Doe: Cupcake Height

PROJECT REPORT


ANALYSIS OF FACTORS AFFECTING CUPCAKE HEIGHT









FOR
DR. D.C. MONTGOMERY

IEE 572





TEAM 12
CELESTE NULL
JIUN-YAN SHIAU
KATINA SKINNER
CHII-LIANG WEE
TABLE OF CONTENTS


ABSTRACT 3


Introduction 1


Response Characteristics 1


Factors and Factor Levels 1


Recipe for Chocolate Cupcakes 2


Measurement 2


ExperimentalDesign 3

Linear Model 3
Quadratic Model 4

Experimental Conditions 4


Results 4

Linear Model 4
Quadratic Model 6

Residual Diagnostics 10


Standard Deviation of Cupcake Height as a Response 13


Time to Spoilage of Cupcake as a Response 14


Conclusions and Recommendations 14


References 15





List of Figures


TABLE 1. HIGH AND LOW LEVELS FOR EACHFACTOR 1
Table 2. Uncontrollable Factors and Methods to Avoid Data Contamination 2
Table 3. Summary of Experimental Design 3
Table 4. Matrix Design for Linear Model 3
Table 5. Aliasing Pattern of Linear Design 3
Table 6. Matrix Design for Axial Points 4
Table 7. Screening Design Height Results 5
Table 8. ANOVA for the Full Linear Model 6
Table 9. Matrix for Addition of Axial Runs 7Table 10. ANOVA for the Full Quadratic Model Predicting Heigh 7
Table 11. Coefficients and Effect Significance 8
Table 12. ANOVA for the Partial Quadratic Model (A, C and A2 included) 8
Table 13. Coefficient Estimates for Partial Quadratic Model 8
Table 14. ANOVA for the Quadratic Model Predicting Standard Deviation 13
Table 15. Coefficient Estimates for Quadratic Model PredictingStandard Deviation 13

Figure 1. Half Normal Probability Plot of Height Effects 5
Figure 2. Effect Plot of Factor A 6
Figure 3. Contour Plot 9
Figure 4. Response Surface Plot 9
Figure 5. Normal Probability Plot of Residuals 10
Figure 6. Residuals vs. Predicted Value 11
Figure 7. Residuals vs. Run Number 11
Figure 8. Residuals vs. Temperature (Factor A) 12
Figure 9. Residuals vs. Milk(Factor C) 12
Figure 10. Response Surface Plot for Standard Deviation Model 14


Abstract

Two phases of experimental design were conducted to determine the factors and factor settings that affect cupcake height and standard deviation of cupcake height. The factors studied were the baking temperature, the amount of baking powder, the amount of milk, and the amount of baking soda. Thefactor levels are shown in the table below.

|Factor |Low Level |Center Level |High Level |
|Oven Temperature |275( |350( |425( |
|Baking Powder Amount |( teaspoon |( teaspoon|¼ teaspoon |
|Milk Amount |( cup |5/12 cup |( cup |
|Baking Soda Amount |( teaspoon |1 ¼ teaspoon |2 teaspoons |

The first phase of experimentation was a fractional factorial 24-1 with one replication. Theresults of this phase showed that the model had curvature. As a result, the second phase that was conducted was six axial points set in the face of the original cube. Results from the second phase produced a model to predict the average height of the cupcakes in a batch. The model to predict the standard deviation was not significant. This height equation involves the oven temperature and theamount of milk and is shown below.

y-hat = 4.24 + 1.39*temperature + 0.55*milk - 1.22*temperature2

Temperature at the median level and milk at the high level should be used to produce the maximum cupcake height. Using the average standard deviation from all the runs, a three-sigma prediction interval was calculated to be plus or minus 0.33 centimeters. Using the equation for maximum...