A comparative analysis of theTaguchi and Shainin DOEtechniques in an aerospace

environmentA.J. Thomas

Cardiff School of Engineering, Cardiff University, Cardiff, UK, and

J. AntonyCentre for Research in Six Sigma and Process Improvement (CRISSPI),

Caledonian Business School, Glasgow Caledonian University, Glasgow, UK

Abstract

Purpose – To highlight the application and to compare the effectiveness of the Taguchi and Shaininexperimental design processes as applied to aerospace structural components.

Design/methodology/approach – This paper applies both the Taguchi and Shainin experimentaldesign techniques to optimizing the design of honeycomb composite joints. The techniques are fullyapplied, the results analysed and their user friendliness is assessed.

Findings – This paper identifies an optimum parameter setting for composite joints gained fromapplying these experimental design techniques. Significant improvements in joint strength areachieved through identifying a new joint setting.

Practical implications – The adoption of the experimental design techniques outlined in this paperand their application to a real engineering problem will enable a company to apply the techniques andto attain improvements in terms of cost and quality.

Originality/value – The analysis of both the Taguchi and Shainin methodologies and the resultingconclusions as to their effectiveness for industry is the real value of this paper. This paper will bevaluable for quality professionals, design engineers and manufacturing specialists in a wide range ofindustries.

Keywords Taguchi methods, Experimental design, Aerospace industry, Composite materials

Paper type Technical paper

1. IntroductionStatistical quality improvement techniques such as design of experiments and Taguchimethods form an essential part of the search for improved product performance.These techniques are finding greater prominence in industry through the developmentand implementation of the Six-Sigma strategy (Antony et al., 2003). However, theeffective implementation of the Taguchi experimental design technique withinindustry can be considered to be poor. Companies cite the complexity of the techniqueas being the major limiting factor as to its use.

It has been argued that the DOE technique developed by Dorian Shainin provides apowerful yet simpler approach that lends itself to easier implementation in anindustrial environment. This paper initially describes both the Taguchi DOE techniqueand Shainin’s key variables search technique (KVST) and then goes onto compare

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Received January 2005Revised June 2005Accepted June 2005

International Journal of Productivityand Performance ManagementVol. 54 No. 8, 2005pp. 658-678q Emerald Group Publishing Limited1741-0401DOI 10.1108/17410400510627516

the accuracy, validity and user friendliness of both approaches through thedevelopment of a case study. Its aim is to provide a new perspective on the applicationof different DOE techniques so as to stimulate greater use and development of thesestatistical methods in industry.

2. Background to DOE techniquesThe statistical approach to design of experiments and the analysis of variance(ANOVA) technique was developed by R.A. Fisher back in the 1930s. The techniqueprovides a very powerful and economical method to determining significant factorsand factor interactions that affect variability within a product. This classical approachto the design of experiments was further developed in the late-1980s when GenichiTaguchi developed his own form of statistical design of experiments.

Whilst the work of Fisher and Taguchi is relatively well known in modernmanufacturing industry, the work of Dorian Shainin receives less acclaim but hisnon-academic statistical technique is gaining greater prominence. The Shainin DOEtechnique permits the luxury of considering as many variables as can be identified(Bhote, 1991). The subsequent grouping of these variables into “families” andidentifying the most influential variables based on statistical significance as opposedto assumptions provides a greater chance of identifying the major factors of variance.Shainin identifies and categorises the major factors contributing to variance as Red X,Pink X and Pale pink X (Goodman and Wyld, 2001). Red X being the major factorcausing variance, Pink X being the second factor and Pale pink X being the third.

This paper develops both the Taguchi DOE and Shainin’s KVST by conductingexperiments on identifying the influencing variables that control the joint strength ofhoneycomb composite tongue and slot joints for aerospace applications.

2.1 The Taguchi DOE techniqueTaguchi methods provide a systematic approach to a better understanding of the processand assists industrial engineers to discover the key process or design factors which affectthe critical product/process characteristics (Taguchi, 1987). The process of performing aTaguchi experiment follows a number of distinct steps (Antony et al., 1998):

(1) Objective/goal of the experiment

(2) Selection of quality characteristics

(3) Identification of control, noise and signal factors

(4) Choice of experimental design

(5) Experimental preparation and requirements

(6) Experimental run

(7) Statistical analysis and interpretation

(8) Confirmatory run/experiment

2.2 The Shainin KVSTThe Shainin KVST is deemed to be a simple yet powerful approach to identifying themost influential variables on a process or system. The technique follows the five-stepmethodology Anthony (1999) and is described further by Shainin and Shainin (1988).The outline of the methodology is:

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(1) Identify a list of input variables and undertake testing using a suitable samplesize. From this, calculate the median average and then calculate DM:R ratio toverify whether the variables selected are suitable.

(2) Compute the control limits for the median values obtained from step 1 so thatfurther analysis can be undertaken to identify if the variables selected arecritical to the experiment.

(3) Separate the critical variables from the non-critical variables.

(4) Conduct a capping run to confirm the critical variables are correct.

(5) Conduct a factorial analysis including factorial plots to determine optimalsettings.

3. Application of Taguchi DOE and Shainin’s KVST3.1 IntroductionAdhesive joints are expected to meet their design load requirements for the entireduration of the service life of a bonded structure. However, service conditions can ofteninvolve exposure to combinations of static and/or fatigue loads that are often difficult topredict and subsequently model. It is, therefore, essential that the designer and analystpossess the necessary tools for selecting and characterising an adhesive system toensure a reliable bond performance is achieved under a range of operating conditions.Optimising joint performance requires an understanding of the joint parameters, failuremechanisms, test methods and design methodologies suitable for predicting joint failure(Broughton, 1998). This, therefore, means that a reliable method for estimating thecontribution of individual processing and design factors on the strength and variabilityin the strength of the joint is needed (Thomas and Antony, 2003a, b).

3.2 Problem analysisAerospace structures make extensive use of honeycomb composite panels in themanufacture of various structural members. The building of such structures involvesthe interlinking of panels via tongue and slot joints. These joints are subsequentlybonded into position using a two-part epoxy based adhesive. Traditional forms ofmanufacture dictate that the application of the adhesive is carried out via a manualprocess. The compromise, however, is that whilst manual adhesive application is slowand highly labour intensive, structural integrity can be ensured due to sufficientadhesive being present at the joint interface.

With the ever increasing requirement for companies to become more “lean” in theirapproach to manufacture, it is suggested that manually applied adhesive methodsshould be replaced by a more “automated” application. In order to facilitate this, amethod of injecting adhesive into the joint through the rear panel skin via a series ofholes has been adopted. However, this approach has its limitations in that under thecurrent joint design criteria, the joint is severely starved of adhesive.

It is possible to redesign the joint interface parameters in order to allow for a greateringress of adhesive into the joint, however, the mechanical interlocking properties ofthe joint may be compromised thus causing further problems. The paper will applyboth the Taguchi DOE and the Shainin variables search techniques in order to identifythe key factors/variables that influence joint strength.

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3.3 Experimental design using the Taguchi methodology3.3.1 Step 1 Objectives of the study. The overall objectives of this study are as follows:

. To identify and/or predict the optimum factor settings in order to achievemaximum joint strength with increased joint strength robustness. Making theprocess insensitive to various sources of noise is achieved through using therobust parameter design technique (Phadke, 1989).

. To identify the correct combination of factors that will allow for the successfulapplication of the injection method of adhesive application whilst ensuring jointstrength is maximized and joint variability is reduced.

. To identify one set of factors that would enable the joint to exhibit increasedstrength for two load conditions.

. To perform confirmatory runs to verify the optimal factor settings.

3.3.2 Step 2 Selection of quality characteristics.3.3.2.1 Problem identification. Significantly lower joint strength values were obtained

from the adhesive injection method. Two load cases were considered namely; tensile andtransverse. Alongside this issue was the fact that large variations were also seen betweensuccessive strength test readings indicating a lack of robustness within the process. Thereason for the reduction in strength was due to adhesive starvation in the slot caused by anincorrect set of design parameters for the adhesive application method used. The currentjoint parameters suited the manual adhesive application method, however, they were notappropriate for the injection method of adhesive application. The key responsecharacteristic was, therefore, the joint strength in each of the two load orientations.

3.3.3 Step 3 Identification of control and noise factors.3.3.3.1 Investigation of the influences on joint strength reduction. A brainstorming

exercise was carried out by a interdisciplinary team of engineers from the company inorder to identify and classify (Kolarik, 1995) the factors that would influence the jointstrength and failure characteristics. Figure 1 shows a cause and effect diagram thathighlights the potential major contributory factors. Nineteen possible factors wereidentified. Extensive testing work was then undertaken in order to provide failure datafor the two load cases on the current joint design. From this testing phase the factorswere further prioritised through conducting a Pareto analysis for the two load cases

Figure 1.Possible factors

influencing joint strength

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(Owen, 1989) and are shown in Figure 2. The major factors contributing to failure of thejoints were plotted against their frequency of occurrence.

For the tensile load case the Pareto analysis showed that 85 per cent of joint failureswere caused by only five factors. For the Transverse load case the analysis highlightedthat 75 per cent of failures were caused by the same five factors. These factors weresubsequently classified as control factors and then ranked in order of importance as:

Tongue length A

Slot width B

Slot length C

Slot depth D

Tongue Depth E

3.3.3.2 Control and noise factor analysis. In prior benchmarking studies on manuallyapplied adhesive joints, large variations in joint strength were observed. Althoughjoint strength variation was large, the overall joint strength was still high. At this stagethe team revisited the C þ E diagram in order to distill the noise and control factors toa suitable range (Dingus, 1989; Quinlan, 1985; Thomas and Antony, 2003a, b; Taguchi,1989). From this study the team felt it safe to assume the only noise factor present wasthe adhesive application method since it was believed that this was the cause ofthe strength variations. Since this factor was to be eventually removed due to therequirement for an automated approach, there was no requirement to develop andsubsequently analyse an array based on noise factors.

The Pareto analysis highlighted the five major control factors affecting jointperformance. It was, therefore, decided to initially test using these five factors (andtheir interactions) and hence employ a simpler orthogonal array (OA).

3.3.4 Step 4 Choice of OA design. The main issue of Taguchi’s experimental designapproach is the use of OAs. Using OAs in experimentation allows for multi-factorexperimentation to occur thus reducing the number of experiments required to reachan optimal set of parameters for joint strength improvement. Having selected theparameter design experiment, the next step was to choose an appropriate OA.

Five main control factors at two levels each were considered for the experiment.Only the interactions A £ B; and A £ E were of interest (Table II for key to factor

Figure 2.Pareto analysis of factorsthat contributed tojoint failure

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identification). Interaction A £ B was investigated in order to see if there would be aneffect on the strength of the joint due to changing the shear bond area around the joint.Interaction A £ E (aliased with B £ CÞ was investigated in order to see if there was anycorrelation between joint strength and the geometrical changes made to the tongue orthe slot rather than the interface. This was important since it is the interaction betweenthe joint interface that is of primary concern here and the team needed to be confidentthat geometrical changes did not affect the strength also. It was not expected thatinteraction effect A £ E would yield any significant result.

Interaction A £ C is aliased main effect “D” and so was considered as part of themain effect analysis. All other interactions (i.e. B £ D; C £ D and so on) were notconsidered as being important since they did not affect the interaction between thetongue and slot interface and hence did little to affect joint strength. For example,interactions B £ D; C £ D affected either the tongue or slot geometry only. If theinteraction A £ E yielded a significant interaction effect then the above interactionswould be required to be analysed further. Interaction C £ E was not considered to beimportant since it affected the longitudinal strength and not the tensile or transversecapabilities of the joint. Since these joints were not subjected to longitudinal loads, itwas decided that testing of this interaction was not required. There are five degrees offreedom associated with the control factor effects (i.e. 1 DOF per factor). In addition,two-two-factor interactions were of interest. Therefore, two degrees of freedom areassociated with the two-factor interactions (i.e. 1 DOF per interaction). The totalnumber of the degrees of freedom is equal to the sum of the degrees of freedom for themain and interaction effects, and is, therefore, seven for the control array. It was,therefore, decided to employ an L8 OA. Table I shows the OA design matrix used forthe analysis.

3.3.4.1 Control factor levels. Control factors were tried at two levels only. Previoustesting of the joints identified the need to either reduce slot length or to increase thetongue length in order to achieve greater mechanical interlocking of the joint.The second level parameters were, therefore, set to allow a minimum clearancebetween the tongue and slot. Table II shows the factors chosen for this experiment.For experimental purposes the factors identified in Table II were coded as 1 and 2.This indicating Level 1 where the factors were set at their current levels and Level 2where the factors were set at a new level set by the engineering team. Coding thefactors aided in simplifying the experimental process since it followed the conventionadopted by Taguchi and, helped in reducing the confusion that could be inducedthrough using actual values as shown in the uncoded levels.

A B AB C D ¼ AC BC ¼ AE E ¼ ABC

1 1 1 1 1 1 11 1 1 2 2 2 21 2 2 1 1 2 21 2 2 2 2 1 12 1 2 1 2 1 22 1 2 2 1 2 12 2 1 1 2 2 12 2 1 2 1 1 2

Table I.Design matrix for theexperiment showing a

coded OA

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3.3.5 Step 5 Experimental preparation. The tongue and slot joints were manufacturedunder standard operating conditions using a Rye CNC router in order to ensure highlevels of dimensional accuracy. The adhesive was prepared using a standard adhesivemixing machine so that consistency of the two part epoxy-based adhesive was assuredthroughout experimentation.

3.3.6 Steps 6 and 7 Experimental run, statistical analysis and results. Havingobtained the response values using an L8 OA (Table III) the following steps were usedto interpret the results from the analysis. A sample of five tests were conducted at eachexperimental point, Table III shows the mean strength values obtained from theseexperiments. Experiment numbers 5 and 7 gave mean response values as N/A. This isdue to the setting requirements for tongue length and slot lengths within the OA, inboth these cases the tongue length was greater than the slot length and so the jointcould not be assembled. This subsequently affects the degrees of freedom associatedwith the ANOVA shown in Table VII.

The resolution of the design was III (Montgomery, 2001) since the main effects areconfounded with two-factor interactions. For this study, all the main effects and thetwo, two-factor interaction effects A £ B; and A £ E; were calculated. Table IVillustrates the estimated main and interaction effects.

Analysis of the mean response was performed to identify the factors and theirinteractions that influenced the mean response (y).

An ANOVA was carried out on the results in order to identify which of the factorsand their interactions were likely to be statistically significant and hence provided thegreatest influence on the joint strength values. The ANOVA table constructed inTable VII shows that for the direct tensile load condition for example, all the mainfactor effects and the AB interaction were judged to be statistically significant. It isworth noting that if none of the factors or their interaction effects from the analysis had

Uncoded level Coded levelName Abbrev Units 1st 2nd 1st 2nd

Tongue length A mm 51 68 1 2Slot width B mm 13 14 1 2Slot length C mm 52 69 1 2Slot depth D mmm 8 10 1 2Tongue depth E mm 7 9 1 2

Table II.Factors and levels used inanalysis

A B C D E ResponseStd order Run number mm mm mm mm mm Tensile Transverse

1 2 51 13 52 8 7 2.0 3.052 5 51 13 69 10 9 2.2 3.13 8 51 14 52 8 9 2.3 3.04 6 51 14 69 10 7 1.6 3.055 7 68 13 52 10 9 N/A N/A6 1 68 13 69 8 7 3.1 2.957 3 68 14 52 10 7 N/A N/A8 4 68 14 69 8 9 4.9 3.1

Table III.Experimental layout usedfor the experiment

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been statistically significant, then there would have been a need to select a new factoror set of factors and/or reconsider the experimentation approach again (Antony andKaye, 1996).

For this study, the objective was to improve the joint strength and reduce variabilityin joint strength. The “larger the better” quality characteristic was chosen in order toidentify the correct parameter settings for each joint load case. However, theidentification of same factors for both load orientations would make the design andmanufacturing process simpler.

The final selection of optimal operational factor settings was based on the responsesobtained from the statistical study shown in Tables V-VIII. The final choice of factorlevels differed under each load case. The tensile load experimentation yielded a2,2,2,1,2 setting whereas the transverse load experimentation yielded a 1,2,2,2,2 jointsetting. These parameter settings are discussed further in Step 8.

Having identified the predicted parameter settings, the ANOVA table constructedin Table V is used to estimate the value of the main and interaction effects. From theANOVA the following results were seen:

. For the direct tensile load case, the main effects A and D were highly significantat both 95 and 99 per cent level of significance.

. For the transverse shear case, no main effects or interactions were seen asstatistically significant at 1 per cent, however, interaction AB statisticallysignificant at a 5 per cent level of significance.

Tables VI and VII calculate the static signal to noise ratio (SNR) for the main effectsand interactions for each load case. The SNR is calculated to provide a measure ofrobustness of the joints in the presence of noise factors. Making the joints moreresistant to the effects of “noise” should in turn reduce the level of variation in strengthof the joints. In this case the “largest is best” SNR is used since maximising jointstrength is the objective of this experiment. Table VIII shows a pooled ANOVA of theSNR (only showing factors A and D in the tensile load case for illustration). The pooledSNR takes all statistically significant factors and interactions from each load case(identified by the ANOVA constructed in Table V) and predicts the improvements inthe level of robustness in each joint. In each case, the pooled ANOVA for the SNRhighlighted that the main effects and interactions were statistically significant and,therefore, confirmed that these factors and interactions were critical to joint robustness.

Average response (kN)Tensile Transverse

Main effect L1 L2 L1 L2

Tongue length (A) 2.025 4 3.05 3.025Slot width (B) 2.43 2.93 3.03 3.05Slot lenght (C) 2.15 2.95 3.03 3.05Slot depth (D) 3.08 1.9 3.03 3.08Tongue depth (E) 2.23 3.13 3.02 3.07InteractionsA £ B 3.03 2.33 3.08 3.0A £ E 2.83 2.53 3.07 3.02

Table IV.Response table of mainand interaction effects

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It is suggested through the accurate adjustment of these factor settings, reductions inthe variation between successive strength values should now be seen.

3.3.7 Step 8 Confirmatory run and analysis of predicted settings. The selection of theoptimal parameter settings is obtained by analysing both the mean response table andthe average SNR table. The selection of each factor level is obtained by analysing themean response and average SNR at each factor level in order to obtain the maximumjoint strength. The results of which are summarised below:

. The predicted direct tensile load capability was a maximum with a 2,2,2,1,2 jointconstruction. The ANOVA table shows all main factor effects as beingstatistically significant and so any changes to this joint formation in an attempt

Factor DOF SS MS F ratio

Tensile-ANOVAA 1 15.60 15.60 167.54 * *

B 1 1.00 1.00 10.74 * *

C 1 2.56 2.56 27.49 * *

D 1 5.57 5.57 59.81 * *

E 1 3.24 3.24 34.79 * *

AB 1 1.96 1.96 21.05 * *

AE 1 0.36 0.36 3.87 * *

Error 22 0.75 0.09 –Total 29 31.04 – –

F 0.05,1,2,2 ¼ 4.33 F 0.01,1,2,2 ¼ 7.95Transverse-ANOVAA 1 0.00 0.00 0.52B 1 0.00 0.00 0.33C 1 0.00 0.00 0.33D 1 0.01 0.01 2.07E 1 0.01 0.01 2.07AB 1 0.03 0.03 5.29 *

AE 1 0.01 0.01 2.07Error 22 0.04 0.00 –Total 29 0.10 – –

F 0.05, 1,2,2 ¼ 4.33 F 0.01, 1,2,2 ¼ 7.95

Note: *Indicates factor/interaction is statistically significant at 5 per cent level of significance* *Indicates factor/interaction is statistically significant at 1 per cent level of significance

Table V.ANOVA of load cases

SNR – (larger the better)Tensile Tranverse

6.01 9.686.82 9.827.21 9.544.03 9.68N/A N/A9.82 9.4N/A N/A13.82 9.82

Table VI.SNR table

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to gain a standard joint construction for both load cases needs to be carefullyconsidered.

. The predicted transverse shear load capability was a maximum with a 1,2,2,2,2joint construction. Factors A and D differed in this case. The ANOVA tableshowed once again that the Factors A and D had minimal statistical significanceand thus could be adjusted to create a 2,2,2,1,2 joint construction with minimalloss in joint strength.

. A single type 2,2,2,1,2 joint construction could, therefore, be used for both loadcriterion.

. The interaction effect A £ E (and hence B £ CÞ was not statistically significantthus indicating that only changes in joint design that affect the joint interfaceactually affected joint strength.

Having obtained the optimal factor settings as 2,2,2,1,2, confirmatory runs wererequired. Although this setting had already been tested (run 4 on the OA), confirmatoryruns were undertaken in order to identify whether improvements were seen in joint

Average SNR Average SNRTensile Transverse

Main effect L1 L2 L1 L2

Tongue length (A) 6.13 12.04 9.69 9.61Slot width (B) 7.71 9.34 9.63 9.69Slot lenght (C) 6.65 9.40 9.63 9.69Slot depth (D) 9.77 5.58 9.63 9.77Tongue depth (E) 6.97 9.91 9.60 9.74Interactions – – – –A £ B 9.63 7.35 9.77 9.54A £ E 9.04 8.06 9.74 9.60

Table VII.Average SNR table

Factor DOF SS MS F ratio

Tensile – pooled ANOVA of SNRA 1 69.86 69.86 46.57 * *

D 1 70.22 70.22 46.82 * *

Pooled error 3 1.50 0.50 –Total 5 141.58 – –

F 0.05,1,1,3 ¼ 10.13 F 0.01,1,3 ¼ 34.12Transverse – pooled ANOVA of SNRAB 1 0.21 0.21 42.32 *

Pooled error 4 0.03 0.005 –Total 5 0.47 – –

F 0.05,1,4 ¼ 7.71 F 0.01,1,1,4 ¼ 21.20

Note: *Indicates factor/interaction is statistically significant at 5 per cent level of significance* *Indicates factor/interaction is statistically significant at 1 per cent level of significance

Table VIII.Pooled ANOVA for the

SNR

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robustness as well as being able characterise the failure modes of the injection bondedjoints against those of the manually bonded joints.

A sample run of five joints for each load case was performed. Table IX shows theresults.

Improved strength values were achieved in all joint cases thus enabling thepossibility of reducing sub-assembly machining times by reducing the number oftongue and slot joints within the panel assembly.

A good correlation was achieved between the predicted strength SNR values andthe actual strength and variance results. Significant reductions in variance were seen inboth load cases due to joint redesign and injection method.

4. Experimental design using the Shainin KVSTThe Shainin KVST begins its approach by identifying the study objectives, in this casethese are:

. To identify the key variables that influence the joint strength performance and todistinguish them from the variables that have the least influence.

. To adjust the tolerances of the least influential variables in order to reduce cost ofmanufacture (Antony, 1999).

. To identify Red X (the major factor affecting joint strength), pink X (thesecond major factor affecting joint strength) and Pale pink X (the third factoraffecting joint strength) from the experiments constructed for two loadorientations.

. To determine the optimal settings for each of the key variables highlightedabove.

. To identify any significant two-order main effect interactions that are likely toimpact on joint strength performance.

The Shainin technique follows the five-step methodology Anthony (1999) and is shownin Section 2.2. Each of the steps identified in this section are developed further in thenext section.

4.1 Step 1 Develop and test a list of input variablesThis initial phase of the experimentation calls for the correct identification of inputvariables for the study. The Pareto analysis identified in Section 3 ranks the variables

Direct tensileStrength (before) Strength (after) Strength increase (per cent)

Strength 3,100 N 4,860 N 36.2Variation (before) Variation (after) Variation reduction (per cent)

Variance 151.4 66.13 56.13Transverse

Strength (before) Strength (after) Strength increase (per cent)Strength 3,050 N 3,250 N 5.6

Variation (before) Variation (after) Variation reduction (per cent)Variance 17.21 16.67 3.1

Table IX.Results of confirmatoryruns

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in order of importance and these are shown in Table X below along with the “high” and“low” settings that will be used for the experimentation phases.

The main input variables were tested in order to identify the high and low values intwo load orientations (tensile and transverse). Table XI shows the high and low valuesand the calculation phase.

In this experimental phase, a total of six joints were constructed for each load case,i.e. three joints were constructed using “High” level settings and three with “Low” levelsettings (Table XI). The joints were tested and the results were recorded. The medianaverage of the strength values were then calculated (MH and ML).

The next stage in the process was to calculate the differences between the medianvalues at the “High” and “Low” level settings for both load cases (Dm). In order tocalculate R; the range values of the high and low settings must be firstly calculated.This is simply the difference between the “High” and “Low” values at each level (RHand RL). R in each case, therefore, being the mean average of the RH and RL values.

The Shainin technique states that the difference between the medians of the threereplications in the experiments must exceed the average of the two ranges by a factorof at least 1.25-1 (i.e. DM: R) (Bhote, 1991). In our case the ratio DM: R was well abovethe minimum requirement (6.7: 1 tensile and 5:1 transverse) and, therefore, thisexperimental phase for each load orientation was considered successful thus provingthat the factors selected in the initial phase of the experimentation were indeed correctand were likely to have sufficient influence on joint strength performance.

Direct tensile Transverse

High settings 4.9 3.55.1 3.55.3 3.6

Low settings 3.0 3.13.2 3.03.1 3.0

MH 5.1 3.5ML 3.1 3.0Dm 2.0 0.5RH 0.4 0.1RL 0.2 0.1R 0.3 0.1Dm: R 6.7:1 5:1

Table XI.Input variable selection

and verification

Main input variable Variable coding High level setting (mm) Low level setting (mm)

Tongue length A 68 51Slot width B 14 13Slot length C 69 52Slot depth D 10 8Tongue depth E 9 7

Table X.List of main input

variables and theirsettings

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4.2 Step 2 Computing the control limits for the medianCalculation of the control limits allows for the determination of whether a variable isimportant or unimportant thus allowing for a decision to be made regarding avariable’s elimination from further experimentation.

The control limit calculations are shown in Table XII below. The constant 2.776is used in the calculations since it corresponds to a two-tailed t-distribution with95 per cent confidence and 4 degrees of freedom (based on 3 þ 3 2 2 degreesof freedom). The value of the statistical constant d2 is equal to 1.693 (based on a samplesize of 3).

The values of MH and ML in the equations represent the median with all factors setat high levels (MH) and at low levels (ML).

4.3 Step 3 Separating the critical variables from the non-critical variablesThe aim of this phase of experimentation is to separate the critical variables from thenon-critical variables. This is achieved by changing the level of each variable fromþ1 to 21 in turn. Shainin uses (þ1) values to signify a variable set to its “High”setting and a (21) value as being set to its “Low” setting. If the result of theexperimentation for each variable falls inside the control limits then the variable is saidto be unimportant. Likewise, if the result of the experimentation falls outside therespective control limits then the variable is said to be important. Table XIII showsthe results of the experimentation work.

From Table XIII, the important variables identified for the tensile load case were A,B and E where the important variables for the transverse load case were identified asA, D and E. It is worth noting here, however, that variable A in both load orientationscould not be tested fully since run 8 could not be undertaken due to the same jointgeometry limitations that were identified in Section 3.3, steps 6 and 7.

4.4 Step 4 Conducting capping runs to confirm the critical variables are correctHaving obtained a list of the most important variables for each load orientation, acapping run phase is introduced. This phase is performed to verify whether or not theremaining unimportant variables in the experiment can be ignored. The capping runsare performed in two stages. The first capping run is conducted by keeping the criticalvariables at the (þ ) level and the unimportant variables at the (2 ) level. The second

Calculating control limitsEquationsCLHþ ¼ MH þ 2:776ðR=d2ÞCLH2 ¼ MH 2 2:776ðR=d2ÞCLLþ ¼ ML þ 2:776ðR=d2ÞCLL2 ¼ ML 2 2:776ðR=d2ÞValuesTensile orientation (kN) Transverse orientation (kN)CLHþ ¼ 5.59 CLHþ ¼ 3.66CLH2 ¼ 4.61 CLH2 ¼ 3.34CLLþ ¼ 3.59 CLLþ ¼ 3.16CLL2 ¼ 2.61 CLL2 ¼ 2.84

Table XII.Control limit calculations

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capping run was conducted by reversing the variables, that is the critical variables setat a (2 ) level and the unimportant variables at the (þ ) level. The unimportantvariables are verified as being unimportant if the results of the capping runs liebetween the control limits.

The results of the capping runs are shown on Table XIV. Step 3 of theexperimentation process confirms that variables C and D on the tensile load case andvariables B and C on the transverse load case are actually unimportant since fromTable XIV it can be seen that the resulting values lie between the control limits thusindicating the variables have little influence on joint strength. This verifies theimportant variables identified in Step 3 of the experiment were solely responsible forthe strength improvements in the joint.

Now that the results obtained from the capping runs were successful, this nowallows the experimentation to progress to the factorial analysis stage.

A B C D E Result

Tensile7 21 1 1 1 1 2.4 Important8 1 21 21 21 21 0.0 Not feasible9 1 21 1 1 1 3.3 Important

10 21 1 21 21 21 2.5 Important11 1 1 21 1 1 0.0 Not feasible12 21 21 1 21 21 3.0 Not important13 1 1 1 21 1 4.9 Not important14 21 21 21 1 21 3.0 Not important15 1 1 1 1 21 4.5 Important16 21 21 21 21 1 2.4 ImportantTransverse7 21 1 1 1 1 2.9 Important8 1 21 21 21 21 0.0 Not feasible9 1 21 1 1 1 3.4 Not important

10 21 1 21 21 21 3.0 Not important11 1 1 21 1 1 0.0 Not feasible12 21 21 1 21 21 3.0 Not important13 1 1 1 21 1 3.0 Important14 21 21 21 1 21 3.2 Important15 1 1 1 1 21 3.1 Important16 21 21 21 21 1 3.3 Important

Table XIII.Separation of variables

A B C D E Result

Tensile17 1 1 21 21 1 5.43 Successful18 21 21 1 1 21 2.45 SuccessfulTransverse17 1 21 21 1 1 3.1 Successful18 21 1 1 21 21 2.9 Successful

Table XIV.Capping run results

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4.5 Step 5 Conducting a factorial analysis including factorial plots to determine theoptimal settingsThe objective of this phase is to determine the main effects, i.e. Red X, Pink X and Pale pinkX and to identify any significant two-order interactions that occur between the main effects.Identification of the main and interaction effects is undertaken using full factorial analysison the results obtained from the experimentation phases. For each variable considered“important”, their main effects and factor combinations are assessed and identified. Red X,Pink X and Pale pink X are identified by the magnitude of the main effects. From Table XV,Red X on the tensile load case is seen as variable A since it achieved the highest main effectvalue from the full factorial analysis, that of 2.12, the next being variable E with a maineffect value of 1.78 and so on. Red X, Pink X and Pale pink X being identified as variables A,E and B, respectively. Table XV also shows the analysis of the interaction effects. Againfull factorial experimentation is undertaken for the interaction effects.

In order to find out whether interactions exist between the main effects A, B and E,Shainin promotes the use of interaction plots as a quick and effective method to highlightany possible interaction effects. Using the interaction plots, it is possible to see whetherinteractions exist since if interactions are present, non-parallel lines are created by thetwo main effects. Plots were drawn for each possible interaction and these are shown inFigure 3. As can be seen, the plots identify the presence of interactions in all three casesnamely A £ B; A £ E and B £ E due to the non-parallel lines being plotted in each case.

Similarly, an analysis of the transverse load case identified Red X, Pink X and Palepink X as variables A, E and D, respectively. The full-factorial analysis conducted on theinteraction effects of these main variables identified interactions A £ D; A £ E andD £ E existed.

Main effects and interactions of variables A and BB Failure load Median Main effect A

Main effectA Mean of main effects at high and low (4.77-2.65)

21 21 3.2, 3.1, 3.0, 2.8, 2.45, 2.0, 2.0 2.8 2.1221 þ1 2.9, 2.4 2.65þ1 21 3.3 3.3þ1 þ1 5.43, 5.3, 5.1, 4.9, 4.9, 4.5 5.0

Main effects and interactions of variables A and EA E Failure load Median Main effect BMain effect

E Mean of main effects at high and low (4.48-2.70)21 21 3.2, 3.1, 3.0, 2.9, 2.45, 2.0, 2.0 2.9 1.7821 þ1 2.8, 2.4 2.6þ1 21 4.5 4.5þ1 þ1 5.43, 5.3, 5.1, 4.9, 4.9, 3.3 5.0

Interactions of variables B and EB E Failure load Median Main effect EMain effect

B Mean of main effects at high and low (3.875-2.73)21 21 3.2, 3.1, 3.0, 2.45, 2.0, 2.0 2.725 1.14521 þ1 3.3, 2.8 3.05þ1 21 4.5, 2.9 3.7þ1 þ1 5.43, 5.3, 5.1, 4.9, 4.9, 2.4 5.0

Table XV.Factorial analysis oftensile testing stage

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Figure 3.Interaction plots A £ B;

A £ E and B £ E

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4.6 Optimum settings and identification of key variablesThe selection of the optimal variable settings is obtained by analysing the factorialanalysis tables for the respected load case. The selection of each factor level is obtainedby identifying the highest figure obtained between the two levels for each factor.Note that whereas the Taguchi method identified an optimum level setting for each ofthe least important factors, the Shainin technique does not assign a factor level for theunimportant variables and, therefore, these variables can theoretically be set at eitherlevel. The unimportant variables are marked with () to show their ability to be movedfrom high to low settings and vice versa to suit the conditions. The results of which aresummarised below:

. The predicted direct tensile load capability was a maximum witha þ 1, þ 1,(1),(1), þ 1 joint construction.

. The predicted transverse shear load capability was a maximum witha þ 1,(1),(1) þ 1, þ 1 joint construction. In this case the unimportant variableswere identified as B and C. In order to achieve a common joint construction,variables B and C can both be changed to þ1 in order to meet this criteria. Also,variable C cannot be set to 21 when variable A is set at þ1 since the slot would betoo small for the tongue thus necessitating a change of variable C toþ1 in this case.

. A single type þ1, þ 1, þ 1, þ 1, þ 1 joint construction could, therefore, be usedfor both load criterion.

Having obtained the optimal factor settings as þ1, þ 1, þ 1, þ 1, þ 1, confirmatoryruns were required, however, since experimentation at this setting had already beenconducted at the start of the experimentation when setting all variables to their “High”levels, (Table XII) there was no requirement to test again. A summary of these resultsalong with the percentage increase in strength gained from moving the variables fromtheir current low settings to high settings are given in Table XVI:

. Calculation of Red X, Pink X and Pale pink X for each load orientation were asfollows in Table XVII.

. Initial analysis prior to experimentation highlighted that tongue length (A) andtongue depth (E) at (þ ) levels may provide greater mechanical interlocking and alarger bond area, the results of the experimentation have verified this prediction.

Direct tensile Strength (before) Strength (after) Strength increase (per cent)

Strength 3,100 N 5,100 N 39Transverse Strength (before) Strength (after) Strength increase (per cent)Strength 3,100 N 3,500 N 11

Table XVI.Analysis of results fromthe Shainin technique

Lead orientation Red X Pink X Pale pink X

Tensile A B DTransverse A D E

Table XVII.Analysis of key variables

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. Variables A and B were seen as significant to the tensile load case, this onceagain verifies the initial analysis since the direct tensile case relies on the shearstrength capabilities of the tongue against the edges of the slot. Widening the slotallows for greater adhesive ingress and hence greater joint strength. A longertongue length allows for greater mechanical interlocking and limits transfer ofshear loads through the adhesive line.

. Improved strength values were achieved in both joint cases (some greater thanothers) thus enabling the possibility of reducing sub-assembly machining timesby reducing the number of tongue and slot joints within the panel assembly. Theidentification of a single joint set-up for both load cases also reduces subassembly and manufacturing costs.

5. Analysis of results and evaluation of the techniquesThe implementation and subsequent use of experimental design techniques within anindustrial environment relies primarily on the ease of application of the technique andits ability to provide accurate and detailed information to the user. The accuracy of theinformation should be further supported by the ease in which the information suppliedto the system can be validated at various stages during the application of the techniqueso as to reduce time and effort during experimentation.

Through the application of both the Taguchi and Shainin DOE techniques, it hasbeen possible to analyse and qualify both the ease of use and the accuracy ofinformation obtained from the techniques. The following conclusions have beendrawn:

. The Shainin technique showed increases in joint strength over and above theincreases identified with the Taguchi technique. A 2.8 per cent increase instrength was shown on the direct tensile load orientation and a 5.4 per centstrength increase was seen on the transverse load orientation.

. Both techniques provided different results with regards to factor/variable levelsettings. Both techniques, however, were able to highlight the least statisticallysignificant factors/variables and this was used to adjust the levels accordinglywithout affecting joint strength to any appreciable extent. This also allowed forthe achievement of a single joint construction in both cases. Table XVIII showsthe factor/variable level settings for each load case. Factors in italics on theTaguchi table show them as the least significant factors with blanks on Shainintable signify variables can be set at any level due to them being unimportant tothe joint.

Shainin TaguchiFactor/variable Tensile Transverse Tensile Transverse

A High High High LowB High High HighC High HighD High High Low HighE High High High

Table XVIII.Comparison of

factor/variable settings

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. The development of a single joint construction capable of providing increases instrength for all load orientations is important for this engineering application.A single joint construction provides design flexibility and improvesmanufacturing efficiency through reducing set-up times, etc. Throughadjusting the least significant variables/factors it was possible to find a singlejoint construction that could be used for both load orientations whilst stillproviding joint strength increases in these load orientations.

. The Shainin technique was significantly easier to implement and to obtainresults. The use of this simple approach enabled the experimentation to takeapproximately 75 per cent less time to complete and utilised 50 per cent fewerhuman resources. However, the amount of testing required to obtain realisticresults was some three times greater through employing the Shainin approach.This was down to the need to undertake full factorial experimentation. This issueis critical to the management of experimental design work since the amount oftesting could have a significant impact on R þ D costs.

. The application of Taguchi’s robust parameter design allowed the team tomeasure and evaluate the variation in the strength readings. This piece of system“additionality” was of particular importance since it allowed the user to identifyif the variation in strength could be adversely affected even though the breakstrength of the joints increased.

. The validity of the results emanating from the Taguchi approach was somewhatsuspect. The Taguchi technique initially computed a joint construction that wasimpossible to manufacture (as seen in the transverse load orientation) wherebythe identification of a tongue length that was too large for the slot length.

. Table XIX shows the relative merits of both experimental design techniques asapplied to the application highlighted in this paper.

6. ConclusionsThis paper has compared the operational effectiveness of the Taguchi and ShaininDOE techniques through their application to improving the joint strength of anaerospace structural problem. The following are general conclusions that haveemerged from the experimentation:

. The Shainin technique allows for the quick and simple identification of the threemajor factors that influence the system, i.e. Red X, Pink X and Pale pinkX. This is achieved through the use of a systematic methodology based aroundfull factorial experimentation. It can be considered primarily as a problem

Characteristic Taguchi Shainin

Validity (on main effects) Poor HighValidity (on interactions) High PoorComplexity High LowImplementation Difficult EasyCost of experimentation Low HighFlexibility Low High

Table XIX.Analysis of Taguchi andShainin DOE techniques

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solving technique in which it attempts to identify the primary root causes of theproblem (De Mast, 2004).

. The Shainin technique relies heavily on using engineering judgement andsimplistic statistical tools to “funnel” down the factors to a point where fullfactorial experimentation can be undertaken. In fact, the Shainin technique reliesvery much upon the correct identification of variables but moreso, in the rankingand subsequent allocation of those variables into the experiment. The Shainintechnique, however, provides the ideal opportunity to solve problems quicklyand effectively by allowing the analyst to change the important factors thataffect the mean response of a system whilst allowing for cost effective action tobe taken on the unimportant factors (i.e. to set them at the most economical levelsince they have little effect).

. In an industrial environment, the Shainin technique provides a powerful andreliable method of experimental design that is easily implemented throughoutthe organisation. It is highly user friendly and can quickly identify the maineffects through full factorial experimentation. The use of interaction plots caneasily and quickly highlight interactions. Its weakness, however, is in the skilland knowledge required to firstly correctly identify the variables and thensecondly, to allocate those variables to the experiment. This relies onpre-experimental analysis to funnel down the variables to a full factorial level.

. The Taguchi approach provides for a powerful product/process enhancementcapability where system robustness can be created through the identification of awider range of influential variables that can affect systems output. The Taguchitechnique provides its strength through being able to accurately identify maineffects and interactions through partial factorial experimentation. This approachwill find relevance in an industrial setting particularly where a large number offactors are considered critical for the experimental process. More complex thanthe Shainin approach, it is likely to be utilised by engineers and managers with amathematical background. Its strength in partial factorial analysis is also itsweakness when it comes to accuracy of factor and interaction identificationsimply because partial factorial analysis does not test every experimentalcombination.

References

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Antony, J. and Kaye, M. (1996), “Optimisation of core tube life using experimental designmethodology”, Journal of Quality World, pp. 42-50.

Antony, J., Kaye, M. and Frangou, A. (1998), “A strategic methodology to the use of advancedstatistical quality improvement techniques”, The TQMMagazine, Vol. 10 No. 3, pp. 169-76.

Antony, J., Forturis, M. and Thomas, A. (2003), “Using Six Sigma”, Manufacturing Engineer,IEE Publication, Stevenage, Herts.

Bhote, K.R. (1991), World Class Quality, American Management Association, New York, NY.

Broughton, W. (1998), “Using the finite element technique for optimising bondedaero-structures”, Institute of Materials Journal, Vol. 5.

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De Mast, J. (2004), “methodological comparison of three strategies for quality improvement”,International Journal of Quality & Reliability Management, Vol. 21 No. 2, pp. 198-213.

Dingus, G. (1989), “An application of Taguchi methods in the foundry industry”, paper presentedat the Seventh Symposium on Taguchi Methods, MI, pp. 517-32.

Goodman, J. and Wyld, D.C. (2001), The Hunt for the Red X: A Case Study in the Use of ShaininDesign of Experiment (DOE) in Industrial Honing Operations, Kennedy-WesternUniversity, Alabama.

Kolarik, W.J. (1995), Creating Quality: Concepts, Systems, Strategies and Tools, McGraw-Hill,Maidenhead.

Montgomery, D. (2001), Design and Analysis of Experiments, 5th ed., Wiley, New York, NY.

Owen, M. (1989), SPC and Continuous Improvement, IFS, Kempston, Bedford.

Phadke, M.S. (1989), Quality Engineering using Robust Design, Prentice-Hall International,Englewood Cliffs, NJ.

Quinlan, J. (1985), “Process improvement by application of Taguchi methods”, Transactions ofthe Third Symposium on Taguchi Methods, MI, pp. 11-16.

Shainin, D. and Shainin, P. (1988), “Better than Taguchi orthogonal tables”, Quality andReliability Engineering International, Vol. 4, pp. 143-9.

Taguchi, G. (1987), System of Experimental Design, 1/2, ASI, Dearborn, MI, 1, 2.

Taguchi, G. (1989), Introduction to Quality Engineering, UNIPUB, New York, NY.

Thomas, A.J. and Antony, J. (2003a), “An integrated approach to improving the adhesive bondstrength of honeycomb composite joints”, Work Study Journal.

Thomas, A.J. and Antony, J. (2003b), “Applying Shainin’s variable search methodology inaerospace applications”, Journal of Assembly Automation.

Further reading

Fisher, R.A. (1935), The Design of Experiments, Oliver and Boyd, Edinburgh.

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