Popcorn Doe Project

Popcorn Experimental Design Project Author: Osagie Alli Objective The Objective of this Popcorn experiment is to apply a simple Design of Experiment technique to quantify the effects of four 4-variable factors at two 2-levels design on the amount of Un-Popped kernel (Response) generated during the experimental runs. This Data generated will provide valuable information on the main effects and interactions that are of statistical significance. These statistically significant effects and interactions can then be used to develop an empirical model that predicts the optimum response of the process and this model will optimise the number of un-popped kernels and so improve the yield of the popcorn in the process.

Method This design of experiment study was carried out at home using a regular microwave of 700watts. To get the experiment stated, I brainstorm on all possible factors to be considered based on the instructions on the popcorn bag label. Part of the instruction is to heat with oil in a pot at between 3-4 minutes at a high temperature setting and to add 2-3 spoons of oil to a handful of the popcorn kernel before cooking. Though the instruction suggested using a regular cooker, I personally then chose to apply a 4-Factor and 2-Level full factorial design to simulate the process in a microwave condition and to aim at determining the best operating conditions that will give optimum response of un-popped kernel and thus improve the yield of pop-corn produced. In this experiment, it is the un-popped kernel that is the response not the popped corn itself. Factors held Constant: 1. For all of the 48 experimental runs of each treatment combination, 50 kernels of Popcorn Brand Kelkin® were used throughout the experiment. 2. Microwave power used through the experiment is 700watts Nuisance Factor: 1. The nuisance factor considered significant for this experiment is the build up of residual temperature inside of the microwave over overtime during the experiment this is considered as a bias factor and to minimise its effects, Randomization of experimental combinations runs would have been best. unfortunately, I decided not to randomly select the treatment combinations and thus follow Minitab design simplified in Table 2, without randomisation, to compensated for this, I ensured that a time of cool down period of 5 minutes be applied between the start of each treatment combinations run.. Variable Factors and Levels Chosen: Table 1

Variable Factors A B C D

Microwave Temperature Run Time Cooking oil Microwave Bowl

2 Levels Low (-)

High (+)

Medium

High

3 mins

4 mins

2.5ml

5ml

Small

Large

Popcorn Experimental Design Project Author: Osagie Alli Equipment 1. 2. 3. 4. 5.

2 bags of Kelkin® Brand Popcorn Sun Flower cooking oil 4 Microwaveable heat resistant bowl and cover (small and large) A pack of 2.5ml and 5ml syringes to dispense the vegetable oil 700watts microwave oven

The experiment was designed around a 2-level and a 4-factor full factorial. Before the start of the experiment, a range finding trial runs were conducted to limit the continuous variables and thereby enable the setting of the low (-) and high (+) levels. During the range finding runs, the Popcorn kernels were either un-popped or over-popped and finally a suitable operating levels condition for all of the factors was chosen as in Fig 1. During the run of the 48 treatment combinations a full factorial design by Minitab as in Table 2 was followed. For illustration and assuming Run no.1, all of the factors were set at the low (-) levels, on completion, all the number of un-popped kernels were counted and recorded, an interval of 5-minutes was allowed to elapse before conducting the next Run No. 2. In the Run 2, factor A (Microwave Temperature) was set at the High (+) level and all other factors B, C, D were set at the low (-) level and at the end of the run, the number of unpopped kernel recorded. This was repeated for all of the 48 Runs allowing a 5 minutes interval between runs to allow the microwave temperature to equilibrate to room temperature and thus minimise any nuisance factor. On completing the first 16 Runs, the experiment was then replicated twice, given a total of 3 replicates through 48 experiments. The results of the main effects and interactions on the response are tabulated below.

Popcorn Experimental Design Project Author: Osagie Alli A Full Factorial 2-Level 4-Factors 3-Replicates Model: Popcorn Design of Experiment

Run

Treat ments

1

(1)

2

a

3

b

4

ab

5

c

6

ac

7

bc

8

abc

9

d

10

ad

11

bd

12

abd

13

cd

14

acd

15

bcd

16

abcd

FACTORS

INTERACTIONS

Replicates

A

B

C

D

AB

AC

AD

BC

BD

CD

ABC

ABD

ACD

BCD

ABCD

+ + + + + + + +

+ + + + + + + +

+ + + + + + + +

+ + + + + + + +

+ + + + + + + +

+ + + + + + + +

+ + + + + + + +

+ + + + + + + +

+ + + + + + + +

+ + + + + + + +

+ + + + + + + +

+ + + + + + + +

+ + + + + + + +

+ + + + + + + +

+ + + + + + + + +

I 46 29 15 12 22 16 14 5 37 14 13 5 34 18 17 3

II 39 17 24 11 21 13 14 9 38 13 16 8 31 26 21 3

III 37 33 28 11 34 17 13 9 38 19 18 13 37 14 17 1

TOTAL

122 79 67 34 77 46 41 23 113 46 47 23 102 58 55 7

Table 2: For this Popcorn Experiment, The above model was applied, though it would have been better to adopt a Randomizes Treatment Combinations approach to minimize the effect of the Nuisance factor arising from the residual heat in the microwave, I decided to to follow the above Treatment Combination model and have it Replicated at three different times after an hour internal on the same day.

Popcorn Experimental Design Project Author: Osagie Alli Results of Full Factorial Design: Full Factorial Design Factors: Runs: Blocks:

4 48 1

Base Design: Replicates: Center pts (total):

4, 16 3 0

All terms are free from aliasing.

Factorial Fit: UN-POPPED versus A, B, C, D Estimated Effects and Coefficients for UN-POPPED (coded units) Term Constant A B C D A*B A*C A*D B*C B*D C*D A*B*C A*B*D A*C*D B*C*D A*B*C*D

Effect -12.708 -14.292 -5.208 -1.458 2.708 0.958 -2.292 1.208 -1.042 4.375 -1.958 0.792 -1.292 -2.208 -2.208

S = 4.22049 R-Sq = 90.38%

Coef 19.646 -6.354 -7.146 -2.604 -0.729 1.354 0.479 -1.146 0.604 -0.521 2.187 -0.979 0.396 -0.646 -1.104 -1.104

SE Coef 0.6092 0.6092 0.6092 0.6092 0.6092 0.6092 0.6092 0.6092 0.6092 0.6092 0.6092 0.6092 0.6092 0.6092 0.6092 0.6092

PRESS = 1282.5 R-Sq(pred) = 78.35%

T 32.25 -10.43 -11.73 -4.27 -1.20 2.22 0.79 -1.88 0.99 -0.85 3.59 -1.61 0.65 -1.06 -1.81 -1.81

P 0.000 0.000 0.000 0.000 0.240 0.033 0.437 0.069 0.329 0.399 0.001 0.118 0.520 0.297 0.079 0.079

R-Sq(adj) = 85.87%

Analysis of Variance for UN-POPPED (coded units) Source Main Effects 2-Way Interactions 3-Way Interactions 4-Way Interactions Residual Error Pure Error Total

DF 4 6 4 1 32 32 47

Seq SS 4740.08 422.29 132.08 58.52 570.00 570.00 5922.98

Adj SS 4740.08 422.29 132.08 58.52 570.00 570.00

Adj MS 1185.02 70.38 33.02 58.52 17.81 17.81

F 66.53 3.95 1.85 3.29

P 0.000 0.005 0.143 0.079

Unusual Observations for UN-POPPED Obs 3 18 37

StdOrder 3 18 37

UN-POPPED 15.0000 17.0000 34.0000

Fit 22.3333 26.3333 25.6667

SE Fit 2.4367 2.4367 2.4367

Residual -7.3333 -9.3333 8.3333

St Resid -2.13R -2.71R 2.42R

R denotes an observation with a large standardized residual.

Popcorn Experimental Design Project Author: Osagie Alli Effects Plot for UN-POPPED

Effects Pareto for UN-POPPED

Effects B, A, C, CD and AB are the statistically significant effects.

Popcorn Experimental Design Project Author: Osagie Alli Discussion on Effects Plot: From the Full factorial estimated effects results above, and as shown in the Normal and Pareto standardized effects plots shows a total of 5 significant effects. From the analysed data, the significant main effects and interactions are A, B, C, C-D and A-B. These are the effects that has a P-value < 0.05%. The biggest effect is time (B) followed by the microwave temperature (A), the next significant effect is the vegetable Oil (C) and this is followed by the interaction effect Oil-Bowl size (C-D) and finally the Temperature-Time (A-B) interaction. A= Microwave Temperature B= Set Time C= Vegetable Oil A-B= Temperature and Time C-D = Vegetable Oil and Bowl All other effect and interactions as the experiment suggests based on the data obtained and analysed are insignificant. The interaction effects A-B is highly significant as the impact of time is dependent on the oven temperature and vice-versa. The effects plot also shows strong interaction between the Oil and pot size meaning that the effect of one is dependent on the other. Overall, the ANOVA shows 3 out of 4 of the main effects according to the p value< 0.05 are significant, 2 out of the 6 two-way interactions are significant. All of the 4-three way interactions and four-way interactions’ are not significant. The constant from the result table also shows to be significant. The constant term will always appear in any model develop in trying to predict the optimum conditions for improvement in number of un-popped kernel and signifies that we must include constant in all model design to optimise and improve the process conditions further. The ANOVA data below also highlighted the main effects: A B C and the 2 way interaction to be significant as P-value < 0.05. The 3&4 way interactions show no significant influence/effect.

Analysis of Variance Results: Analysis of Variance for UN-POPPED, using Adjusted SS for Tests Source A B C D A*B A*C A*D B*C B*D C*D A*B*C A*B*D A*C*D B*C*D A*B*C*D Error Total

DF 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 32 47

S = 4.22049

Seq SS 1938.02 2451.02 325.52 25.52 88.02 11.02 63.02 17.52 13.02 229.69 46.02 7.52 20.02 58.52 58.52 570.00 5922.98

Adj SS 1938.02 2451.02 325.52 25.52 88.02 11.02 63.02 17.52 13.02 229.69 46.02 7.52 20.02 58.52 58.52 570.00

R-Sq = 90.38%

Adj MS 1938.02 2451.02 325.52 25.52 88.02 11.02 63.02 17.52 13.02 229.69 46.02 7.52 20.02 58.52 58.52 17.81

F 108.80 137.60 18.27 1.43 4.94 0.62 3.54 0.98 0.73 12.89 2.58 0.42 1.12 3.29 3.29

P 0.000 0.000 0.000 0.240 0.033 0.437 0.069 0.329 0.399 0.001 0.118 0.520 0.297 0.079 0.079

R-Sq(adj) = 85.87%

Comment: The R-Sq adjusted indicates that 85.87% of the total variation has been accounted for. the P-Value from the ANOVA result shows that, main effects A, B, C are statistically significant even at 1% confidence limit, the 2-way interactions A*B and C*D are also statistically significant.

Popcorn Experimental Design Project Author: Osagie Alli Analysis of Variance for UN-POPPED, using Adjusted SS for Tests Source A B C D A*B C*D Error Total

DF 1 1 1 1 1 1 41 47

S = 4.59371

Seq SS 1938.02 2451.02 325.52 25.52 88.02 229.69 865.19 5922.98

Adj SS 1938.02 2451.02 325.52 25.52 88.02 229.69 865.19

R-Sq = 85.39%

Adj MS 1938.02 2451.02 325.52 25.52 88.02 229.69 21.10

F 91.84 116.15 15.43 1.21 4.17 10.88

P 0.000 0.000 0.000 0.278 0.048 0.002

R-Sq(adj) = 83.26%

The above shows the ANOVA for the main effects and Interaction effects. Factor D is not statistically significant. Response Graphs: Main Effect Plot

The main effects plot shows that factor A and B are the most statistically significant in terms of the response to these factors, both factors shows a magnitude in response at the high level settings. Factors C (oil) shows a slightly significant response at the high level while factor D shows negligible effect at the low level.

Popcorn Experimental Design Project Author: Osagie Alli Response Graphs: Interaction Plot

Response Graphs: Residual Plot

Popcorn Experimental Design Project Author: Osagie Alli Interaction Plot: The interaction plots shows that all the factors exacts some sort of effects on the response based on influences of interaction. All of the plots shows no parallel plots suggesting the presence of interaction effects. The degree of the interaction varies between factors. The interaction effect between C*D seemed more pronounced and most significant. The interaction between A*B also seemed significant. The interaction effects for both A*B and C*D are positive interaction as the influence of one factor on another significantly enhances response.

Residual Plots: In the normal Probability plot above, the normality assumption is not violated as the graph shows a straight line and the 50% percentile occurs at a residual value of approximately zero indicating that the normal distribution of the residuals are symmetrical about the mean. The assumption of equal variance is satisfied as the residuals are evenly spread about the mean Nu=0 The dot plot shows that data are scatted evenly about the mean, no unusual pattern such as funnel shape, concave or convex shaped as a result the equal variance assumption is satisfied. The independence assumption is satisfied as the run order plot shows no unusual pattern in the sequence of the positive and negative residual plot about the Nu=0

The Empirical Model: From the main effects plot and interactions plots, the statistically significant effects are A, B, C, A*B and C*D. The empirical model is one that will lead to having a lower response in the number of un-popped Kernel. To satisfy this purpose requires a model to optimise the process as follows Model is B(+), A(+), C(+), there is relative influence when D is operated at the High though its effect is not statistically significant yet it is a factor to recon with. As a result the empirical model is to operate the process with all settings at the high level.

Predicting the optimum response: Y= 19.646 + (-6.354)+ + (-7.146)+ + (-2.604)+ +(1.354)++ + (2.187)+++ Y = 19.646 – 6.354 – 7.146 – 2.604 + 1.354 + 2.187 Y=7 A confirmatory Run at the optimum condition based on the empirical model yielded 3 un-popped kernels.

Popcorn Experimental Design Project Author: Osagie Alli CONCLUSION: Popping Popcorn involves heating the corn until the pressure inside the kernel is great enough to cause it to burst, cooking oil surrounds and soften the kernel shell and provides the medium through which heat can be transferred to the inside of the corn. Results show that it is best to operate and make popcorn at the highest power setting, and at a high time. The impact of the interaction of time and power is greater than the single effect of individual factor. The full factorial design allows the estimate of all main effects, 2-factos and 3-factors interactions. Influences includes the normal variation in the popcorn, the operating environment, the effect of the residual heat on continuous use during the experimental run. The 5 largest effects A, B, C. A*B and C*D represents the vital few. The non parallel lines are characteristic of a powerful 2 two factor interaction.