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Catapult DOE Case Study

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Page 1: Catapult DOE Case Study

Catapult Case Study

6Green Belt Training

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Page 2: Catapult DOE Case Study

Catapult Exercise

• You have been pre-selected (based on your skills and past performance records) for the openings posted for Her Majesty’s Catapult Squad.

• Problem Statement: Catapult launching is not capable of meeting Her Majesty’s requirements over the target range of 5-12 feet +/- 6 inches.

• Goal: Your mission is to optimize the inputs to be able to hit a target repeatedly within this range so that Her Majesty can conquer the evil Empire.

• A successful catapult squad can place a payload to the target every time. (Only 3.4 misses per million!)

• The distance from the target varies due to several factors; consequently, you don’t know the distance until you’re in position.

• May the FORCE be with You!! Heads rolled on the last crew which is why we have postings for the current positions!

Page 3: Catapult DOE Case Study

Project DefinitionProject DefinitionProblem Statement: Catapult launching is not capable of meeting Her Majesty’s requirements over the target range of 5-12 feet +/- 6 inches.

CTS’s:Target distance (5 to 12 feet)Consistency (+/- 6 inches)Speed (rapid set up and launch capability)

Defect Definition:Payloads outside of the target specification

Metrics: Distance (inches)Standard deviation (inches)

Project Objective:To develop a standard process and y = f(x) equation so that the catapult can be shot to meet the customer requirements (distance) and minimize variation (< 6 inch radius).

Current/Goal/Stretch GoalCurrent DPMO/Zst - TBDGoal DPMO/Zst - TBD

Benefits:• improved accuracy• reduced variation• customer satisfaction• we live!

Progress to Date:• Team members selected

Page 4: Catapult DOE Case Study

Catapult Nomenclature

Rubber band attachment point Arm stop position

Front arm tension point

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12

3

4

5

123

4

Draw-back angle

Ball type

Cup location

Number of rubber bands

Page 5: Catapult DOE Case Study

Update Recommended Update Recommended Actions To DateActions To Date

Description of potential Root cause or potential vital X

What leads me to believe this is a potential X (Data, local knowledge, Oberservation, Tool?)

What change is being proposed to the X to possibly generate a process improvement

To be tested (team agreement)

Rubber band C&E Matrix, FMEA Constant time between shots

No

Operator C&E Matrix, FMEA ANOVAEqual Variances

Evaluate using previous data

Standard Operating Procedures

There currently is none An SOP was implemented to

stabilize the launches

Create prior to Hypothesis Testing

and/or DOE

Ball type C&E Matrix, FMEA Test the ball type in a 2 sample t-test

Equal Variance Test

Yes

Page 6: Catapult DOE Case Study

Step 7: Screen Potential Step 7: Screen Potential CausesCauses

Narrow it Down Screening is done using Graphical Tools,

Experiments, and Hypothesis Tests to identify and prove which are the vital X’s

This is the middle of the funnel for most projects (multiple X’s or with variable relationships between X’s)– for some simpler projects with a single X, this is the

bottom of the funnel, the final vital X

Important X’s for Y = f(X1, X2, …, Xn) – we still need to determine “f”

Page 7: Catapult DOE Case Study

Hypothesis Testing For Hypothesis Testing For Sources of VariationSources of Variation

What potential sources of variation can be explored using Hypothesis Testing ? What are sources of data that can be analyzed

– Passive: existing data– Active: sampling the process

Ball Type– Whiffle versus Ping Pong?

Mean or variation?

Catapult Setup – Floor type– Table top or floor? Tile or carpet?

Mean or variation?

Operator– Is there a difference between operators?

Mean or variation?

Page 8: Catapult DOE Case Study

Update Recommended Update Recommended Actions To DateActions To Date

Description of potential Root cause or potential vital X

What leads me to believe this is a potential X (Data, local knowledge, Oberservation, Tool?)

What change is being proposed to the X to possibly generate a process improvement

To be tested (team agreement)

Ball Type 2 sample t-testEqual Variance

DOE – test 2 different types

Completed

Draw Back Angle C&E Matrix, and FMEA

DOE – test 2 different settings

Yes

Front Tension Pin C&E Matrix, and FMEA

DOE – test 2 different settings

Yes

Rubber band C&E Matrix FMEA Time between shots NoOperator 2 sample t-test 1 operator for DOE No

Standard Operating Procedures

There currently is none An SOP was implemented to

stabilize the launches

Not at this time; SOP’s to be applied in DOE

Pin Height C&E Matrix, FMEA DOE – test 2 different settings

Yes

Page 9: Catapult DOE Case Study

22KK Full Factorial Design of Full Factorial Design of ExperimentsExperiments

Catapult ExerciseCatapult Exercise

Page 10: Catapult DOE Case Study

The Breakthrough StrategyImproveThe Breakthrough StrategyImprove1. Select Output Characteristics2. Define Performance Standards3. Validate Measurement System4. Establish Process Capability5. Define Performance Objectives6. Identify Variation Sources7. Screen Potential Causes8. Discover Variable Relationships9. Establish Operating Tolerances10.Validate Measurement System11.Determine Process Capability12.Implement Process Controls

Page 11: Catapult DOE Case Study

Step 8: Discover Variable Step 8: Discover Variable RelationshipsRelationships

How the X’s affect Y Evaluate how my Vital X’s affect Y, either independently

or in combination with other Vital X’s. This is primarily done through the use of DOE or Regression.

This is the bottom of the funnel, I know which X’s affect my Y and I know how they affect Y

The function Y = f(X1, X2,…, Xn) is called a “transfer function” – it describes how a change in one or more of the X’s transfers to a change in Y

We now know what Y = f(X1, X2, …, Xn) is

The variable relationships within many Green Belt projects are frequently established simply through the use of standard hypothesis tests.

Page 12: Catapult DOE Case Study

Step 9: Establish Operating Step 9: Establish Operating TolerancesTolerances

How To Set My Xs I know which X’s are important. What settings do I use to

improve my project? In the case of a variable X (e.g. PSI on an air feed), I have

to provide a setting tolerance (e.g. a target amount ± an allowed amount of variation about the target)

In the case of a non-variable X (e.g. Supplier), I know which value of the variable provides the best value of Y, therefore I have specified the absolute operating tolerance

Make use of what we know about Y = f(X1, X2, …, Xn)

In our case study we will “set the X’s” at the settings of our improved process.

Page 13: Catapult DOE Case Study

Improve PhaseImprove Phase

We will conduct a 2k factorial experiment in order to identify the proper factors and levels to achieve the highest capability (Zst). – You only have enough resources to investigate three

X’s at 2 levels – Determine your factors and their respective levels. – Use the knowledge you learned in DMA and as a team

determine what factors and the respective levels you want to use to conduct the DOE

Page 14: Catapult DOE Case Study

Philosophy of ExperimentationPhilosophy of Experimentation

Catapult

Process

Responses

Distance

Variation

Controllable X’s

Draw Back Angle

Fr Arm Tension

Stop Pin

Uncontrollable X’s

“Noise”

Adjustment X’s

“SOP’s”

Temp Air flowDistractions

Setup Ball Type

ReleaseOperator

Page 15: Catapult DOE Case Study

Step 2: Factors, Level Settings Step 2: Factors, Level Settings and Sample Sizeand Sample Size

Use the Strategy for Experimentation to complete the following:

Conduct a 3 factor, 2 level full factorial design with 6 repeats to optimize the catapult settings to hit a target within +/- 6”

Factors: A: Stop Pin: 2 and 4 B: Draw back angle: 140 and 180

C: Front Tension Pin: 2 and 4

Page 16: Catapult DOE Case Study

Step 4: Create The Design In Step 4: Create The Design In MinitabMinitab

Stat>DOE>Factorial>Create Factorial Design

• Select the number of factors (3)

• Open the ‘Designs…’ window

• Highlight the ‘Full Factorial’

• Maintain all other defaults

• OK

Page 17: Catapult DOE Case Study

Creating The Design, Cont’dCreating The Design, Cont’d

• Un-check the ‘Randomize runs’ box

• OK

• Enter Factor Names

• Enter Factor Low & High Settings

• OK

Page 18: Catapult DOE Case Study

Resultant Design In The WorksheetResultant Design In The WorksheetSession Window Output:

Factorial DesignFull Factorial Design

Factors: 3 Base Design: 3, 8 Runs: 8 Replicates: 1 Blocks: none Center pts (total): 0

All terms are free from aliasing

Worksheet Output:

Page 19: Catapult DOE Case Study

Step 5: Conduct The ExperimentStep 5: Conduct The Experiment

Populate the worksheet with the results of your experiment and calculate the Row Averages and Row Standard Deviations:

AvrgD Calculation: Calc>Row Statistics, Check ‘Mean’, Input Variables: ‘Y1 through Y6’,

Store Result in: ‘AvrgD’

SD Calculation: Calc>Row Statistics, Check ‘Standard deviation’, Input Variables: ‘Y1

through Y6’, Store Result in: ‘SD’

CATAPULT Round 5 DOE Example.mtw

Page 20: Catapult DOE Case Study

Graphical Analysis: Factorial Graphical Analysis: Factorial PlotsPlots

Stat>DOE>Factorial> Factorial Plots…

• Complete setups for • Main Effects Plot

Page 21: Catapult DOE Case Study

Graphical Analysis: Factorial Graphical Analysis: Factorial Plots Cont’dPlots Cont’d

Complete setups for – Cube plot– Interaction plot

Page 22: Catapult DOE Case Study

AvrgD: Main Effects PlotAvrgD: Main Effects Plot

Which factor has the greatest effect on the Average Distance?

StopPin DrawAngle TensionPin

40

50

60

70

80

Avrg

D

Main Effects Plot (data means) for AvrgD

Page 23: Catapult DOE Case Study

AvrgD: Interaction PlotAvrgD: Interaction Plot There appears to be one potential interaction:

– StopPin*DrawAngle

– The effect that Stop Pin has on Distance also depends on the Draw Back Angle

20

60

100 20

60

100StopPin

DrawAngle

TensionPin

2

4

140

180

Interaction Plot (data means) for AvrgD

Page 24: Catapult DOE Case Study

AvrgD: Cube PlotAvrgD: Cube PlotIs a distance of 70” achievable with the

Tension Pin at setting 2?Is a distance of 50” achievable with the

Draw Back Angle at 140?

36.00

59.83

60.54

93.25

15.50

33.13

63.50

109.63

2 4

StopPin

DrawAngle

TensionPin

140

180

2

4

Cube Plot (data means) for AvrgD

Page 25: Catapult DOE Case Study

Step 6: Perform The Step 6: Perform The DOE Analysis For The DOE Analysis For The

Full ModelFull ModelStat>DOE>Factorial>Analyze Factorial

Design:

Page 26: Catapult DOE Case Study

Step 6: Full Model Analysis Step 6: Full Model Analysis Cont’dCont’d

Page 27: Catapult DOE Case Study

Running the Full ModelRunning the Full Model

0 10 20 30 40

AC

ABC

A

BC

AB

C

B

Pareto Chart of the Effects(response is AvrgD, Alpha = .10)

A: StopPinB: DrawAnglC: TensionP

• With all terms in the model, only one appears above the significance level (red line)

Page 28: Catapult DOE Case Study

Step 8: Reducing The ModelStep 8: Reducing The Model

0 5 10

A

BC

AB

C

B

Pareto Chart of the Standardized Effects(response is AvrgD, Alpha = .10)

A: StopPinB: DrawAnglC: TensionP

0 1 2 3 4 5 6 7

A

AB

C

B

Pareto Chart of the Standardized Effects(response is AvrgD, Alpha = .10)

A: StopPinB: DrawAnglC: TensionP

Page 29: Catapult DOE Case Study

AvrgD: Final Reduced ModelAvrgD: Final Reduced ModelEstimated Effects and Coefficients for AvrgD (coded units)Term Effect Coef SE Coef T PConstant 58.922 3.091 19.06 0.000StopPin 6.969 3.484 3.091 1.13 0.342DrawAngl 45.615 22.807 3.091 7.38 0.005TensionP 30.073 15.036 3.091 4.87 0.017StopPin*DrawAngl -16.635 -8.318 3.091 -2.69 0.074

Analysis of Variance for AvrgD (coded units)Source DF Seq SS Adj SS Adj MS F

PMain Effects 3 6067.3 6067.3 2022.42 26.47

0.0122-Way Interactions 1 553.5 553.5 553.47 7.24

0.074Residual Error 3 229.2 229.2 76.42Total 7 6850.0

Estimated Coefficients for AvrgD using data in uncoded unitsTerm CoefConstant -378.724 StopPin 70.0260DrawAngl 2.38802TensionP 15.0365StopPin*DrawAngl -0.415885

Use the uncoded coefficients to create

the equation

Page 30: Catapult DOE Case Study

Creating the y = f(x) for AvrgDCreating the y = f(x) for AvrgDCreate the equation from the un-coded

coefficients:

AvrgDuncoded = -378.72 + 70.03 * StopPin + 2.39 * DrawAngle + 15.04 * TensionPin - 0.42 * StopPin*DrawAngle

Estimated Coefficients for AvrgD using data in uncoded unitsTerm CoefConstant -378.724 StopPin 70.0260DrawAngl 2.38802TensionP 15.0365StopPin*DrawAngl -0.415885

Page 31: Catapult DOE Case Study

Setting Pin Positions To Minimize VariationSetting Pin Positions To Minimize VariationGiven a target of 60”, where would you set the pin positions to minimize variation?

3.118

2.463

6.026

14.716

0.548

2.011

1.844

3.694

2 4

StopPin

DrawAngle

TensionPin

140

180

2

4

Cube Plot (data means) for SD

36.00

59.83

60.54

93.25

15.50

33.13

63.50

109.63

2 4

StopPin

DrawAngle

TensionPin

140

180

2

4

Cube Plot (data means) for AvrgD

Settings at approx. 60”

There are 4 possible combinations to hit the target. Which one minimizes variation?

Page 32: Catapult DOE Case Study

Recommended Pin Factor Level SettingsRecommended Pin Factor Level Settings Stop Pin: 2 Front Tension Pin: 2 Recall the equation for AvrgD:

– AvrgD = -378.7 + 70.03 * StopPin + 2.39 * DrawAngle + 15.04 * TensionPin - 0.42 * StopPin*DrawAngle

Enter the fixed settings into the equation for AvrgD:– AvrgD = -378.7 + (70.03 * 2) + 2.39 * DrawAngle + (15.04 *

2) - 0.42 * (2*DrawAngle) Reduce the equation:

– AvrgD = -378.7 + 140.06 + 2.39 * DrawAngle + 30.08 - 0.84 * DrawAngle

– AvrgD = -208.6 + 1.55*DrawAngle Substitute the target (60”) for AvrgD and solve for Draw Angle

– DrawAngle = 173.3 degrees

Page 33: Catapult DOE Case Study

Okay… Your Turn!Okay… Your Turn!Round #5: DOERound #5: DOE

Open the DOE design in Minitab: – CATAPULT Round 5 DOE Worksheet.mtw

Conduct the experiment and record the data Analyze the experiment

– Graphically– Analytically

Obtain a prediction equation for Distance Present your cube plots to the instructor to receive your targetObtain a target value from the instructorEstablish Pin factor levels based on goal to minimize variationConduct a validation run

– Launch 10 shots using the predicted settingsCalculate the mean and standard deviation Flipchart your results

Page 34: Catapult DOE Case Study

Catapult Nomenclature

Rubber band attachment point Arm stop position

Front arm tension point

12345

12

3

4

5

123

4

Draw-back angle

Ball type

Cup location

Number of rubber bands

Page 35: Catapult DOE Case Study

Step 10: Validate Measuring Step 10: Validate Measuring SystemSystem

Can I Measure My Xs & Y? In the case of a variable X (e.g. PSI on an air feed), I need

to validate that it can be measured (a vital X MSA) In the case of a non-variable X, I need to validate that I can

tell whether the X is the right value (e.g. is this from Supplier A?)

Also, I might have improved my Y so much that I can no longer “read” my process, and may have to improve my measurement system to truly measure the improvement

Can’t control Y = f(X1, X2, …, Xn) if you can’t measure it

Page 36: Catapult DOE Case Study

Case Study 2: The CatapultCase Study 2: The Catapult

Control

Page 37: Catapult DOE Case Study

The Breakthrough StrategyThe Breakthrough StrategyControlControl

1. Select Output Characteristics2. Define Performance Standards3. Validate Measurement System4. Establish Process Capability5. Define Performance Objectives6. Identify Variation Sources7. Screen Potential Causes8. Discover Variable Relationships9. Establish Operating Tolerances10. Validate Measurement System11. Determine Process Capability12. Implement Process Controls

Page 38: Catapult DOE Case Study

Case Study 2: The CatapultCase Study 2: The Catapult

Final Capability

Page 39: Catapult DOE Case Study

Step 11: Determine Process CapabilityStep 11: Determine Process CapabilityWhere Am I? This measures the capability of controlling my Xs at

their optimal settings This is also the time when we determine formal

results by comparing a new capability analysis with the baseline capability analysis (step 4) and our goals (step 5)

Common tools:– Six Sigma Capability Analysis (Normal) for continuous

data– Six Sigma “Product Report” for discrete data

Can you consistently make X1, X2, …, Xn to produce “good” Y’s?

For our case study, we will rerun the Capability Analysis in MINITAB using our new process to see before and after.

Page 40: Catapult DOE Case Study

Improved CapabilityImproved CapabilityMethod 1 – Capability Analysis (NormalMethod 1 – Capability Analysis (Normal))Based on the Project work conducted by the

team, shown below is the improved capability.

30 35 40 45 50

LSL USL

Process Capability Analysis for Improved Dis

USLTargetLSLMeanSample NStDev (Within)StDev (Overall)

Z.BenchZ.USLZ.LSLCpk

Cpm

Z.BenchZ.USLZ.LSLPpk

PPM < LSLPPM > USLPPM Total

PPM < LSLPPM > USLPPM Total

PPM < LSLPPM > USLPPM Total

41.0000 *

37.000038.9405

1000.3925070.416816

4.915.254.941.65

*

4.614.944.661.55

0.000.000.00

0.380.080.46

1.620.392.00

Process Data

Potential (Within) Capability

Overall Capability Observed Performance Exp. "Within" Performance Exp. "Overall" Performance

Within

Overall

Page 41: Catapult DOE Case Study

Case Study ExerciseCase Study ExerciseRound #6: Process CapabilityRound #6: Process Capability

Objective: To determine Capability for your improved process–Catapult settings based on:

Optimum conditions from the DOEResults from validation runSOP’s

–Each of 5 Operators will launch 5 balls at a time–Alternate Operators until you have launched 50 balls–Enter into: Catapult Round 6 Cap Worksheet.mtw–Generate the Process Capability (Normal) using n=5

Deliverable: Using the table on the following page, record on a flip chart the following for your team– Final Average, inches– Final Standard deviation, inches– Final Short term capability (Zst)– Final DPMO

Time: 30 minutes

Page 42: Catapult DOE Case Study

Catapult Project MetricsCatapult Project MetricsParameter Team 1 Team 2 Team 3 Team 4 Team 5BASELINEAverage, in.St. Dev., in.Zst

DPMO

Objective DPMOFINALAverage, in.St. Dev., in.Zst

DPMO

% Reduction in DPMO

Page 43: Catapult DOE Case Study

Step 12: Implement Process Step 12: Implement Process ControlsControls

Let’s Not Do This Again The X’s you have determined as vital, their settings, and

other actions you have taken to make the improvement must be:– nailed down– set in concrete– fully implemented (NOT just agreed to)– put into a rigorous audit schedule– Documented in a Control Plan

BEFORE you can say a project is closed!

How do you control X1, X2, …, Xn to always produce “good” Y’s?

Page 44: Catapult DOE Case Study

Controls – Two RequirementsControls – Two Requirements1) The actual controls Controls must be placed on completed projects to make sure that they do

not decay – Energy must be expended on processes to keep them in their optimum condition.– The degree of control is proportional to the risk of the process

decaying from its final project derived settings.2) The Control Plan The controls must be documented carefully, answering:

– What is being done?– Who is to do it (position not name of person)?– When is to be done?– What will be action if process does decay?– What will make it difficult to change the project settings OR controls?

“If it isn’t written down, It doesn’t exist”

Page 45: Catapult DOE Case Study

Case Study 2: The CatapultCase Study 2: The Catapult

SPC, Variable Data

Page 46: Catapult DOE Case Study

Why Use SPC for Variables?Why Use SPC for Variables?

SPC for variable data is used to:Keep process centeredMinimize variationReduce excursionsValidate improvementsFocus Six Sigma® process activity

Page 47: Catapult DOE Case Study

What is SPC for Variables?What is SPC for Variables?SPC for variable data is Industry standard control language Reliable, easy method of determining

– Common cause variation– Special cause variation

Graphical communication Set of statistical tools for analyzing variables

performance data

Statistical Process Control Is application of statistical tools and methods to

provide feedback Sets limits of variation Provides trigger for action

Page 48: Catapult DOE Case Study

SPC FunctionSPC Function

SPC Charts Used to monitor and control process under

local responsibilityRequire process owners to

– take measurements– Plot and interpret data– Take action

Provide a history of the process

Page 49: Catapult DOE Case Study

Components of a Control Components of a Control ChartChart

109876543210

0 5 10 15 20

Upper Control Limit

Lower Control Limit

Mean

Nonrandom Variation Region

‘Special Cause Variation’

Observation number

Obs

erva

tion

valu

e

Random Variation Region

‘Common Cause Variation’Observation 10

Page 50: Catapult DOE Case Study

Statistics of a Control ChartStatistics of a Control Chart

109876543210

0 5 10 15 20

Nonrandom Variation Region

Observation number

Obs

erva

tion

valu

e

Random Variation Region

LCL

- 3

UCL

+ 3

Mean

99.73% area

Page 51: Catapult DOE Case Study

Establishing Process Control Establishing Process Control LimitsLimits

Control limits are Are statistical limits set +/- 3 standard deviations

from the mean Set when process is in control

– Fixed at baseline value– Adjusted for improvements– Never widened

Control limits are not related to specification limits

Control Limits are not specification limits

Page 52: Catapult DOE Case Study

Definition of Control Definition of Control

In control is A statistical term for process variation

– Within three standard deviations of the mean– That is random without cause– That does not show run patterns– That does not show trend patterns

No assignable cause variation

Page 53: Catapult DOE Case Study

Control Chart RoadmapControl Chart RoadmapVariable

Data

Xbar-R Chart

I-MR Chart

Xbar-s chartN<10

No

Yes

N=1NoYes

Page 54: Catapult DOE Case Study

Xbar-R Chart PrinciplesXbar-R Chart Principles

Xbar-R Charts (and Xbar-s) are two separate charts of the same subgroup data

Xbar chart is a plot of the subgroup means R chart is a plot of the subgroup ranges (or if s, plot

of subgroup standard deviation) Most sensitive charts for tracking and identifying

assignable cause of variation Based on control chart factors that assume a normal

distribution within subgroups Establish three sigma process limits

Page 55: Catapult DOE Case Study

Xbar-R Chart ExerciseXbar-R Chart Exercise

Open the Minitab file: Catapult Variable SPC Example.mtw

This was a teams’ initial (Round 3) capability study

5 operators launched 5 shots each– Sequence was repeated 4 times– Total observations: 100

Page 56: Catapult DOE Case Study

Xbar-R Minitab InstructionsXbar-R Minitab Instructions

Stat>Control Charts>Xbar-R…

Page 57: Catapult DOE Case Study

Example Xbar-R ChartsExample Xbar-R Charts

0Subgroup 10 20343536373839404142

Sam

ple

Mea

n

1 11

1 1 1

Mean=38.65

UCL=41.15

LCL=36.15

0

5

10

15

Sam

ple

Rang

e

1

R=4.337

UCL=9.172

LCL=0

Xbar/R Chart for Dist.

Page 58: Catapult DOE Case Study

Exercise: Catapult Xbar-R ChartsExercise: Catapult Xbar-R Charts Individually with your team, plot your Catapult

capability data from Round #6 Create the standard Xbar-R chart

– Is your process in control? Sort the data by Operator Create a Xbar-R chart with control limits by ‘Operator’

– Is there a visual difference between operators with respect to Central tendency? Variation?

– Are they individually in control?

What happens to the control chart if the subgroup size is the total number of shots per operator?

Page 59: Catapult DOE Case Study

I-MR Chart PrinciplesI-MR Chart Principles

Individual and Moving Range Charts are two separate charts of the same data

I chart is a plot of the individual data MR chart is a plot of the moving range of the previous

individuals I-MR charts are sensitive to trends, cycles and patterns Used when subgroup variation is zero or no subgroups

exist– Destructive testing– Batch processing

Page 60: Catapult DOE Case Study

Example: How to Create an I-MR ChartExample: How to Create an I-MR Chart

Stat>Control Charts>I-MR…

Page 61: Catapult DOE Case Study

Example I-MR ChartExample I-MR ChartCompare this chart to the Xbar-R chart

0Subgroup 50 10030

40

50

Indi

vidu

al V

alue

11

1

11

Mean=38.65

UCL=43.97

LCL=33.33

0

5

10

Mov

ing

Ran

ge

11 1

11

R=2

UCL=6.535

LCL=0

I and MR Chart for Dist.

Page 62: Catapult DOE Case Study

SPC ExerciseSPC ExerciseCatapult Variable SPC Example II.mtwCatapult Variable SPC Example II.mtw

A catapult team decided that they needed to be able to control the Draw Back Angle.

An observer requested an operator to launch consecutive balls at an angle of 180 degrees.

The observer, through special visual imaging equipment, recorded the angle and the distance of each launch.

Is the operator able to control the angle? Generate a control chart and flip chart your

response.

Page 63: Catapult DOE Case Study

Case Study 2: The CatapultCase Study 2: The Catapult

Audit

Page 64: Catapult DOE Case Study

Catapult Control Plan ExerciseCatapult Control Plan ExercisePurpose: To develop a Control Plan that sustains the gains of the work our Six Sigma Team performed that optimizes the capability of the catapult to deliver conforming product.

You and your Six Sigma team have have successfully completed a project by identifying the critical X’s and their respective levels in order to achieve your project objective. It is now time to hand the project over to the Process Owner, therefore a Control Plan needs to be developed. This Control Plan needs to contain the proper information that will allow the Process Owner to sustain the gains your team has achieved.

Any six sigma project must have a control plan

Page 65: Catapult DOE Case Study

Catapult Control Plan FormCatapult Control Plan FormCatapult Control Plan.pptCatapult Control Plan.ppt

KPOV KPIV

Measurement Method

Who MeasuresProcess Step Control Tool KPIV/KPOV

Requirement

Specification/ Requirement

USL LSL

CTQ Sample Size Frequency Where

Recorded SOP Reference Decision Rule/ Corrective Action

Page 66: Catapult DOE Case Study

Optional Round #7: AuditOptional Round #7: AuditTrain a Replacement/Audit Prove that your experimental results can sustain the test of time over a

broad inference space.– Poke-Yoke your process so that it is robust to the many operators

that are likely to run the device.– Your Crack Marketing Team received a letter from Her Majesty in

which she described the test as follows: “The winning design will be the one that is able to launch ammunition into

a fine goblet from various distances.” Further, the marketing team overheard that Her Majesty herself would fire

the catapult after a short tutorial from the gunsmith.

After you have completed the control plan and documented your SOP’s, I will give you a new target to hit. You will have 5 minutes and 3 launches (within those 5 minutes) to identify a new set of operating conditions. You will set up the catapult at these new conditions. I will read your Standard Operating Procedures and then launch 10 balls. The capability of these launches will be included in the final competition calculations.

Page 67: Catapult DOE Case Study

Case Study 2: The CatapultCase Study 2: The Catapult

Summary

Page 68: Catapult DOE Case Study

Project Debriefs / SummaryProject Debriefs / Summary

Parameter Team 1 Team 2 Team 3 Team 4 Team 5Baseline Zst

Final Zst

Baseline DPMO

Final DPMOBaseline Average, in.Final Average, in.Baseline St. Dev., in.Final St. Dev., in.

Page 69: Catapult DOE Case Study

ReviewReview

In preparation for closing out your project, include:– Strategy, action plan and goals for the

project– Tools and techniques used during the project– Brief technical discussion of what was

learned by completing the project– Brief discussion of team dynamics


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