teaching experimental design techniques to industrial ... · teaching experimental design...

Teaching Experimental Design Techniquesto Industrial Engineers*

JIJU ANTONY and NICK CAPONPortsmouth Business School, University of Portsmouth, Milton Site, Portsmouth, PO4 8JF, UK.E-mail: [email protected]

Experimental Design (ED) is a powerful technique for understanding a process, studying theimpact of potential variables or factors affecting the process and thereby providing spontaneousinsight for continuous quality improvement possibilities. ED has proved to be very effective forimproving the process yield, process capability, process performance and reducing processvariability. However research has shown that the application of this powerful technique by theengineering fraternity in manufacturing companies is limited due to lack of skills and expertise inmanufacturing, lack of statistical knowledge required by industrial engineers and so on. This paperillustrates some of the recent research findings on the problems and gaps in the state-of-the-art inED. In order to bridge the gap in the statistical knowledge required by engineers, the articlepresents a paper helicopter experiment which can be easily carried out in a class-room to teachexperimental design techniques. The results of the experiment have provided a greater stimulus forthe wider application of ED by industrial engineers in real-life situations for tackling qualityproblems.

INTRODUCTION

EXPERIMENTAL DESIGN (ED) is a strategy ofplanning, conducting, analysing and interpretingexperiments so that sound and valid conclusionscan be drawn efficiently, effectively and eco-nomically. It provides the experimenters a greaterunderstanding and power over the experimentalprocess. ED has seen an increased application overfifteen years, as both manufacturing and serviceindustries have attempted to refine and improveproduct, process and service quality. ExperimentalDesign technology is not new to industrial andmanufacturing engineers in today's modern busi-ness environment. ED was developed in the early1920s by Sir Ronald Fisher at the RothamstedAgricultural Field Research Station in London,England. After World War II, English prac-titioners of experimental design brought it tothe US, where the chemical process industry wasamong the first to apply it [1].

A number of successful applications of ED forimproving process performance, reducing processvariability, improving process yield etc. have beenreported by many manufacturers over the lastfifteen years [2, 4]. Research has shown that theapplication of ED techniques by the engineeringfraternity in both manufacturing and serviceindustries is limited and when applied they areoften performed incorrectly [5]. In other words,there is a cognitive gap in the knowledge ofstatistics required by engineers in using ED asa problem-solving tool. Moreover, the most

common remark made by many engineers is `Ican do the text book and class room examplesbut I am not comfortable while applying theconcepts and principles of ED in my work area'.These findings point to the following issues [6]:

. Statistical education for engineers at universitylevel is generally inadequate. The courses cur-rently available in engineering statistics oftentend to concentrate on the theory of probability,card shuffling, probability distributions and themore mathematical aspects of the subject ratherthan the techniques which are more practicallyuseful to the engineering fraternity. Thus manyengineers would deem statistics as useless intheir late careers in industries.

. The lack of communication between the indus-trial and the academic worlds restricts the appli-cation of ED in many manufacturing and serviceindustries.

. Lack of skills and expertise required by engi-neers in manufacturing, especially in problemformulation and definition.

. The existing methodologies in ED provide noinsight into problem analysis and classification.Thus many engineers experience difficulties inanalysing a particular process quality problemand then converting the engineering probleminto statistical terms from which appropriatesolutions can be chosen.

. Current software systems and expert systems inED often tend to concentrate on data analysisand do not properly address interpretation ofdata. Thus many industrial engineers havingperformed the statistical analysis would not* Accepted 15 August 1998.

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Int. J. Engng Ed. Vol. 14, No. 5, pp. 335±343, 1998 0949-149X/91 $3.00+0.00Printed in Great Britain. # 1998 TEMPUS Publications.

know what to do with the results withoutassistance from statistical consultants in thefield.

BENEFITS OF EXPERIMENTAL DESIGN

ED enables industrial engineers to study theeffects of several variables affecting the responseor output of a certain process [7]. ED methodshave wide potential application in the engineeringdesign and development stages. It is the strategy ofthe management in today's competitive worldmarket to develop products and processes insensi-tive to various sources of variation using ED. Thepotential applications of ED in industries are:

. reducing product and process design anddevelopment time;

. studying the behaviour of a process over a widerange of operating conditions;

. minimising the effect of variations in manu-facturing conditions;

. understanding the process under study andthereby improving its performance;

. increasing process productivity by reducingscrap, rework etc.;

. improving the process yield and stability of anon-going manufacturing process;

. making products insensitive to environmentalvariations such as relative humidity, vibration,shock and so on;

. studying the relationship between a set ofindependent process variables (i.e., processparameters) and the output (i.e., response).

The following steps are useful while one may beperforming an industrial experiment;

1. Definition of the objective of the experiment.2. Selection of the response or output.3. Selection of the process variables or design

parameters (control factors), noise factors andthe interactions among the process variables ofinterest. (Noise factors are those which cannotbe controlled during actual production condi-tions, but may have strong influence on theresponse variability. The purpose of an experi-menter is to reduce the effect of these undesir-able noise factors by determining the best factorlevel combinations of the control factors ordesign parameters. For example, in an injectionmoulding process, humidity and ambient tem-perature are typical noise factors.)

4. Determination of factor levels and range offactor settings.

5. Choice of appropriate experimental design.6. Experimental planning.7. Experimental execution.8. Experimental data analysis and interpretation.

PAPER HELICOPTER EXPERIMENT

The following section describes the applicationof ED for optimising the time of flight of a paperhelicopter which can be made from A4-size paper.The experiment was carried out by the first authorin a class-room for a post-graduate course inquality management at University of Portsmouth.The experiment requires paper, scissors, ruler,paper clips and a measuring tape. It would take

Fig. 1. Model of a paper helicopter design.

J. Antony and N. Capon336

about 5 ±6 hours to design the experiment, collectthe data and then perform appropriate statisticalanalysis. The model of a paper helicopter design isshown in Fig. 1.

The objective of the experiment was to deter-mine the optimal settings of the design parameterswhich would maximise the time of flight. For theapplication of ED in solving process and productquality problems, it is essential that the objective ofthe experiment must be specified clear, brief andconcise. Having defined the objective of the experi-ment, the possible parameters which might influ-ence the time of flight were determined through athorough brainstorming session. These parameterswere then classified into control parameters andnoise parameters. Control parameters are thosewhich can be controlled easily by the operatorduring the experiment. For example, shrinkage ofparts in an injection moulding process is quitecritical, as it badly affects the final assembly. Thecontrol factors which might have an impact on theparts shrinkage are screw speed, mould tempera-ture, cycle time and mould pressure. Noise para-meters are those which are hard to control orexpensive to control by the operator during theexperiment [8]. For example in the above process,relative humidity is a noise factor.

The following control parameters were selectedfor the paper helicopter experiment:

. paper type

. wing length

. body width

. body length

. number of clips attached

. wing shape.

The two noise factors which could not be directlycontrolled during the experiment were:

. draft

. operator.

In order to minimise the effect of these noisefactors on the time of flight, extra caution wastaken during the experiment. For instance, theexperiment was conducted in a closed room inorder to dampen the effect of draft. The sameperson (i.e., operator) was responsible to minimisethe reaction time of hitting the stopwatch when thehelicopter is released and when it hits the floor.

Once the design parameters are selected, thenext stage is to determine the number of levels inwhich the parameters should be studied for the

experiment. The level of a parameter is the speci-fied value of a setting. For example, in the aboveinjection moulding experiment, 2108C and 2508Care the low and high levels of mould temperature.It was decided to set each parameter at two levelsor values as this forms the building block forstudying parameters at three and higher levels.Design or process parameters at three levels aremore complicated to teach in the first place andmoreover the authors strongly believe that it mightturn off engineers from learning ED any further[9]. It is usually best to experiment with the largestrange feasible to observe the effect of a designparameter on the output or response. Here effectrefers to the change in average response when adesign (or process) parameter goes from a low levelto a high level.

Table 1 illustrates the list of control parametersand their selected ranges for the experiment. In thecontext of ED, a `response' is the quantity anexperimenter wants to measure during the experi-ment in order to judge the performance of theproduct. In this case the response or performancemonitored is the time of flight measured inseconds. Note that selection of an appropriateresponse for any industrial experiment is criticalfor its success [10]. For teaching purposes, it isgood practice to choose continuous responses (e.g.surface roughness, strength, efficiency, life, etc.)than those which are attributes (e.g. taste, colour,appearance etc.).

Interactions of interestTwo factors, say, X and Y are said to interact

with each other if the effect of control parameter Xon the response (or output) is different at differentlevels of control parameter Y or vice versa [11]. Ifthe effect of control parameter X on the response isthe same at all levels of control parameter Y, thenthe interaction between the control parameters issaid to be zero.

For industrial experiments with two controlparameters X and Y considered at two levels(referred to as 2-level parameters), the interactioneffect can be computed by the equation:

Interaction effect � 12�Effect of control parameter

X at high level of Y

ÿ Effect of control parameter

X at low level of Y �

Table 1. List of control parameters for the experiment

Control parameters Parameter labels Low level �ÿ1� High level ��1�Paper type A Normal BondWing length B 80 mm 130 mmBody width C 20 mm 35 mmBody length D 80 mm 130 mmNo. of clips E 1 2Wing shape F Flat Angled 45 up

Teaching Experimental Design Techniques to Industrial Engineers 337

or

Interaction effect � 12�Effect of control parameter

Y at high level of X

ÿ Effect of control parameter

Y at low level of X �

Choice of experimental design and design matrixfor the experiment

The choice of experimental design depends onthe number of degrees of freedom associated withmain and interaction effects and cost and timeconstraints. Here the degrees of freedom is thenumber of independent and fair comparisons thatcan be made from a set of observations [12]. Forexample, if a control parameter is set as 2-level,then only one fair and independent comparisonbetween the levels (i.e., low and high) can be made.For a control parameter at 3-level, the number offair and independent comparisons that can bemade among the levels is two. Therefore, thenumber of degrees of freedom associated with acontrol parameter at p levels is � pÿ 1�. Thenumber of degrees of freedom associated with aninteraction is the product of the number of degreesof freedom associated with each main effectinvolved in the interaction. For example, if acontrol parameter X is at 2-level and anothercontrol parameter Y at 3-level, then the numberof degrees of freedom associated with theirinteraction is 2 (i.e., 1� 2).

For the helicopter experiment, as we are inter-ested in studying six main effects and three inter-action effects, the total number of degrees offreedom is equal to nine ( i.e., 6� 3). It is impor-tant to meet the criterion that the number ofexperimental trials required for a certain experi-ment must be greater than the number degrees offreedom associated with the main and interactioneffects to be studied for the experiment. A factorialexperiment is an experiment where one may vary

all the control parameters (or factors) in theexperiment at their respective levels simultaneously[13]. A factorial experiment can be either fullfactorial or fractional factorial. A full factorialexperiment (usually represented by 2k) is preferredwhen both main and interaction effects are to beevaluated independently. The standard number ofexperimental trials or runs for a factorial experi-ment are 4, 8, 16, 32, 64 and so on. This can beeasily derived using the formula: Number ofexperimental trials � 2k where k is the number ofcontrol parameters at 2-level.

However, in many situations this type of experi-ment may be not feasible and practical due to timeand cost constraints. Under such circumstances,fractional factorial experiments provide a reason-able alternative that still allows the experimentersto evaluate main effects [14]. Fractional factorialexperiment will consume only a fraction of the fullfactorial experiment and is generally representedby 2�kÿl �, where 1

2l yields the fraction. For example,

2�5ÿ2� implies that the experimenter wishes to studyfive control parameters in eight experimental trials.This is a 1

4of a full factorial experiment (i.e., 25).

For more information on fractional factorialexperiments, the readers are advised to consult[15].

For the helicopter experiment, as the totalnumber of degrees of freedom is equal to nine,the closest number of experimental trials that canbe employed for the experiment is 16 (i.e., 2�6ÿ2�fractional factorial). This implies that only aquarter replicate of a full factorial experiment isneeded for the study. The experiment wasperformed based on the design matrix as shownin Table 2. Each trial was randomised to minimisethe effect of noise. Randomisation is a method ofsafeguarding the experiment from systematic biaswhich causes variation in response or output.

The design matrix displays all the controlparameter settings for the experiment. Havingconstructed the design matrix, the flight timeswere recorded (see Table 2) corresponding toeach trial condition.

Table 2. Design matrix for the helicopter experiment: ( ) represents the experimental trials in random order

Trial no./run A D B C E F Time of flight (s)

1 (6) Normal 80 80 20 1 Flat 2.492 (9) Bond 80 80 20 2 Flat 1.803 (11) Normal 130 80 20 2 Angled 1.824 (15) Bond 130 80 20 1 Angled 1.995 (12) Normal 80 130 20 2 Angled 2.116 (2) Bond 80 130 20 1 Angled 1.967 (16) Normal 30 130 20 1 Flat 3.198 (14) Bond 130 130 20 2 Flat 2.279 (10) Normal 80 80 35 1 Angled 2.12

10 (1) Bond 80 80 35 2 Angled 1.5811 (7) Normal 130 80 35 2 Flat 2.1512 (3) Bond 130 80 35 1 Flat 2.0513 (8) Normal 80 130 35 2 Flat 2.6014 (4) Bond 80 130 35 1 Flat 2.0915 (5) Normal 130 130 35 1 Angled 2.6316 (13) Bond 130 130 35 2 Angled 2.18


STATISTICAL ANALYSIS ANDINTERPRETATION OF RESULTS

Having obtained the response values, the nextstep is to analyse and interpret the results so thatnecessary actions can be taken accordingly. Thefirst step in the analysis involves the computationof both main and interaction effects. For computa-tion purposes, the low and high levels in the designmatrix (refer to Table 2) must be replaced by ÿ1and �1 respectively. For example, control para-meter `A' column must be replaced by ÿ1, �1, ÿ1,�1 and so on. The same procedure must be appliedto other control parameters. The resulting codeddesign matrix for the experiment is shown in Table3. This table is used for all computations of mainand interaction effects.

Calculation of main effectsThe effect of a main/interaction effect is the

difference in the average response at low andhigh levels. For example, the effect of controlparameter A can be calculated as follows:

. Average time of flight at high level of A � 1:99

. Average time of flight at low level of A � 2:39

. Effect of control parameter A � 2:39ÿ 1:99 �ÿ0:40

A negative sign indicates that the slope of the lineconnecting the low and high values is negative. Inother words, the average time of flight at the lowlevel is higher than that at the high level. Similarly,the effects of other control parameters can be

estimated. Table 4 illustrates the estimated maineffects for the experiment.

In order to assist people with limited mathema-tical skills, the authors recommend a graphical plotof main effects. The notion behind the use of thisgraphical representation is to provide novices abetter picture on the importance of the effects ofthe chosen control parameters. Figure 2 illustratesthe main effects plot of the control parameters.

The main effects plot shows that the mostdominant control parameter on the time of flightis paper type, followed by wing length, wing shapeand number of clips. The control parameter bodywidth has no impact on the time of flight.

Calculation of interaction effectsFor the helicopter experiment, we were inter-

ested to study the following three interactions:

. Wing length Body width (B � C)

. Wing length Body length (B � D)

. Paper type Number of clips (A � E)

Consider the interaction between the control para-meters B and D. In order to compute the inter-action, we must obtain the average time of flight ateach level combination of these control para-meters. There are all together four combinationsof levels between these two parameters:

Bÿ1Dÿ1, Bÿ1D�1, B�1Dÿ1 and B�1D�1. Theaverage time of flight at these combinations areillustrated in Table 5.

Interaction effect �B�D�� 1

2�Effect of B at high level of D

ÿ Effect of B at low level of D�� 1

2��2:568ÿ 2:003� ÿ �2:190ÿ 1:998��

� 0:187

An alternative approach for computing the inter-action effect between B and D can be achieved bymultiplying the coded levels of B and D in each

Table 4. Table for main effects for the experiment

Controlparameters

Average athigh level

Average atlow level

Effect

A 1.99 2.39 ÿ0.40D 2.29 2.09 0.20B 2.38 2.00 0.38C 2.20 2.18 0.02E 2.06 2.32 ÿ0.26F 2.04 2.34 ÿ0.30

Table 3. Coded design matrix for the helicopter experiment

Trial no./run A D B C E F Time of flight (s)

1 (6) ÿ1 ÿ1 ÿ1 ÿ1 ÿ1 ÿ1 2.492 (9) �1 ÿ1 ÿ1 ÿ1 �1 ÿ1 1.803 (11) ÿ1 �1 ÿ1 ÿ1 �1 �1 1.824 (15) �1 �1 ÿ1 ÿ1 ÿ1 �1 1.995 (12) ÿ1 ÿ1 �1 ÿ1 �1 �1 2.116 (2) �1 ÿ1 �1 ÿ1 ÿ1 �1 1.967 (16) ÿ1 �1 �1 ÿ1 ÿ1 ÿ1 3.198 (14) �1 �1 �1 ÿ1 �1 ÿ1 2.279 (10) ÿ1 ÿ1 ÿ1 �1 ÿ1 �1 2.12

10 (1) �1 ÿ1 ÿ1 �1 �1 �1 1.5811 (7) ÿ1 �1 ÿ1 �1 �1 ÿ1 2.1512 (3) �1 �1 ÿ1 �1 ÿ1 ÿ1 2.0513 (8) ÿ1 ÿ1 �1 �1 �1 ÿ1 2.6014 (4) �1 ÿ1 �1 �1 ÿ1 ÿ1 2.0915 (5) ÿ1 �1 �1 �1 ÿ1 �1 2.6316 (13) �1 �1 �1 �1 �1 �1 2.18


row of Table 3. Having obtained the levels for theproduct (B�D), we will then calculate the averageflight times corresponding to low and high levels of(B�D). The interaction effect between B and Dcan now be estimated in a similar manner to themain effects:

Interaction effect �B�D�� Average flight time at high level of �B�D�ÿAverage flight time at low level of �B�D�

Similarly, the interactions between B and C , i.e.,(B� C), and the interaction between A and E,i.e., (A� E) can be computed. The results aresummarised in Table 6.

Interaction plotThis is a very powerful graphical tool for inter-

preting the interaction effects. It provides a betterand rapid understanding of the nature of inter-actions among the control parameters underconsideration. Non-parallel lines in the interactionplot connotes the existence of interaction amongthe parameters, whereas parallel lines indicates thenon-existence of interaction among the parametersfor investigation. Consider the interaction betweenwing length (B) and body length (D) for the aboveexperiment. The interaction plot is shown in Fig. 3.As the lines are non-parallel, there is an interactionbetween the control parameters B and D.

The main effects plot and interaction plothowever does not tell us which of the main and/or interaction effects are statistically significant.Under such circumstances, it is good practice toemploy normal probability plots [16]. For normalprobability plots, the main and interaction effectsof control parameters should be plotted againstcumulative probability (%). Inactive main andinteraction effects tend to fall roughly along astraight line whereas active effects tend to appearas extreme points falling off each end of a straightline. These active effects are judged to be statis-tically significant. Figure 4 shows a normalprobability plot of effects (both main and inter-action) of control parameters at 99% confidencelevel (or 1% significance level). Here significancelevel is the risk of saying that a factor issignificant when in fact it is not. In other words,it is the probability of the observed significanteffect (either main or interaction) being due topure chance. For experimental design problems,we generally consider both 5% and 1% significancelevels. If � measures the significance level, then�1ÿ �� measures our confidence for an effect to bestatistically significant [17]. The graph (Fig. 4)shows that main effects A, B, E and F arestatistically significant. The interaction between Band D was not statistically significant at 1%significance level (or 99% confidence level)though it appeared to be important in theinteraction graph (refer to Fig. 3).

Fig. 2. Main effects plot of the control parameters.

Table 5. Average response table

B D Average time of flight

ÿ1 ÿ1 1.998ÿ1 �1 2.003�1 ÿ1 2.190�1 �1 2.568

Table 6. Table of interaction effects

Interaction effects Estimate of the effect

B � D 0.187B � C 0.021A � E 0.186


Determination of optimal control parametersettings

Having identified the significant control para-meters, the next step is to determine the optimalsettings of these parameters that will maximise theflight time. In order to arrive at the optimalcondition, the mean time of flight at each levelof these parameters was analysed. As none of theinteraction effects were statistically significant,the main concern was the average flight times atthe low and high level of the main effects (refer toTable 4). From Table 4, the final optimal settingsof control parameters was derived (see Table 7). Itis quite interesting to notice that the optimalcontrol parameter settings is one which correspondto trial condition 7 (see Table 2). The time of flightwas maximum when wing length and body length

were kept at high levels. A confirmatory experi-ment was carried out to verify the results from theanalysis. Five helicopters were made based on theoptimal combination of control parameter levels.The average flight time was estimated to be 3.26 s.

Fig. 3. Interaction plot between parameters B and D.

Fig. 4. Normal probability plot of effects.

Table 7. Final optimal control parametersettings

Control parameters Optimum level

Paper type Normal (low level)Wing length 130 mm (high level)Body width 20 mm (low level)Body length 130 mm (high level)Body length 130 mm (high level)Number of clips 1 (low level)Wing shape Flat (low level)


Significance of the workThe purpose of this section is to bring the

importance of teaching experimental designtechniques to engineers with limited statisticalskills for tackling quality engineering problems inmany organisations. It is quite important to notethat this experiment is quite old in its nature andhas already been widely used for some time bymany statisticians for teaching purposes. Never-theless the focus here was to minimise the statis-tical jargon associated with the technique andbring modern graphical tools for better and rapidunderstanding of the results to non-statisticians.

This experiment was conducted in a class-roomto help students come to grips with experimentaldesign. As it is an extremely simple experiment, theconcept and the objective of the experiment wasquite straight forward. The students of the classfound this particular experiment interestingspecifically in terms of selecting the appropriateexperimental design, conducting the experimentand interpreting the results of the experiment.Many students were quite astounded with the useof graphical tools and its reduced involvement ofnumber crunching. The experiment helped them tounderstand the importance of brainstorming foridentifying the key variables and understandingthe concept and nature of interactions among thevariables. The authors strongly believe that theexperiment provided a simple and beneficial wayto help students view on experimental design in amore approachable manner which consequentlyled to their eagerness to apply it in their ownwork environment. As many of the students hadmarketing background, they commented that

experimental design could be applied in reducingthe cycle time for new products, maximising theresponse for a certain advertisement and com-paring competitive strategies and decision-makingprocesses.

CONCLUSIONS

Experimental design is a very powerful problem-solving technique that assists industrial engineersfor tackling quality control problems effectivelyand economically. Research has shown that theapplication of ED by industrial engineers is limiteddue to lack of skills in manufacturing and lack ofstatistical knowledge. The paper illustrates thecognitive gap in the knowledge required by indus-trial engineers for understanding the potentialbenefits of this powerful-problem solving tech-nique. The purpose of this paper is to bridge thisgap by illustrating a simple experiment which canbe easily carried out in a room to teach experi-mental design techniques to engineers. In order tokeep the experiment simple, all the control para-meters were studied at 2-level. The authors believethat control parameters at 2-level will form a firmfoundation for studying the parameters at 3-leveland higher. The results of the experiment hasprovided a greater stimulus for the wider appli-cation of ED by industrial engineers in real-lifesituations.

AcknowledgementsÐThe authors would like to thank twoanonymous referees for their valuable and useful commentson an earlier draft of this paper.

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Jiju Antony is a Research Fellow with the Portsmouth Business School, University ofPortsmouth. He received a BE in Mechanical Engineering from the University of Kerela,South India, M.Eng.Sc. in Quality and Reliability Engineering from the NationalUniversity of Ireland and a Ph.D. in Quality Control for Manufacturing from theUniversity of Portsmouth. He has published over 25 refereed papers in the areas ofreliability engineering, design of experiments, Taguchi methods for improving processquality, robust technology development and problem solving using quality tools andtechniques. Dr Antony has applied design of experiments and Taguchi methods in morethan five manufacturing companies.

Nick Capon is a Senior Lecturer with the Portsmouth Business School. His researchinterests are in the areas of operations management and quality management, with currentresearch into business process re-engineering and risk management. He has an industrialbackground as a manufacturing manager, including experience in materials managementand systems analysis in aerospace engineering and electronics. He has published over 10articles.


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