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Six Sigma Green Belt Exercises

Six Sigma Green Belt Exercises


Classroom Exercises

Six Sigma Training

March 2016


Six Sigma (SS) candidates have to first learn the methodology and theory of SS.

While the educational aspect of SS is important, the real goal for the candidate is to

apply their knowledge to solving real life business problems. The following

exercises are intended to be used after green belt training as a way of transitioning

candidates to working real life problems.

The Classroom Exercise is based on the use of Quincunx boards, sometimes referred

to as a factory in a box, to generate data and allow candidates to apply the DMAIC

steps of SS. There are two types of problems that candidates can solve involving the

quincunx boards:

1. A Process Variability Improvement Problem

2. An Equipment Capability Problem

A third type of cycle time improvement problem is also included to provide practice

in dealing with transactional types of business problems.

3. A Cycle Time Reduction Problem

Following is a description of each of the problems. The first two problems utilizing

the quincunx work on the principle that the candidates can only see the data

generated by the quincunx boards, but not the funnel location or pin block. This

requires the creation of some type of hood that hides the top portion of the board,

both front and back, but still allows access to the bead release lever in order to

generate data. (Most instructors just tape a piece of heavy paper or cardboard over

the top half. Do the same for the back if students can see the back of the board.)

Process Variability Problem

This problem consists of combining two ingredients, A and B, in order to make a

third item C. In reality this is a mix problem and for simplicity sake we will assume

that the distribution of A+B=C. The challenge is to understand the distributions for

items A & B and predict what distribution C will look like, how to improve it, and

ultimately control the process.

Additional hypothetical information about the process, the level of non-conformity,

the associated costs, etc. etc. has to be developed so that the students can Define the

problem and create the value proposition for the project.

We will be using two different quincunx boards to generate data for A and B. There

are two major adjustments on the quincunx board, the funnel position which

influences the average of a distribution, and the number of pin block rows engaged,

which influences the variability of the distribution. For this demonstration the


channels/columns are numbered from 1 to 25 across the face of the quincunx and a

ball in column 12 is a data element of 12, a ball in column 13 is a 13, and so on. The

statistical measures of the distribution are determined from the histogram of balls

displayed across the columns.

The engineering specifications for A and B are at the discretion of the instructor.

Distribution A can be located inside, outside, or straddling the low end of the

specification for distribution A. Once this is predetermined the funnel and pin block

are adjusted to create a data distribution at the low end of the A specification and

the top of the board is covered with a hood to hide the funnel and pin block.

Candidates can measure the average, range, and standard deviation of distribution A

by calculating it manually or filling in the data values on a supplied excel

spreadsheet. (spreadsheet is included with materials).

Distribution B is set up on a second quincunx board such that the distribution is

located near the high end of the specification for item B with all of the pin block

rows engaged in order to achieve the maximum variability. Again, the funnel can be

positioned inside, outside, or straddling the upper specification limit.

Again, candidates can measure the average, range, and standard deviation of

distribution B by calculating it manually or filling in the data values on the supplied

excel spreadsheet.

All of the data collection and analysis up to this point would be part of the Measure


The Analyze phase of this project is to analyze the data and describe what and how

they would change processes A and B in order to improve the final process C. Given

that we have determined that A + B = C the students will have to figure out how to

combine A and B and determine the initial out come of process C with the initial sets

of data. Candidates may struggle with this for a while or they immediately recognize

that they can combine the data sets from the A and B spread sheets into one

spreadsheet and then recalculate the statistics.

The Improve stage will vary according to each group’s recommendation. One

would hope that candidates would readily recognize that they need to adjust the

means of A and B to both be centered with the engineering specification for C.

Following this they should also recognize that they should reduce the variability of

item A, B, or both. You can add another dimension to the problem by presenting

different hypothetical costs in order to change the parameters of the quincunx

setup. For example, moving the funnel for factor A costs $5000 an inch to move,

changing a pin block setting costs $15000 a row, so on and so forth. Once

candidates see the top section of the quincunx they can readily see the solution of

centering the funnels and disengaging rows of pins in the pin block. But if the

solution also has cost constraints they will have to think in terms that are closer to


real world realities. Changing the specifications for item C will also drive candidates

to approach the improve stage differently.

The Control stage will require different kinds of control methods as determined by

individual groups. They could specify controlling the process by completing a

process FMEA and putting critical items in a control plan, controlling the process via

a variable control chart, creating a fool proof method like locking the funnel, etc.

Equipment Capability Problem

This problem represents a process that has gone out of control and producing a

large amount of non-conforming material. The challenge is to determine how to

improve the process by following the DMAIC steps. Like the previous problem,

some hypothetical information has to be established in order for candidates to

determine the value proposition for the project, which is part of the Define phase.

Once the quincunx is set up the top of the unit has to be hidden from the candidates.

The only thing they can do is generate data and analyze it. Like the previous

problem, cost constraints can be introduced to simulate a certain level of practicality

such as $500 per data point when running data and/or costs to move the funnel,

disengage rows of pins, etc. (Note that by setting a budget for accessing data you will

prevent candidates from just running data with no constraints. Gathering data and

running tests have real costs and time constraints in life. Try to simulate the same

with a budget or limit to data acquisition for this exercise.)

The Measure phase will most likely consist of taking data samples and analyzing it

via the excel spreadsheet. The difference in this example is that hidden behind the

quincunx hood is a unique funnel setting where is it slid all the way to one side and

taken out of the process. Beads then drop directly from the reservoir down to the

pin block pins and bounce significantly. This bounce is different than the normal 50-

50 chance of falling to the left or right when a ball hits a pin. In this case they bounce

erratically all over producing a very erratic non-normal distribution. Students who

think they have only to draw a simple data sample, and then determine how much to

move the funnel will definitely be thrown a curve ball. Just taking more data at $500

a ball will drive up the cost quickly.

Candidates will have to determine some form of normality test whether it is

graphical, performed with a stat package like Minitab, a control chart, etc. They will

then be able to prove that the equipment is “out of control”. This conclusion can be

reached in the Measure or Analyze phase depending on the group. When the team

proves that the machine is “out of control” they will be told that it will cost $900,000

to rebuild the machine. When they agree a small funnel movement will then bring

the funnel back into play but the mean and variance will still be far off from the

target. They will have to then go back through the Analyze phase again and take

more data to determine their next steps.


Costs will also be assessed for each inch of funnel movement and/or disengaging

rows of pins. Perhaps one price for one row with 3x to 10x to 100x more for each

additional row of pins to disengage. The ultimate requirement should require that

the funnel be centered in the engineering specification with two rows of pins

disengaged in order to reach +/- 4 σ requirements. (Note that with SS we would

normally be driving towards +/- 6 σ. However this would push the limits of the

quincunx board to demonstrate this level of quality, e.g. we would need more than

25 columns to catch the beads). Given this is a capability problem we use the 4

sigma short term requirement versus 3 sigma long term to address the notions of

long and short term capability.

The Improve phase should get the team to the point where they can determine the

amount and cost of funnel movement and pin block rows to disengage in order to

get to a 4 sigma level. They will ultimately have to prove their solution with a final

sample of data and calculation. (Note: The instructor will have to determine the

required specification limits by setting up the quincunx with a centered funnel and

two rows of pins disengaged. Run the data sample, calculate the standard deviation

and then determine the 4 sigma level specifications for the problem. This

requirement will be part of the Define phase supplied information. )

The Control phase will be similar to the previous exercise as a team determines the

appropriate control activities.

Cycle Time Reduction

The cycle time reduction exercise requires the use of the CTS-100 Cycle Time

Simulator demonstration. This kit is based on participants signing 3x5” cards,

placing it into a wooden card holder or pallet, and passing it the next station for

another signature and so on down the line. At the end there is a number of cards

with the signatures of each person in the process, which represents the unique steps

of the process. Stacking the cards in a wooden pallet for transporting from station to

station represents non-value added activity. The demonstration includes calculating

the cycle time or the amount of time it takes for a card to pass through the entire

process along with the productivity (number of cards/minute). When you reduce

the non-value added time by reducing the number of cards in the wooden pallets

prior to passing, the cycle time goes down and the productivity goes up. The

demonstration evolves from passing 5 cards in a pallet at a time to 3 cards to 1 and

eventually to a pull system. In the end there is a discussion of value add versus nonvalue

added activity. One item of particular importance is the amount of wait time in

most processes. It is easy to bridge from here to discussions about business

problems to determine how long it takes to process paper work, fill orders, and the



This demonstration can be used with the SS DMAIC steps to show how it applies to

business transactional processes. After the team does the initial demonstration

together, they are ready to complete the Design and Measure phase for reducing

the process cycle time. The Measure phase should also include a process map to

show all of the steps in the process and associated cycle time information. The

instructor leads the team in identifying on the process map each NVA activity. At

the end of the discussion the team should agree that the only value added activity is

when the pencil is in contact with the card, everything else is NVA. Now if this is

true and we want to double the improvement again, how could this be

accomplished? This now becomes the Improve phase challenge for this problem.

The comments on page 10 of the CTS-100 instruction manual discusses how many

teams approach the notion of process time versus cycle time. Some focus on how to

speed up the process time by signing the card at the same time or utilizing marks or

symbols in lieu of signatures. Others will focus on the non-value added portions of

the overall cycle time and hopefully make a ratio comparison of process time versus

overall cycle time. If there is a big disparity between the two it means there is still a

lot of NVA in the process to be identified and removed. While the knee jerk instinct

of most is to try and speed up the process time, the biggest opportunity for

improvement in most situations is to eliminate waiting or delays.

If a specific process being studies has inherent disparities in the individual process

times, or the line is out of balance from an industrial engineering perspective, then

the section on managing constraints may be helpful.

The Control phase will be dictated by the improvement actions in the previous




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