to be stable with average of 8�9 minutes

and a process standard deviation (sp) of 1�77� Our experience indicates the customer is likely to be

dissatisfied if the task takes longer than 11 minutes� Moreover, our own experience with this process

leads us to believe employees make more mistakes if they attempt to complete the process in less than

7 minutes� So, the organization decided to use an Upper Specification Limit (USL) of 11 minutes and

a Lower Specification Limit (LSL) of 7 minutes�

Cp measures the ratio of the allowed tolerance to the estimated process variation (using 6 times the

process standard deviation, or sp)�

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The Cp of 0�38 indicates the estimated process variation (the denominator) is much larger than the

allowed tolerance (numerator)� So, we know the process will not consistently meet our requirements

because the process variation is too large�

Also, the Cp does not consider where the process is centered or how close the center (average) might

be to a specification limit� To provide that information, we use the Cpk�

Cpk enhances Cp by considering the average of the process relative to the specification limits�

Note that Cpk is a minimum of two calculations�

Note that the Cpk is close to the Cp since the process average is close to the center of the tolerance�

However, the Cpk is also poor because the process contains too much variation�

Technically, the Cpk must be at least 1�0 for us to say we have a process that is (barely) capable� Many

organizations set a higher minimum Cpk (for example, 1�33)�

This process is not capable of meeting the specifications that have been established (that is, a USL of

11 and a LSL of 7)� See the graph below�

Figure 16

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Pp measures the ratio of the allowed tolerance to the estimated process variation (using 6 times the

sample standard deviation, or s)� The sample standard deviation (using the all the data available) for

this example is 1�63�

The Pp of 0�41 also indicates the estimated process variation (the denominator) is much larger than the

allowed tolerance (numerator)� So, we know the process will not consistently meet our requirements

because the process variation is too large�

Ppk enhances Pp by considering the average of the process relative to the specification limits (again,

using the sample standard deviation, s)�

Note that Ppk is a minimum of two calculations�

Again, the Ppk is close to the Pp since the process average is close to the center of the tolerance� Also,

the Ppk is also poor because the process contains too much variation�

Technically, the Ppk must be at least 1�0 for us to say we have a process that is (barely) capable� Many

organizations set a higher minimum Ppk (for example 1�50)�

As before, this process is not capable of meeting the specifications�

Remember, the objective of capability analysis is to assess whether or not our process is capable of

meeting our requirements� The two sets of metrics above (Cp, Cpk and Pp, Ppk) consider two different

aspects of the process data� The difference between them is the approach each uses to capture the

variation in the process� It is good practice to calculate both sets of metrics�

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Tollgate Review: Baseline Performance Measurement At the baseline performance management tollgate review meeting, the sponsor will want the following

information:

• Charts and graphs that depict the measure(s), the target, and difference between the two�

• This might involve calculating the actual sigma measurement and/or conducting a capability study

by measuring process capability, Pp and Ppk�

• Any necessary information to make some final updates to the charter�

• An up-to-date version of the charter�

Conclusion to the Measure Phase

Tollgates of Measure

The measurement phase requires that the team has completed the following:

1� Selected process performance indicators�

- You know what needs to be measured�

- Many process improvement efforts struggle or fail merely because they’re not measuring the

right things�

2� Created the Data Collection that includes (at a minimum)�

- Type of data�

- Amount of data needed�

- How you’ll collect it�

- Created operational definitions�

3� Established and measured baseline performance�

- Established a target and a gap�

- Calculated Sigma�

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The Next Phases of DMAIC

There are several possible outcomes as you conclude the measure phase:

1� You may discover the problem is much worse than originally believed�

2� If this is the case, you may want to reconsider the scope of the project or ask for additional resources�

3� The data may suggest there’s not actually a problem�

4� You can stop the project and apply resources to another opportunity that needs improvement�

5� You will proceed to the next phases of DMAIC�

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Notes