A Six Sigma Black Belt Case Study- G.E.P. Boxs Paper Helicopter Experiment Part B

A ‘‘Six Sigma’’# Case Study: G.E.P. Box’s Paper HelicopterExperiment—Part B

J. A. Johnson, S. Widener, and H. GitlowSchool of Business Administration, University of Miami, Coral Gables, FL

E. PopovichSterling Enterprises, Inc., Boca Raton, FL

This article presents an application of the ‘‘Six Sigma’’DMAIC model to G.E.P. Box’s famous ‘‘paper helicopter’’experiment. The Improve and Control Phases are presentedhere. The Define, Measure, and Analyze Phases were pre-sented in an earlier paper. The intent of this article is topresent the reader with a case study for structuring a ‘‘SixSigma’’ project.

Keywords Case study; Control; DMAIC model; Improve;Paper helicopter experiment; Six Sigma mana-gement.

INTRODUCTION

This article presents the Improve and Control Phasesof an application of the ‘‘Six Sigma’’ DMAIC model toG.E.P. Box’s famous ‘‘paper helicopter’’ experiment(Box, 1992; Johnson et al., in review). The intent of thisarticle is to present the reader with a case study for struc-turing a ‘‘Six Sigma’’ project. Similar work has been donewith this type of case (Rasis et al., 2002).

In the previous article (Johnson et al., 2006), whichcontained the first three phases of the DMAIC model(Define, Measure, and Analyze Phases), the LilliputianNational Army (LNA) was moving toward a siege-breaking technique based upon aerial assault, insteadof traditional land-based attack methods. By followingthe first three phases of the model, the process to beimproved was determined to be the Helicopter

Construction Process, and the CTQ in question wasidentified to be the flight time in seconds.

The Lilliputian scientists and engineers studied theeffects of the seven variables, or Xs, on the flight time, orCTQ, in the Improve Phase. The Xs are paper type (X1),body length (X2), body width (X3), wing length (X4),paper clip (X5), body tape (X6), and wing joint tape (X7).

IMPROVE PHASE

The Improve Phase optimizes the CTQ(s) bymanipulated the Xs and their interactions. It has threesteps: (1) design and run experiments to isolate the sig-nificant Xs and their interactions, (2) interpret theresults of these experiments to determine the settingsof the Xs which optimize the spread, shape, and centerof the CTQ(s), and (3) conduct a pilot study to test thesettings of the Xs.

The deliverables of the improve phase are:

(1) the levels of the Xs that optimize the CTQ(s)(2) the optimized process map with the optimized set-

tings of the Xs(3) the results of a pilot study of the revised process(4) the estimated capability (sigma level and=or

DPMO) of the revised process(5) the statistical gap between the original and the

revised system capabilities

Design of Experiments

Designing the Experiment

The designed experiment contained seven Xs, whichwere identified in the Analyze Phase of the project. Theexperiment was initially viewed as a full factorial design

#‘‘Six Sigma’’ is a registered trademark of the MotorolaCorporation.

Address correspondence to H. Gitlow, Professor ofManagement Science, School of Business Administration,University of Miami, Coral Gables, FL 33124, USA. E-mail:[email protected]

Quality Engineering, 18:431–442, 2006Copyright # Taylor & Francis Group, LLCISSN: 0898-2112 print=1532-4222 onlineDOI: 10.1080/08982110600719415

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with two replications per trial, resulting in 27 trials runtwice, whichwould have required 256 independent trials.

Manufacturing each prototype requires approxi-mately 60 man-days just to build the machine if all ofthe components are available and ready to go. Flight test-ing setup requires an additional day to prepare all of thescientific equipment. Although the actual test is brief, thework put into making each test a success is quite exten-sive. This comes to a head in considering the amountof time available to actually run the experiment. Asstated in the Define Phase, war with the Lilliputian Free-dom Fighters (LFF) is imminent, and spending over sixmonths in testing is not an option. Therefore, the timemust be cut. However, this is not the only constraint,as the budget is also limited.

Realizing that the total material budget for theexperiment is 15,000,000 gold florins, and that the costsof production are essentially fixed for retoolingmachinesand changing the setups, the LNA’s financial analystshave concluded that each prototype, including overheadexpenses, cost about 100,000 gold florins and the testing,including overhead expenses, was an additional 10,000gold florins. Considering that these figures included theoverhead, which covered salaries of the workers andstaff, essentially the entire budget could be dumped intothis experiment. This was the AAC’s (Army Air Corp)motivation for allocating funds away from helicopterpurchases and into development. As a result of this,quick arithmetic showed that 128 total runs were possi-ble, with a small pool of leftover money in the budgetto help offset any potential bumps along the way. It isworth noting that these figures do not include the3,300,000 gold florins that were allocated to the pilot test.

128 total runs for the experiment was compatiblewith the time constraint, and as a result, it was thenumber of trials chosen for the experiment. The pro-blem became that of experimental clarity. Running128 individual trials in the full factorial design, whichwould then be replicated, requires a total of 256individual trials. This will fully show all interactionsand relationships between the variables, but it requirestoo much time. Therefore, reducing the design to a halffractional factorial, requiring 64 randomized indivi-dual trials, plus a randomized replication, for 128 totalindividual trials is a better solution. However, the costof saving the time and money of the trials is the inabil-ity to distinguish between the effects of certain interac-tions. This is known as confounding.

Potential Confounding Problems

The half-fractional design reduces the number ofruns, but at a loss of information due to confounding.

This 27-1 design has a resolution of VII. In this case,this means that the main effects and two-way interac-tions will not be confounded with each other. Themain effects are confounded with the six-way interac-tions and the two-way interactions are confoundedwith the five-way interactions. This confounding isacceptable because field expertise dictates that high-order interactions are safely ignored. The resolutionVII confounding description continues throughoutthe design, so that the three-way interactions are con-founded with four-way interactions.

Given that five-way and six-way factor interactionsare extremely rare, the chances of significantly con-founding the main effects or the two-factor interactionsare very small. The problem lies in the three-factorinteractions being confounded by the four-factor inter-actions. Since three-factor interactions do happen,although not very often, and four-factor interactionsare more uncommon than three-factor interactions,the chances of these effectively clouding each other issmall, especially when weighted against the costs ofrunning a full factorial to ensure that all of the effectsare isolated. Therefore, the Lilliputians have not backedthemselves into a corner through confounding as itmight seem, but instead have taken a calculated riskto minimize the cost and duration of the experiment.

Gearing Up for Running the Experiment

Two aircraft of each of the 64 prototypes weremanufactured. This ensured that two separate aircraftwere available for testing, which served two purposes.First, this helped to determine within-prototype varia-tion. Second, in the event of a catastrophe, a secondunit was available for the experiment.

The aircraft were manufactured using the sameprocesses as they would see in real-time production.The Flight Testing was done in the laboratory insteadof the usual facilities. However, the inspection was stillperformed to ensure that the aircraft, were it standard,would be fully functional, operable, and ready for usein the field.

Running the Experiment

Each aircraft was marked with a number corre-sponding to its position on the design layout. It isworth noting that the design layout was randomized,to curb the effects of lurking variables. Each aircraftwas individually dropped and the times were recordedper the directions laid out in the Measure Phase. Next,team members obtained the results of the experiment.

432 J. A. Johnson et al.


Interpretation of the Experiments

Preliminary Interpretation

Figure 1 shows a Pareto chart of the Xs, and theirinteractions, that significantly impact flight time.

The bars in Figure 1 that extend past the dottedline (5% level of significance) represent the Xs or inter-actions of potential interest. It can be seen that themain effects, with the exception of D, are the mostimportant in the explanation of the Xs impact on theflight time. Furthermore, Figure 1 shows that thereare potentially four two-way interactions, FG, AE,BF, and AB, that could be working in this design.

In-Depth Analysis

Team members studied the Analysis of Variance(ANOVA) output for the experiment to identify whichfactors and interactions significantly effect flight time(see Table 1). The second part of Table 1, ‘‘Analysisof Variance for Flight’’ numerically reiterates theimpact of the two way interactions and the main effectsthat was illustrated in the Figure 1. This gives somefurther insight as to what will actually be found inthe first part of Table 1, ‘‘Estimated Effects and Coef-ficients for Flight.’’

The first part of Table 1, ‘‘Estimated effects andcoefficients for flight,’’ shows the p-values for eachmain (factor) effect and interaction effect. All effectsthat are statistically significant are indicated by ap-value less than 0.05. The statistically significant maineffects and interactions have been condensed intoTable 2.

Figure 2 shows that wing length is the most signif-icant X. Paper, clip, width, and length are of secondaryimportance. Body taping and joint taping are the leastsignificant of all the factors.

All interactions supercede all main effects to deter-mine what value of the individual design factor shouldbe set at. With this in mind, it would be wise to start atthe bottom of Table 2, and work up, analyzing eachsignificant interaction. The first interaction isLength!Wing, and going to Figure 3, it can be seenthat the longer wing, 4.75 inches, and the shorterlength, 3.00 inches, optimize the flight time, as that isthe highest point within the box where the Lengthand Wing columns or rows intersect. Both combina-tions in the table will yield the same result, as thetwo plots are inverses of each other. The next inter-action is Clip!Length, and using the same methods tofind the highest point within the relevant boxes onFigure 3 shows that the length should be 3.00 inchesand that no paper clip should be used. Continuingup Table 2, the next interaction is Paper!Width, andusing the relevant boxes in Figure 3, shows that thewidth of the helicopter’s body should be 1.42 inchesand that the helicopter should be made with whitepaper. The final interaction is Paper!Clip, and usingFigure 3, it can be found that white paper should beused with no paper clip. These results are then com-piled and summarized in the Table 3.

Note that in Table 3 there is no indication for thefactors labeled ‘‘Body Tape’’ or ‘‘Joint Tape.’’ This isbecause there were no interactions for these factors,and as a result, no known information can bedisplayed.

With all of the interactions from Table 2 havingbeen analyzed, the remaining effects, known as maineffects, or single factor effects can be analyzed. Theanalysis for these is found in Figure 2, and the firstof these effects from Table 2 is Wing. ConsultingFigure 2, the optimal wing length is 4.75 inches. In thiscase, it can be seen that this is consistent with the winglength that was determined by analyzing the relevantinteraction. If there is a conflict between the analysesof the interactions and the main effects, in general,the interaction affect is given consideration first.

The next two items found in Table 2, Length andWidth, show that the analysis of the main effects forbest results is consistent with the interaction analysis.However, the next item in Table 2, Body tape, mustbe considered.

Body Tape is listed as one of the unknowns inTable 3; therefore the main effect is relevant to deter-mining the level for the factor in the final design ofthe aircraft. Consulting Figure 2, it can be seen thatFigure 1. Pareto chart of the standardized effects.

GEP Box’s Paper Helicopter Experiment—Part B 433


Table 1Original ANOVA output from Minitab

Estimated effects and coefficients for flight (coded units)

Term Effect Coef SE Coef T P

Constant 2.10523 0.01089 193.39 0.000Paper 0.14734 0.07367 0.01089 6.77 0.000Clip "0.12797 "0.06398 0.01089 "5.88 0.000Bodytape "0.05828 "0.02914 0.01089 "2.68 0.009Jointtape "0.00516 "0.00258 0.01089 "0.24 0.814Width "0.17797 "0.08898 0.01089 "8.17 0.000Length "0.16391 "0.08195 0.01089 "7.53 0.000Wing 0.49297 0.24648 0.01089 22.64 0.000Paper!Clip "0.04484 "0.02242 0.01089 "2.06 0.043Paper!Bodytape "0.02641 "0.01320 0.01089 "1.21 0.230Paper!Jointtape "0.01828 "0.00914 0.01089 "0.84 0.404Paper!Width "0.05172 "0.02586 0.01089 "2.38 0.021Paper!Length "0.04078 "0.02039 0.01089 "1.87 0.066Paper!Wing "0.01328 "0.00664 0.01089 "0.61 0.544Clip!Bodytape 0.01953 0.00977 0.01089 0.90 0.373Clip!Jointtape "0.01859 "0.00930 0.01089 "0.85 0.396Clip!Width 0.01984 0.00992 0.01089 0.91 0.365Clip!Length "0.04984 "0.02492 0.01089 "2.29 0.025Clip!Wing 0.03016 0.01508 0.01089 1.39 0.171Bodytape!Jointtape "0.02141 "0.01070 0.01089 "0.98 0.329Bodytape!Width "0.01797 "0.00898 0.01089 "0.83 0.412Bodytape!Length 0.01672 0.00836 0.01089 0.77 0.445Bodytape!Wing 0.03359 0.01680 0.01089 1.54 0.128Jointtape!Width "0.01797 "0.00898 0.01089 "0.83 0.412Jointtape!Length 0.01672 0.00836 0.01089 0.77 0.445Jointtape!Wing "0.00703 "0.00352 0.01089 "0.32 0.748Width!Length "0.03047 "0.01523 0.01089 "1.40 0.166Width!Wing 0.00078 0.00039 0.01089 0.04 0.971Length!Wing "0.05516 "0.02758 0.01089 "2.53 0.014Paper!Clip!Bodytape 0.04141 0.02070 0.01089 1.90 0.062Paper!Clip!Jointtape 0.00078 0.00039 0.01089 0.04 0.971Paper!Clip!Width "0.00391 "0.00195 0.01089 "0.18 0.858Paper!Clip!Length "0.00297 "0.00148 0.01089 "0.14 0.892Paper!Clip!Wing 0.01641 0.00820 0.01089 0.75 0.454Paper!Bodytape!Jointtape "0.03953 "0.01977 0.01089 "1.82 0.074Paper!Bodytape!Width 0.01703 0.00852 0.01089 0.78 0.437Paper!Bodytape!Length 0.00734 0.00367 0.01089 0.34 0.737Paper!Bodytape!Wing "0.00766 "0.00383 0.01089 "0.35 0.726Paper!Jointtape!Width "0.01672 "0.00836 0.01089 "0.77 0.445Paper!Jointtape!Length 0.03234 0.01617 0.01089 1.49 0.142Paper!Jointtape!Wing 0.00297 0.00148 0.01089 0.14 0.892Paper!Width!Length 0.03453 0.01727 0.01089 1.59 0.118Paper!Width!Wing "0.01609 "0.00805 0.01089 "0.74 0.462Paper!Length!Wing "0.02766 "0.01383 0.01089 "1.27 0.209Clip!Bodytape!Jointtape 0.03641 0.01820 0.01089 1.67 0.099Clip!Bodytape!Width "0.01141 "0.00570 0.01089 "0.52 0.602Clip!Bodytape!Length "0.01297 "0.00648 0.01089 "0.60 0.553Clip!Bodytape!Wing "0.03422 "0.01711 0.01089 "1.57 0.121Clip!Jointtape!Width "0.01516 "0.00758 0.01089 "0.70 0.489Clip!Jointtape!Length 0.00078 0.00039 0.01089 0.04 0.971

(Continued)



in the Body tape box, the line is tipped slightly up onthe left side. Reading the top shows that the high sideis associated with no taping, therefore the main effectindicates that there should be no tape on the body.This value can then be added to the table for the finaldesign.

Continuing along with the analysis of Table 2, twomore factors are found, Clip and Paper, yet both of

these were determined by interaction. A summary ofthe analysis of Table 2 to achieve a final design isshown in Table 4.

The problem that remains is that there is still nosolution to the Joint Tape problem, which is listed asan ‘‘Unknown’’ in Table 4. Since this was not listedas a significant factor in either the interactions orthe main effects, the level of this factor is essentially

Table 1Continued

Estimated effects and coefficients for flight (coded units)


Clip!Jointtape!Wing 0.00391 0.00195 0.01089 0.18 0.858Clip!Width!Length 0.04109 0.02055 0.01089 1.89 0.064Clip!Width!Wing 0.02172 0.01086 0.01089 1.00 0.322Clip!Length!Wing 0.00328 0.00164 0.01089 0.15 0.881Bodytape!Jointtape!Width "0.00422 "0.00211 0.01089 "0.19 0.847Bodytape!Jointtape!Length "0.00641 "0.00320 0.01089 "0.29 0.770Bodytape!Jointtape!Wing "0.01391 "0.00695 0.01089 "0.64 0.525Bodytape!Width!Length 0.00766 0.00383 0.01089 0.35 0.726Bodytape!Width!Wing "0.03359 "0.01680 0.01089 "1.54 0.128Bodytape!Length!Wing 0.01734 0.00867 0.01089 0.80 0.429Jointtape!Width!Length 0.02078 0.01039 0.01089 0.95 0.343Jointtape!Width!Wing "0.04234 "0.02117 0.01089 "1.94 0.056Jointtape!Length!Wing "0.00516 "0.00258 0.01089 "0.24 0.814Width!Length!Wing 0.00703 0.00352 0.01089 0.32 0.748

Analysis of variance for flight (coded units)

Source DF Seq SS Adj SS Adj MS F P

Main effects 7 10.9781 10.9781 1.56830 103.40 0.0002-Way Interactions 21 0.6043 0.6043 0.02878 1.90 0.0263-Way Interactions 35 0.5369 0.5369 0.01534 1.01 0.473Residual Error 64 0.9707 0.9707 0.01517Pure Error 64 0.9708 0.9708 0.01517

Total 127 13.0900

Table 2Significant effects from Table 1


Constant 2.10523 0.01089 193.39 0.000Paper "0.14734 "0.07367 0.01089 "6.77 0.000Clip "0.12797 "0.06398 0.01089 "5.88 0.000Bodytape "0.05828 "0.02914 0.01089 "2.68 0.009Width "0.17797 "0.08898 0.01089 "8.17 0.000Length "0.16391 "0.08195 0.01089 "7.53 0.000Wing 0.49297 0.24648 0.01089 22.64 0.000Paper!Clip "0.04484 "0.02242 0.01089 "2.06 0.043Paper!Width "0.05172 "0.02586 0.01089 "2.38 0.021Clip!Length "0.04984 "0.02492 0.01089 "2.29 0.025Length!Wing "0.05516 "0.02758 0.01089 "2.53 0.014



irrelevant to the design. Ideally, the AAC would like toeliminate costs, and as a result, not taping the jointwould save some labor and extra material. Further-more, this decision is justified by the main effect shownin Figure 2 related to Joint Tape. The line in that box isalmost horizontal indicating no effect, hence its lack ofsignificance. (If there is another CTQ not studied herethat is impacted by Joint Tape [such as time to providehelicopter maintenance], then it is reasonable to con-sider Joint Tape. We do not see any reason to use JointTape.) Therefore the finalized design parameters, tak-ing into account interactions, main effects, and costcutting moves are shown in Table 5.

Pilot Study

The final section of the Improve Phase is takingthe optimized design and conducting a pilot study todetermine its effectiveness in improving the distribu-tion of the CTQ. A revised flowchart can be seen inFigure 4.

A scaled production line was assembled and thenew improved prototypes were built. It was determined

that the new helicopters required 62 man-days to build,versus the previous 60 man-days, due to complicationswith the longer wing structures. As each helicopterrolled off the line it was subjected to the same testsas a full-scale version. The results of those flight timesare shown in Figure 5.

The new process resulted in a stable process with alower control limit above the lower specification limit of2.60 seconds, shown in Figure 1. Recall, it is acceptableto place specification limits on an Individuals chart.However, it is also of note that the variation hasincreased as a result of this upward shift in flight time,as R-bar has increased from Figure 1’s 0.05885 secondsto Figure 4’s 0.08138 seconds. When the variationincreases as the mean time increases this is often the case

Figure 3. Interaction plot on flight times for the helicopters.

Figure 2. Main effects plot on flight times for the helicopters.

Table 4Final design parameters based on main effect and

interaction analysis

Variable name Variable Optimizing value

Paper Paper type White paperClip Paper clip No clipBodytape Body tape No tapeJointtape Joint tape UnknownWidth Body width 1.42 inchesLength Body length 3.00 inchesWing Wing length 4.75 inches

Table 5Design parameters for new aircraft


Paper Paper type White paperClip Paper clip No clipBodytape Body tape No tapeJointtape Joint tape No tapeWidth Body width 1.42 inchesLength Body length 3.00 inchesWing Wing length 4.75 inches

Table 3Factors determined through analysis of interactions


Paper Paper type White paperClip Paper clip No clipBodytape Body tape UnknownJointtape Joint tape UnknownWidth Body width 1.42 inchesLength Body length 3.00 inchesWing Wing length 4.75 inches



in skewed time distributions. However, the skewness intime distributions is usually to the right (greater values)side. In other words, higher values may appear as partof the new process but that is acceptable as the goalwas to exceed 2.6 seconds. The flight times have signifi-cantly improved. Figure 6 compares the distributions ofthe former Prototype 1 units with the newly developedunits.

CONTROL PHASE

The Control Phase establishes the ongoingcontrols necessary to sustain the benefits from theSix Sigma project. It comprises four steps: stand-ardization, mistake-proofing, documentation, andgiving control of the process back to the processowner.

Figure 4. Improved LNA AAC helicopter construction flowchart.



The deliverables from the control phase are:

(1) an implemented standardization and mistakeproof control plan

(2) documentation of the revised process(3) demonstration of significant and sustainable

improved performance(4) a lesson-learned document(5) a project replication=leverage plan(6) a project financial benefit document(7) return of the revised process to the control of the

process owner for continuous turns of the PDSAcycle

Standardization

Standardization was not viewed to be a significantproblem given that the process already operates from asingle flowchart. Reasonable care will be taken toensure that the new process flowchart is incorporatedon the production floor and further problems will beaddressed in the rest of the Control Phase.

Mistake-Proofing

Team members identified potential risk elementsthat could be carried through the process by usingFailure Mode Effects Analysis, or FMEA (see Table 7).These risk elements are:

(1) employees not being educated about the new winglength

(2) employees folding the body in the wrong direc-tions, i.e., folding at positive 180 degrees for bothfolds or vice versa

(3) employees folding the wings in the same direction,i.e., folding both wings at positive 90 degrees orvice versa

(4) employees folding the wings at angles other than#=" 90 degrees

(5) process owner tampering with the process

Each of the Risk Elements is subjected to a rating on a1 to 10 scale on Likelihood of Occurrence, Severity,and Likelihood of Detection, with high numbers beingmore problematic. The Risk Priority Number (RPN) iscalculated as the product of those three scales.

Risk Element 1—Employee Awareness of the NewWing Length—RPN $ 360

Employee education will alleviate many of theemployee awareness problems concerning the newwing length by teaching the employees exactly howtheir job relates to the operation and structure of theentire helicopter. This awareness can be instilledthrough a short one-day training course.

Another measure that could be implemented toavoid confusion, and potential mistakes, about thewing length would be to lock in the calibrations ofthe War Paper Machine so only one wing length couldbe cut. The war paper machine is discussed fully inRisk Element 4, and can be seen later in Figure 9. Thiswould reduce the RPN to 100. Furthermore, a com-pleted mock-up of the helicopter can be kept on nearbydisplay for quick visual comparison and as a guide.

Figure 5. Flight times for helicopters built on the improvedflowchart.

Figure 6. Comparing the distributions of the new helicop-ters and prototype 1.

Table 6Process capability with the new design

Yield DPMO Sigma

CTQ Current Desired Gap Current Desired Gap Current Desired Gap

Flight time 99.90888600% 99.90000000% "0.00888600% 911.14 1000.00 "88.86 4.62 4.59 "0.03



Risk Element 5—Tampering with the Process—RPN $ 336

The process owner will be thoroughly educatedwith regards to the impact of process tampering per-forming the famous funnel experiment (Gitlow et al.,1995). The RPN should drop to 150 based on theeducational program.

Risk Element 4—Incorrect Wing Folds by Angle—RPN $ 135

Lilliputian workers cannot reliably fold at a 90-degree angle. This problem can easily be circumventedusing the ‘‘wing tolerance tool.’’ This tool requires thatthe angle of the wings be within one degree of specifi-cation, 90 degrees, for the tool to fit onto the helicop-ter. The RPN drops to a value of 6 given use of thewing tolerance tool.

Problem 2—Incorrect Body Folds—RPN $ 24

Requiring employees to check that the body hastwo edges can circumvent the problem of folding thebody in the wrong directions (see Figure 7).

Figure 7 will be posted on the production floorand will be included in the training manual. In additionto this commonsense circumvention measure for RiskElement 2, there is an additional precaution that incor-porates instructions into the design (see Figure 8).

Employees should be able to read the word ‘‘Out-side’’ and should not be able to read the word ‘‘Inside’’on a completed helicopter. This is not a substitute forthe first control measure because this precaution is notcapable of preventing the body folding problem.

While it may seem a simpler solution to have texton both sides of the paper, the War Paper Machinedoes not replicate designs that require objects on bothsides of the paper, and forcing it to do so would create

Tab

le7

Failure

modeeffectsan

alysis(FMEA)

Riskelem

ents

Failure

mode

Likelihoodof

Occurrence

Severity

Likelihoodof

detection

RPN

Action

Likelihoodof

occurrence

Severity

Likelihoodof

detection

RPN

1)Employee

awareness

ofwinglength

Incorrectwing

length

89

536

0Helicoptereducation

seminar

55

410

0

2)Incorrectbody

folds

Singleedge

folds

62

224

Redesignoftemplate

andwarning

sign

withpicture

ofcorrectfold

22

28

3)Incorrectwing

foldsby

direction

Wings

facingthe

samedirection

210

120

Redesignoftemplate

and

integrationofwing

tolerance

tool

110

110

4)Incorrectwing

foldsbyan

gle

Unbalan

cedwings

93

513

5Integrationofwing

tolerance

tool

23

16

5)Process

tampering

Process

spiraling

into

chao

s7

86

336

New

process

flowchart

andcontrolplan

55

615

0

Figure 7. Correct and incorrect body folds.



an endless cycle of recalibration that is otherwise unne-cessary. Figure 9 shows a picture of the War PaperMachine. The RPN drops to 8 given these precaution-ary measures.

Risk Element 3—Incorrect Wing Folds by Direction—RPN $ 20

This risk is catastrophic, but it is blatantly obviousbecause it will appear as though the helicopter is miss-ing a wing. This has not been a problem in the past dueto ease of detection; however, reducing the risk is quitesimple. The design of the helicopter template has beenmodified to make it easier to determine folds, as shownin Figure 8. The words ‘‘Bottom Side’’ should only bevisible from below the helicopter and vice versa for‘‘Top Side.’’ The new design should be communicatedto all relevant employees.

The wing tolerance tool that was developed forRisk Element 4 provides an additional control for RiskElement 3 because it is nearly impossible for incorrectwing folds to go undetected. Therefore, the RPNdrops to 10.

It is worth noting that all of these items do notdirectly impact the new flowchart for the HelicopterConstruction Process that was generated in theImprove Phase, but are instead supplemental, in thatthey impact other processes’ flowcharts. For example,the redesigned templates would change the HelicopterTool and Die Flowchart, and the Helicopter Construc-tion Employee Training Flowchart would have to beupdated to account for teaching the new body foldingmechanisms as well as a thorough understanding ofhow the helicopter works.

Documentation

The primary piece of documentation required isthe new flowchart that was generated in the ImprovePhase. This flowchart needs to be inserted into all rele-vant training manuals, as well as into any standardoperating procedures kept on the production floor.Additionally, copies of all relevant control chartsshould be kept on the production floor to monitorthe process. ISO documentation needs to include thenew Standard Operating Procedure.

Demonstration of Significant and SustainableImproved Performance

Team members observed 100 trials of the new heli-copter design in the field (see Figure 10). The distribu-tion of flight times for the new design was stable andnormally distributed with a mean and standard devia-tion very close to the pilot test mean and standarddeviation. Team members were confident that thenew helicopter design provided sustained performancesignificantly better than the original helicopter (seeFigure 1 in Box, 1992) design.

Figure 8. New war paper design.

Figure 9. The war paper machine Figure 10. Sustained improvement in flight time.



Lesson Learned Document

The most significant lesson learned from this pro-ject was the value of Six Sigma methods in improvingand innovating the LNA to better fight the LFF. Con-sequently, the training arm of the LNA developed SixSigma courseware and offer it on demand to any divi-sion of the LNA desirous of such a training program.

Project Replication/Leverage Plan

A project replication=leverage plan was developedand put into play by contacting all of the top-rankingofficers of the LNA (Lilliputian National Army) andmaking them aware of the benefits and availability ofSix Sigma theory and methods training programs. Itwas a real success in that many generals signed upfor the program.

Project Financial Benefit Document

The financial analysis discussed in Box (1992) didneed to be updated in that it accurately represented thebenefits and costs of the new helicopter design. Thenew design is a big winner for the LNA and AAC.

Returning Process Control to the Process Owner

The final step of the Control Phase is returningcontrol of the process back to the process owner,which requires a control plan so the process improve-ments are not lost. A big piece of this control plan isthe documentation described in the previous section,plus relevant control charts. A copy of the revisedflowchart must go to the process owner for futureplanning for the iterations of the Plan-Do-Study-Actcycle known as the PDSA or Deming Cycle.

These are traditional items in a control plan, how-ever; in this case, there are two special issues that wereidentified in the FMEA. These two issues were that ofthe knife-induced defects and the calibration of the WarPaperMachine. The first issue that the process ownerwillhave to deal with is that the design of the War PaperMachine is not robust enough to maintain calibrations.Samples must be taken that measure the dimensionalaccuracy of the War Paper Machine. This informationshould be recorded in case future investigative work withregard to the flight time control charts in needed.

The second issue that the process owner will need todeal with is dull knives. Dull knives create burrs whichnegatively effect flight time. The number of linear feet

between the first burr caused by a dull knife should berecorded to determine the optimal number of linear feetbetween changing or sharpening the knife blade. Thisinformation should be analyzed using a control chart.

This concludes the project. The improved processis turned over to the process owner with control plansfor future turns of the PDSA cycle. The team disbandsand celebrates their success.

SUMMARY

The purpose of this paper was to demonstrate anapplication of the DMAIC model. It is hoped that thispaper will be used as a model for Six Sigma projects.

APPENDIX 1: RESULTS RELATIONSHIP TOTHE G.E.P. BOX EXPERIMENT’S HELICOPTERDESIGN

The helicopter created in this project through thedesigned experiment is actually much different thanthe helicopter generated by Box (1992). According toBox, who used eight factors instead of seven, the wingwas the chief effect related to the flight time of the heli-copter, as was seen in this experiment. From there, thesimilarities end.

The key thing to remember when comparing thetwo experiments is that Box used a 16th fractional fac-torial, which heavily confounds all of the interactionterms. However, the main effect terms are only con-founded with third-order interactions, and from hisstated goal of trying to teach experimental design, thiswas a great route to take.

Another major difference between the two experi-ments is that the Box experiment used another 4 feet ofdrop, as his flight was over 12 feet instead of the 8 usedhere. This led to a linear series of time effects, as theyrelated to the flight time. However, given that the dropwas significantly further, comparing these numberswith the effects generated in this experiment is not afair representation of the data. However, Box’s experi-ment can be compared to itself.

One difference was that Box found that a heavierbond paper promoted a longer flight time. A varietyof reasons could be attributed to this finding, the mostprobable being that a heavier paper would be morerigid, and would have less of a tendency to ‘‘disinte-grate’’ from its shape in flight. It is possible that withthe 8-foot drop, the bond paper never had the chanceto fully utilize the benefits of the heavier paper.However, this accounted for only 0.13 seconds ofadditional flight time according to Box, and in this



experiment, the paper type was actually determined byan interaction.

Another difference according to Box was the paperclip. Box claims that the paper clip added another 0.05seconds to the flight time from 12 feet, whereas in thisexperiment, it was found to add excess weight and dragthe helicopter faster than without the clip. Engineers inthis experiment found that the non-clipped helicoptersopened up a bit and acted more as a parachute on theway down. Given the shorter drop, this prevented apotential death-spiral, as the paper did not have timeto leave its lazy fall, and turn sideways to plummetto the ground. Box did not have this luxury, as his heli-copters had an extra 4 feet to drop, which could havegiven the helicopter more time to roll over and plum-met to the ground. However, this clipping decisionwas also accounted for by an interaction, and the maineffect was disregarded.

The third differing result was that of the joint tap-ing. Box’s information shows that there is a 0.17 secondgain by taping the wing joint. Given the heavier paperused, this may have caused the wings to not fold upas much during the drop, but this is purely speculation.

The final difference was that Box chose the widerbody helicopter, as it adds 0.02 seconds to the flighttime. In this experiment, the body width was deter-mined by an interaction.

What do these differences mean? Given that thesewere two separate experiments, with different dropheights, it suggests that these are two different, yet cor-rect, solutions to the same problem. The experiment ranhere was geared for a short time drop. However, Box’sexperiment was for a much longer period, and as aresult, the helicopter had to behave differently. Keepingin line with the aircraft theme, saying these helicopterdesigns should be the same would be like saying thata carrier-based fighter and a cargo plane should havethe same design, which is far from the truth, but the dif-ferences maximize the capabilities of both.

ABOUT THE AUTHORS

Adam Johnson graduated from Auburn Universityin December of 2000 with a Bachelor of Science inMechanical Engineering. He is currently a candidatefor a Master of Business Administration at the Univer-sity ofMiami.He plans on pursuing a Ph.D. in Statistics.He is a Six Sigma Black Belt.

Scott Widener graduated from Iowa State Univer-sity in May of 2001, with a Bachelor of Science in Cera-mic Engineering, and again from the University ofMiami in May of 2003 with a Master of Business

Administration in Quality Management. He is a SixSigma Black Belt.

Dr. Popovich is Vice President of Process Excel-lence at Boca Raton Community Hospital. Formerly,he was a consultant to many large manufacturing com-panies, financial services companies, medical servicesorganizations, state and county government, foreignarmed services, and overseas organization. Clientshave included GE, Motorola, Lockheed Martin,Johnson & Johnson, Intuit, Sony, Bell South, FirstData, Singapore Air Force, Hanley Hazelden Centerat St. Mary’s, NCR, [P Morgan, Wachovia, A&P,and Samsung, among others. Dr. Popoivch earnedhis Ph.D.] in statistics (1983), his Masters degree(1979) and his B.S. in mathematics (1977) at theUniversity of Florida. He has taught at the Universityof Florida, University of Central Florida, FloridaAtlantic University, Nova Southeastern Universityand guest-lectured at several other universities.

Dr. Howard S. Gitlow is Executive Director of theInstitute for the Study of Quality and a Professor ofManagement Science, University of Miami, CoralGables, Florida. He received his Ph.D. in Statistics(1974), M.B.A. (1972), and B.S. in Statistics (1969)from New York University. Dr. Gitlow is a Six SigmaMaster Black Belt, a Fellow the American Society forQuality, and a member of the American StatisticalAssociation. He has consulted on quality, productivity,and related matters with many organization, includingseveral Fortune 500 companies. Dr. Gitlow has coau-thored 10 books and over 50 academic articles. Whileat the University of Miami, Dr. Gitlow has receivedawards for Outstanding Teaching, Outstanding Writ-ing, and Outstanding Published Research.

REFERENCES

Box, G. E. P. (1992). Teaching engineers experimental designwith a paper helicopter. Quality Engineering, 4(3):453–459.

Gitlow, H., Oppenheim, A., Oppenheim, R. (1995). QualityManagement: Tools and Methods for Improvement, 2nded. Boston, MA: Irwin McGraw-Hill.

Johnson, A., Widener, S., Popovich, E., Gitlow, H. (2006).A ‘‘six sigma’’ black belt case study: G.E.P. Box’s PaperHelicopter Experiement – Part A. Quality Engineering,18(4):413–430.

Rasis, D., Gitlow, H., Popovich, E. (2002). Paper organizersinternational: A fictitious six sigma green belt case study –Part 1. Quality Engineering, 15(1):127–145.

Rasis, D., Gitlow, H., Popovich, E. (2002). Paper organizersinternational: A fictitious six sigma green belt case study –Part 2. Quality Engineering, 15(2):259–274.



A Six Sigma Black Belt Case Study- G.E.P. Boxs Paper Helicopter Experiment Part B

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