STATISTICAL TOOLS FOR PROCESS IMPROVEMENT

1 PI QUALITY July / August 1993 (revised 2/98 by MJA) z:originals/flyers/popcorn

Applying DOE toMicrowave Popcorn

Design of experiments identifies which factors matterand which ones dont, as well as helping

find optimal settings.BY MARK J. ANDERSON and HANK P. ANDERSON

ook it hot enough, not too long, anda little bit off the floor of the oven.And preheating the oven by heating

a glass of water for 1 min. has no effect.Dont even bother.

Those were the conclusions we madefrom applying the design of experiments(DOE) technique to the problem ofpreparing microwave popcorn. The studywas conducted at home, using a commonmicrowave oven designed for the cons-umer market. Since the study examinedsomething with which everyone has some

Table 1: Factors and LevelsFactor Low

(-)High(+)

Price Generic BrandTime 4 min. 6 min.Power Medium HighPreheat No YesElevate No Yes

experience, it provides a good examplefor understanding how to apply DOE inadjusting process industry recipes.

In particular, cooking microwave pop-corn demonstrated how DOE helps applythe Pareto principle. In other words, ithelps to identify what Juran calls the vitalfew factors from among the trivial many.

Independent variablesTo begin, a brainstorming session was

held to identify all possible factors thatcould be studied as independent variables.For this study, five major factors wereselected from a broader range of ideas.The five factors were brand, cooking time,microwave oven temperature, preheattime, and tray elevation.

The idea for the study grew out of thelast two factors. A quick study of micro-wave popcorn instructions at the local su-permarket showed that all packages pret-ty much say the same thing. The instruc-tions advise that the consumer perform a

range-finding operation, cooking the pop-corn pouch for 2-5 min. on a high settinguntil the rate of popping subsides to aninterval of about one pop every threeseconds.

Two unusual instructions caught ourattention. One involved having the mi-crowave bag resting on a microwave-saferack at about the center of the chamber, asopposed to resting on the floor of theoven. The second involved the pre-heatingstep. One of these unusual factors didinfluence the results, the other didnt.

Our study was designed around a two-level factorial model. Some of the factorswere by their nature discrete and binary;others were continuous. All variables hadonly two values. To limit the continuousvariables, range-finding trials wereconducted to set low and high levels foreach of the experiments.

During some of the range-finding runs,the popcorn was seriously over-

DESIGN-EASE PlotUnpopped

A: BrandB: Time C: SettingD: PreheatE: Elevation

Nor

mal

% p

roba

bilit

y

Normal plot

Effect

-0.95 -0.66 -0.37 -0.08 0.21

1

510

2030

50

7080

9095

99

ABC

E

DESIGN-EASE PlotTaste

A: BrandB: Time C: SettingD: PreheatE: Elevation

Nor

mal

% p

roba

bilit

y

Normal plot

Effect

-2.82 -1.95 -1.09 -0.22 0.64

1

510

2030

50

7080

9095

99

B

CBC

Figure 1: Analysis of unpopped kernels Figure 2: Analysis of taste

C

STATISTICAL TOOLS FOR PROCESS IMPROVEMENT

2 PI QUALITY July / August 1993 (revised 2/98 by MJA) z:originals/flyers/popcorn

cooked. A kitchen filled with smoke, wefound, was a small price to pay for theeducation gained.

The brand factor was selected basedon the central intent of the study, todetermine if there is a strong correlationbetween the quality of the finished prod-uct and the price of the package on thegrocery store shelf. The brands testedwere selected to contrast a nationallydistributed big-name brand against a lo-cal grocery store (generic) brand ofmicrowave popcorn. The national brandwas purchased at $1.79 per package, thegeneric brand for $1.25 per package. (Acomplete listing of the two-level factorscan be found in Table 1.)

Most of these factors should be famil-iar to the reader. The preheating variablemay be unusual to some, so let us explainit in more detail. It was in fact a part ofwhat initially raised our curiosity.

The instructions on one package ofpopcorn that we had tried suggested thatusing a preheating step could increase theyield of the cooking process. If the occur-rence of corn that remains unpopped (wecall these bullets) is high, the instructionssuggested, the yield can be increased byoperating the oven with a glass of waterinside for a period of one minute.

Our question was, does this preheat-ing stepwhich also would raise thehumidity inside the ovenreally help?We shall see.

A statistically desirable array of com-binations of the low and high levels wasbuilt, for a total of 16 runs, half the totalnumber (32) of combinations possible.Such a fractional factorial design is suffi-cient to learn all we needed to know aboutpopping popcorn. In fact, making moreruns would not add to our know-ledge. Itis not necessary to run all 32 combinationsto study the interactions between factors.The runs were randomized to protect thestudy against lurking variablessuch aschanges in the environmentthat couldotherwise confound the study. To simplifythe administration of such a study, weused a Design-Ease software for designof experiments. It handled randomizingthe samples and the statistical analysis.

Table 2 shows the standard (Std)array for five factors and 16 experiments.It also shows the run order and observed

responses. To estimate pureerror, two repeat runs wereplanned. These extra exper-iments were meant to be run atmid-level (coded as zero) of thetime factor, with the otherfactors fixed at low (-) or high(+). However, the runs were notexecuted as planned. Also, onerun in the standard array wasbotched and another one wasmissed. The software accom-modated these accidental vari-ations, and they had no impacton the results.

Response analysis

To measure the effects of thevariable factors in each run,three response factors wereconsidered. First the unpoppedkernels (bullets) were weighedand the weight recorded. Like-wise, burnt popcorn was col-lected from each sample run andweighed. However, thisresponse turned out to be unreliable.

The third response - taste -wassubjective, but finding people willing toserve on a judging panel was not difficultin this case. Taste evaluations wererecorded using a scale from 1-10, with 10being high or good. Observed valuesranged from 1.0 to 9.0.

Observations from the 18 runs werethen entered in the Design-Ease package.The software calculated the effect eachindependent variable and combination ofvariables had on the responses.

What yield told usThe software automatically produced a

graph, called the normal plot of effects,that helped isolate the factors that werekey to determining the yield - thepercentage of unpopped bullets. Figures 1and 2 show the main effects and two-factor interactions for the two measurableresponses. The trivial many factors, whichhad no influence, fall on a straight linenear the zero effect level.

One of these factors was the pre-heating step (D). Preheating thus had noimpact the responses. This is an important

outcome because it means we dont haveto wait an extra minute for the popcorn.

The four remaining factors (brand,time, temperature, and elevation)significantly affected the bullets (seeFigure 1). Residual analysis by Design-Ease revealed the possibility that run 2was an outlier for bullets. This experimentproduced an unusually low amount ofpopcorn, but since no special cause couldbe attributed to this, and it did not greatlyaffect the findings, its included in theresults.

Figure 2 shows the normal plot ofeffects for the taste response. It reveals ahighly significant interaction between time(B) and power (C). The biggest effectcomes from the time alone, but its impactdepends on the level of power. As theinteraction plot in Figure 3 shows, whenthe time was limited to its low (-) level of4 minutes, the predicted taste responseswere roughly equal, around 7.5. (Thepoints fall within the 95 % confidenceleast significant difference barsdisplayed by the software.) With time setat its high (+) level of 6 minutes, however,the taste response varies significantlydepending on other factors

Table 3: Array of factors and responsesStd Run A B C D E Bullets Taste

1 12 -1 -1 -1 -1 1 1.5 7.52 9 1 -1 -1 -1 -1 1.4 8.03 6 -1 1 -1 -1 -1 1.9 9.04 18 1 1 -1 -1 1 0.6 6.55 1 -1 -1 1 -1 -1 1.8 7.06 14 1 -1 1 -1 1 0.3 7.57 7 -1 1 1 -1 1 0.2 2.58 5 1 1 1 -1 -1 0.9 1.09 17 -1 -1 -1 1 -1 1.7 7.0

10 15 1 -1 -1 1 1 0.8 6.011 3 -1 1 -1 1 1 0.6 4.512 16 1 1 -1 1 -1 0.9 4.013 4 -1 -1 1 1 1 0.6 9.014 13 1 -1 1 1 -1 1.3 7.515 NA -1 1 1 1 -1 Missing ---------16 NA 1 1 1 1 1 Missing ---------

x 2 -1 -1 -1 1 -1 3.2 8.5x 8 1 0 1 1 1 0.1 4.0x 11 1 0 1 -1 -1 0.8 5.0x 10 -1 0 1 1 -1 1.6 5.5

STATISTICAL TOOLS FOR PROCESS IMPROVEMENT

3 PI QUALITY July / August 1993 (revised 2/98 by MJA) z:originals/flyers/popcorn

- in this case, the temperature or setting ofthe microwave oven. When set on high,enough of the popcornburned to pull the tasteresponse value down tounder 2. Set on medium-high, taste responsedropped some-what lessto around 6.

With this infor-mation, we feel - thatpreheating the micro-wave oven is a waste oftime. On the other hand,elevating the pouch inthe oven is a good idea.No matter how powerfulyour home oven is,cooking microwavepopcorn at a high settingand for a shorter r