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    Preparation of Microwavable Popcorn

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    ACKNOWLEDGEMENT

    We wish to express our profound gratitude to Dr. Harrison Kelly III who gave us valuable

    support and inputs on a regular basis to complete this project successfully. We also thankUniversity at Buffalo for providing us this wonderful learning opportunity.

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    ABSTRACT

    There can be a lot of factors which can affect the output of this process. We have shortlisted this

    list of factors to twelve. The variation in the output can arise due to the process or due to the

    gage variability. Firstly we chose gauges and conducted a linearity study to find their range of

    applicability and their inherent bias. Then we had to perform a gauge repeatability and

    reproducibility study to verify whether the gage could differentiate between two different batches

    and whether it could give the same measurement for the same batch as well.

    Next step in the project was to conduct a study to find the significant factors and how they

    contribute towards the variation. The task in hand was to collect data in an efficient manner. We

    definitely were not going to do a 4096 runs to find the effects. We chose a design to minimize

    our data collection and effectively find how each factor affected the output. Thereon we obtain

    the model of our process.

    We analyze the model and optimize this model to give us the best settings required. As we havethis optimum setting we make sure whether the settings do lead to the best batch. We used to

    SPC to assign causes to variation in the output and used capability analysis to find whether our

    process was in control or not.

    Our model has been found to be adequate for this project. We have proceeded in performing this

    best batch and our process is in control. The variations have all been assigned causes. This

    project has given the precise understanding to tackle an industrial setting problem.

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    DEFINE

    Project scope and goal

    To achieve following three important responses:

    1) Increase the Volume of kernels

    2) Increase the Taste

    3) Decrease the number of unpopped kernels

    Project Charter

    Project DescriptionThe goal of the project is tomaximize the volume andnumbers of kernels popped as well as improve the taste

    Start and Completion

    date18

    thJan, 2011 to 28

    rdApril, 2011.

    Baseline MetricsKPOVs: Accuracy, repeatability, aesthetics of helicopter,features, conformance to standards, impact.

    Primary metrics Cost for making one helicopter

    GoalTo reduce the number of un-popped kernels and improve the

    taste and volume .

    Benefits

    Customer Better taste and more popped kernels per bag.

    Financial Increase in sales, profit, customer satisfaction

    Internal

    productivity

    More efficient design. Well defined approach, Teamdynamics, trouble-spots, and points of disagreement during

    this process.

    Phasemilestones

    Define Project Statement, Scope, Constraints.

    Plan Project &

    metrics

    Define KPOV, Identification of internal & external customers,

    duration of the project.

    Baseline

    Project

    Whether the process in control or not.

    MSA Data integrity, Gage R&R, Appropriate hypothesis Testing,

    Wisdom of

    Organization

    Process Flowchart, Cause and effect diagram,.

    Team Support

    Dr. Harrison Kelly III

    Aanjan Ravi

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    Ashwin Santhanam

    Karthik Thirukonda Viswanath

    Krishna NG

    Prabhakar Narayanaswamy

    Sabh arish Murali

    Srihari Sankararaman

    Surendar Soundararajan

    Vikram Thuruvas Dinakaran

    Yuvaraj Kondaswamy

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    MEASURE

    The end product variation can be explained by process variation or measurement gage variation.

    To quantify the variation due to gage we conduct a Gage Repeatability and Reproducibility(GR&R) study and a Gage Linearity study. By doing such a study we can measure the bias

    present throughout the range of operation. We also measured the applicability of the gage

    throughout the range and verify whether the gage is sufficient for the sake of this project.

    In this phase we look into the Gage Measurement Variation. We can have many operators who

    measure taste, volume and count of un-popped kernels for a process. There can be measurement

    differences between the values given by each operator for the same batch of popcorn. Thus we

    have to standardize our measurement gage and define precisely the measurement gage for output

    parameters such as taste since taste palate could differ for each person. Also we need to find

    whether the gage has no discrepancies throughout the range.

    The gages that we used were measuring jar, normal counting and human palette.

    Count:

    For Count we measure the number of un-popped kernels. We make a batch of popcorns and then

    pick out all popped corn and slightly popped kernels and then count all thats left out.

    Volume:

    For Volume we measured the volume of all popped kernels. We had a glass beaker with least

    count of 1ml. We assumed that the highest point in the surface would be the volume of popped

    kernels.

    Taste:

    For the taste of the kernels, we pre-decided on a scale. This scale was based on how much the

    batch was cooked.

    Taste Measurement

    1 Not cooked

    2 Slightly cooked

    3 Perfectly cooked

    4 Slightly overcooked

    5 overcooked

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    Gage Linearity Study

    In order to find the performance of the gage we perform the Gage Linearity study. To explain we

    use Count .

    From the graph layout we can see that the p-value for Bias is less than 0.05. Therefore we reject

    the null hypothesis that the bias is equal to zero. This means we have some bias and this can be

    seen from the graph. Its evident that we are counting less than the master value (i.e. most precise

    value) as the count increases. Likewise we also see the p-value for constant and slope is

    insignificant.

    For Volume:

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    For Taste:

    Gage Repeatability and Reproducibility (GR&R):

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    Now that we know that the gage can measure accurately within a small degree of error we need

    to verify whether the gage can identify between two different batches. It should accurately

    differentiate between the batches.

    To ensure that the gage does differentiate between batches, we perform a GR&R study.

    Gage R&R Study - ANOVA Method

    Two-Way ANOVA Table With Interaction

    Source DF SS MS F P

    Parts 9 5385.15 598.350 2626.90 0.000

    Operator 2 0.23 0.117 0.51 0.608

    Parts * Operator 18 4.10 0.228 0.02 1.000

    Repeatability 30 321.50 10.717

    Total 59 5710.98

    Alpha to remove interaction term = 0.25

    Two-Way ANOVA Table Without Interaction

    Source DF SS MS F P

    Parts 9 5385.15 598.350 88.2088 0.000

    Operator 2 0.23 0.117 0.0172 0.983

    Repeatability 48 325.60 6.783

    Total 59 5710.98

    Gage R&R

    %Contribution

    Source VarComp (of VarComp)Total Gage R&R 6.783 6.44

    Repeatability 6.783 6.44

    Reproducibility 0.000 0.00

    Operator 0.000 0.00

    Part-To-Part 98.594 93.56

    Total Variation 105.378 100.00

    Study Var %Study Var

    Source StdDev (SD) (6 * SD) (%SV)

    Total Gage R&R 2.6045 15.6269 25.37

    Repeatability 2.6045 15.6269 25.37

    Reproducibility 0.0000 0.0000 0.00

    Operator 0.0000 0.0000 0.00

    Part-To-Part 9.9295 59.5768 96.73Total Variation 10.2654 61.5922 100.00

    Number of Distinct Categories = 5

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    %Study gives how much of the total variability is due to each term. We can see the R&R% is25.37% which means this gage is marginally acceptable. In this gage we can see that most of the

    variation is coming from part to part meaning its recognizing the difference between each batch.

    This means that gage is performing well.

    Gage R&R for Count

    For Taste:

    Gage R&R Study - Nested ANOVA

    Gage R&R (Nested) for Taste

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    Source DF SS MS F P

    Operator 2 5.7333 2.86667 4.00000 0.030

    Parts (Operator) 27 19.3500 0.71667 1.38710 0.192

    Repeatability 30 15.5000 0.51667

    Total 59 40.5833

    Gage R&R

    %Contribution

    Source VarComp (of VarComp)

    Total Gage R&R 0.624167 86.19

    Repeatability 0.516667 71.35

    Reproducibility 0.107500 14.84

    Part-To-Part 0.100000 13.81

    Total Variation 0.724167 100.00

    Study Var %Study Var

    Source StdDev (SD) (6 * SD) (%SV)

    Total Gage R&R 0.790042 4.74025 92.84

    Repeatability 0.718795 4.31277 84.47

    Reproducibility 0.327872 1.96723 38.53Part-To-Part 0.316228 1.89737 37.16

    Total Variation 0.850980 5.10588 100.00

    Number of Distinct Categories = 1

    Gage R&R (Nested) for Taste

    For Volume:

    Gage R&R Study - ANOVA Method

    Two-Way ANOVA Table With Interaction

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    Source DF SS MS F P

    Parts 9 162508 18056.4 546.276 0.000

    Operator 2 31 15.5 0.469 0.633

    Parts * Operator 18 595 33.1 0.147 1.000

    Repeatability 30 6734 224.5

    Total 59 169868

    Alpha to remove interaction term = 0.25

    Two-Way ANOVA Table Without Interaction

    Source DF SS MS F P

    Parts 9 162508 18056.4 118.258 0.000

    Operator 2 31 15.5 0.102 0.904

    Repeatability 48 7329 152.7

    Total 59 169868

    Gage R&R

    %Contribution

    Source VarComp (of VarComp)

    Total Gage R&R 152.69 4.87

    Repeatability 152.69 4.87

    Reproducibility 0.00 0.00

    Operator 0.00 0.00

    Part-To-Part 2983.96 95.13

    Total Variation 3136.65 100.00

    Study Var %Study Var

    Source StdDev (SD) (6 * SD) (%SV)

    Total Gage R&R 12.3567 74.140 22.06

    Repeatability 12.3567 74.140 22.06

    Reproducibility 0.0000 0.000 0.00Operator 0.0000 0.000 0.00

    Part-To-Part 54.6256 327.754 97.54

    Total Variation 56.0058 336.035 100.00

    Number of Distinct Categories = 6

    Gage R&R for Volume

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    ANALYZE:

    The team started a screening test with all the variables to identify the significant factors. The

    alpha value was taken as 0.1.

    Fractional Factorial Design

    Factors: 12 Base Design: 12, 32 Resolution: IV

    Runs: 32 Replicates: 1 Fraction: 1/128

    Blocks: 1 Center pts (total): 0

    Factorial Fit: Unpopped versus Block, Kernel Type, Size, ...

    Estimated Effects and Coefficients for Unpopped (coded units)

    Term Effect Coef SE Coef T P

    Constant 88.05 1.123 78.37 0.000

    Block 7.10 1.086 6.54 0.000

    Kernel Type -8.08 -4.04 1.086 -3.72 0.004

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    Size -20.45 -10.22 1.123 -9.10 0.000

    Amount 49.43 24.71 1.123 22.00 0.000

    Type of NaCl -5.85 -2.92 1.123 -2.60 0.026

    Amt NaCl -5.82 -2.91 1.123 -2.59 0.027

    Cooking time -16.97 -8.49 1.123 -7.55 0.000

    Cooking Power -29.60 -14.80 1.123 -13.17 0.000

    Microwave -14.48 -7.24 1.152 -6.28 0.000

    Bag Venting 8.39 4.20 1.152 3.64 0.005Kernel Type*Size -26.52 -13.26 1.152 -11.51 0.000

    Kernel Type*Amount -9.14 -4.57 1.152 -3.97 0.003

    Kernel Type*Amt NaCl -12.14 -6.07 1.152 -5.27 0.000

    Kernel Type*Microwave 13.45 6.72 1.123 5.98 0.000

    Size*Type of NaCl 4.70 2.35 1.123 2.09 0.063

    Size*Bag Venting -14.04 -7.02 1.086 -6.46 0.000

    Amount*Amt NaCl 6.85 3.42 1.123 3.05 0.012

    Type of NaCl*Microwave -8.02 -4.01 1.152 -3.48 0.006

    S = 5.67962 PRESS = 2870.54

    R-Sq = 99.31% R-Sq(pred) = 93.83% R-Sq(adj) = 98.06%

    Analysis of Variance for Unpopped (coded units)

    Source DF Seq SS Adj SS Adj MS F P

    Blocks 1 2590.6 1379.3 1379.3 42.76 0.000

    Main Effects 9 36857.0 32616.0 3624.0 112.34 0.000

    Kernel Type 1 1461.7 446.4 446.4 13.84 0.004

    Size 1 2927.1 2671.1 2671.1 82.81 0.000

    Amount 1 22180.9 15611.2 15611.2 483.95 0.000

    Type of NaCl 1 3.6 218.3 218.3 6.77 0.026

    Amt NaCl 1 2.4 216.5 216.5 6.71 0.027

    Cooking time 1 985.5 1840.2 1840.2 57.05 0.000

    Cooking Power 1 5591.6 5596.6 5596.6 173.50 0.000

    Microwave 1 3703.9 1273.9 1273.9 39.49 0.000

    Bag Venting 1 0.2 427.9 427.9 13.26 0.005

    2-Way Interactions 8 6785.7 6785.7 848.2 26.29 0.000

    Kernel Type*Size 1 3079.7 4271.4 4271.4 132.41 0.000Kernel Type*Amount 1 127.3 507.8 507.8 15.74 0.003

    Kernel Type*Amt NaCl 1 522.7 895.7 895.7 27.77 0.000

    Kernel Type*Microwave 1 979.0 1155.2 1155.2 35.81 0.000

    Size*Type of NaCl 1 107.5 140.9 140.9 4.37 0.063

    Size*Bag Venting 1 1207.8 1347.5 1347.5 41.77 0.000

    Amount*Amt NaCl 1 371.2 299.4 299.4 9.28 0.012

    Type of NaCl*Microwave 1 390.5 390.5 390.5 12.11 0.006

    Residual Error 10 322.6 322.6 32.3

    Total 28 46555.9

    Unusual Observations for Unpopped

    Obs StdOrder num 3 Fit SE Fit Residual St Resid

    7 10 28.000 18.688 4.472 9.312 2.66R

    R denotes an observation with a large standardized residual.

    Estimated Coefficients for Unpopped using data in uncoded units

    Term Coef

    Constant 88.0478

    Block 7.10366

    Kernel Type -4.04116

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    Size -10.2231

    Amount 24.7144

    Type of NaCl -2.92276

    Amt NaCl -2.91057

    Cooking time -8.48526

    Cooking Power -14.7978

    Microwave -7.24085

    Bag Venting 4.19665Kernel Type*Size -13.2591

    Kernel Type*Amount -4.57165

    Kernel Type*Amt NaCl -6.07165

    Kernel Type*Microwave 6.72307

    Size*Type of NaCl 2.34807

    Size*Bag Venting -7.02134

    Amount*Amt NaCl 3.42276

    Type of NaCl*Microwave -4.00915

    Normal Probability Plot of the Residuals- the residuals appear to follow a straight line. No

    evidence of nonnormality, skewness, outliers, or unidentified variables exists.

    Residual Plots Residuals versus Fits- the residuals appear to be randomly scattered about zero.No evidence of nonconstant variance, missing terms, or outliers exists.

    Residual Plots Residuals versus Order-the residuals appear to be randomly scattered aboutzero. No evidence exists that the error terms are correlated with one another.

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    Main Effects plot for Count:The greater the difference in the vertical position of the plotted points (the more the line is not

    parallel to the X-axis), the greater the magnitude of the main effect. From the graph, we infer that

    the cooking time and cooking power are main effects which have major effect on count.

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    Factorial Fit: Taste versus Block, Kernel Type, Size, ...

    Estimated Effects and Coefficients for Taste (coded units)

    Term Effect Coef SE Coef T PConstant 2.6998 0.05791 46.62 0.000

    Block -0.1691 0.05947 -2.84 0.019

    Kernel Type -0.7868 -0.3934 0.05947 -6.61 0.000

    Size -0.2941 -0.1471 0.05677 -2.59 0.029

    Amount of fat 0.3578 0.1789 0.05791 3.09 0.013

    Type of NaCl 0.7255 0.3627 0.05791 6.26 0.000

    Cooking time 1.3505 0.6752 0.05791 11.66 0.000

    Cooking Power 0.6005 0.3002 0.05791 5.18 0.001

    Bag Venting 0.2328 0.1164 0.05791 2.01 0.075

    Kernel Type*Size -0.3578 -0.1789 0.05791 -3.09 0.013

    Kernel Type*Amount of fat 0.2941 0.1471 0.05677 2.59 0.029

    Kernel Type*Type of NaCl 0.9118 0.4559 0.05947 7.67 0.000

    Kernel Type*Cooking time 0.5368 0.2684 0.05947 4.51 0.001

    Kernel Type*Cooking Power 0.5368 0.2684 0.05947 4.51 0.001

    Kernel Type*Bag Venting 0.4191 0.2096 0.05677 3.69 0.005Size*Cooking Power 0.2941 0.1471 0.05677 2.59 0.029

    Size*Bag Venting 0.9118 0.4559 0.05947 7.67 0.000

    Amount of fat*Type of NaCl -0.4828 -0.2414 0.05791 -4.17 0.002

    Type of NaCl*Cooking Power -0.4755 -0.2377 0.05791 -4.11 0.003

    Cooking time*Bag Venting -0.4828 -0.2414 0.05791 -4.17 0.002

    S = 0.292424 PRESS = 8.16391

    R-Sq = 97.42% R-Sq(pred) = 72.66% R-Sq(adj) = 91.98%

    Analysis of Variance for Taste (coded units)

    Source DF Seq SS Adj SS Adj MS F P

    Blocks 1 4.9144 0.6915 0.6915 8.09 0.019Main Effects 7 9.9135 17.0273 2.4325 28.45 0.000

    Kernel Type 1 0.8107 3.7415 3.7415 43.75 0.000

    Size 1 0.1015 0.5739 0.5739 6.71 0.029

    Amount of fat 1 0.1897 0.8163 0.8163 9.55 0.013

    Type of NaCl 1 0.5545 3.3554 3.3554 39.24 0.000

    Cooking time 1 7.4419 11.6269 11.6269 135.97 0.000

    Cooking Power 1 0.7240 2.2988 2.2988 26.88 0.001

    Bag Venting 1 0.0911 0.3456 0.3456 4.04 0.075

    2-Way Interactions 11 14.2645 14.2645 1.2968 15.16 0.000

    Kernel Type*Size 1 0.5216 0.8163 0.8163 9.55 0.013

    Kernel Type*Amount of fat 1 0.0476 0.5739 0.5739 6.71 0.029

    Kernel Type*Type of NaCl 1 2.5106 5.0248 5.0248 58.76 0.000

    Kernel Type*Cooking time 1 0.4814 1.7415 1.7415 20.37 0.001

    Kernel Type*Cooking Power 1 0.6897 1.7415 1.7415 20.37 0.001

    Kernel Type*Bag Venting 1 0.6019 1.1654 1.1654 13.63 0.005Size*Cooking Power 1 0.2761 0.5739 0.5739 6.71 0.029

    Size*Bag Venting 1 5.5042 5.0248 5.0248 58.76 0.000

    Amount of fat*Type of NaCl 1 0.8760 1.4863 1.4863 17.38 0.002

    Type of NaCl*Cooking Power 1 1.2691 1.4413 1.4413 16.86 0.003

    Cooking time*Bag Venting 1 1.4863 1.4863 1.4863 17.38 0.002

    Residual Error 9 0.7696 0.7696 0.0855

    Total 28 29.8621

    Unusual Observations for Taste

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    Obs StdOrder Taste Fit SE Fit Residual St Resid

    13 8 4.00000 3.65931 0.24290 0.34069 2.09R

    R denotes an observation with a large standardized residual.

    Estimated Coefficients for Taste using data in uncoded units

    Term Coef

    Constant 2.69975

    Block -0.169118

    Kernel Type -0.393382

    Size -0.147059

    Amount of fat 0.178922

    Type of NaCl 0.362745

    Cooking time 0.675245

    Cooking Power 0.300245

    Bag Venting 0.116422

    Kernel Type*Size -0.178922

    Kernel Type*Amount of fat 0.147059

    Kernel Type*Type of NaCl 0.455882

    Kernel Type*Cooking time 0.268382Kernel Type*Cooking Power 0.268382

    Kernel Type*Bag Venting 0.209559

    Size*Cooking Power 0.147059

    Size*Bag Venting 0.455882

    Amount of fat*Type of NaCl -0.241422

    Type of NaCl*Cooking Power -0.237745

    Cooking time*Bag Venting -0.241422

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    Factorial Fit: volume versus Block, Kernel Type, Size, ...

    Estimated Effects and Coefficients for volume (coded units)

    Term Effect Coef SE Coef T P

    Constant 171.53 3.512 48.84 0.000

    Block -30.84 3.443 -8.96 0.000

    Kernel Type -27.69 -13.85 3.443 -4.02 0.003

    Size 27.93 13.96 3.512 3.98 0.003

    Amount 167.30 83.65 3.512 23.82 0.000

    Type of NaCl 34.20 17.10 3.512 4.87 0.001

    Amt NaCl 42.30 21.15 3.512 6.02 0.000

    Cooking time 61.57 30.79 3.512 8.77 0.000

    Cooking Power 145.45 72.72 3.512 20.71 0.000Microwave 61.08 30.54 3.607 8.47 0.000

    Bag Venting -40.30 -20.15 3.607 -5.59 0.000

    Kernel Type*Size 131.17 65.59 3.607 18.18 0.000

    Kernel Type*Amount 30.55 15.27 3.607 4.23 0.002

    Kernel Type*Amt NaCl 84.30 42.15 3.607 11.69 0.000

    Kernel Type*Cooking Power 23.69 11.85 3.443 3.44 0.007

    Kernel Type*Microwave -58.18 -29.09 3.512 -8.28 0.000

    Size*Type of NaCl -43.18 -21.59 3.512 -6.15 0.000

    Size*Bag Venting 47.32 23.66 3.443 6.87 0.000

    Amount*Amt NaCl -21.95 -10.97 3.512 -3.12 0.012

    Type of NaCl*Microwave 48.67 24.34 3.607 6.75 0.000

    S = 17.7361 PRESS = 27209.3

    R-Sq = 99.50% R-Sq(pred) = 95.18% R-Sq(adj) = 98.44%

    Analysis of Variance for volume (coded units)

    Source DF Seq SS Adj SS Adj MS F P

    Blocks 1 46207 25239 25239 80.23 0.000

    Main Effects 9 360491 348517 38724 123.10 0.000

    Kernel Type 1 805 5088 5088 16.18 0.003

    Size 1 2991 4972 4972 15.81 0.003

    Amount 1 126989 178435 178435 567.24 0.000

    Type of NaCl 1 240 7456 7456 23.70 0.001

    Amt NaCl 1 673 11408 11408 36.26 0.000

    Cooking time 1 10324 24170 24170 76.83 0.000

    Cooking Power 1 139413 134865 134865 428.73 0.000

    Microwave 1 78941 22548 22548 71.68 0.000Bag Venting 1 115 9816 9816 31.20 0.000

    2-Way Interactions 9 154420 154420 17158 54.54 0.000

    Kernel Type*Size 1 69447 104003 104003 330.62 0.000

    Kernel Type*Amount 1 4 5640 5640 17.93 0.002

    Kernel Type*Amt NaCl 1 27299 42953 42953 136.54 0.000

    Kernel Type*Cooking Power 1 1736 3725 3725 11.84 0.007

    Kernel Type*Microwave 1 14876 21576 21576 68.59 0.000

    Size*Type of NaCl 1 10127 11884 11884 37.78 0.000

    Size*Bag Venting 1 12173 14855 14855 47.22 0.000

    Amount*Amt NaCl 1 4438 3071 3071 9.76 0.012

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    Type of NaCl*Microwave 1 14320 14320 14320 45.52 0.000

    Residual Error 9 2831 2831 315

    Total 28 563949

    Unusual Observations for volume

    Obs StdOrder vol3 Fit SE Fit Residual St Resid6 9 290.000 318.309 14.267 -28.309 -2.69R

    R denotes an observation with a large standardized residual.

    Estimated Coefficients for volume using data in uncoded units

    Term Coef

    Constant 171.526

    Block -30.8401

    Kernel Type -13.8474

    Size 13.9632

    Amount 83.6507

    Type of NaCl 17.0993

    Amt NaCl 21.1507Cooking time 30.7868

    Cooking Power 72.7243

    Microwave 30.5386

    Bag Venting -20.1489

    Kernel Type*Size 65.5864

    Kernel Type*Amount 15.2739

    Kernel Type*Amt NaCl 42.1489

    Kernel Type*Cooking Power 11.8474

    Kernel Type*Microwave -29.0882

    Size*Type of NaCl -21.5882

    Size*Bag Venting 23.6599

    Amount*Amt NaCl -10.9743

    Type of NaCl*Microwave 24.3364

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    IMPROVE

    Response surface methodResponse surface methods are mainly used to examine the relationship between the factors

    and the response. These methods are usually employed after identifying the significant factor and

    when we want to find the ideal factor settings that will optimize the response. For thisexperiment we have created central composite half design with following characteristics:

    Five factors After pooling we did response optimizer for ten significant factors andfound optimal operating settings for all the ten factors. So in order to carryout response

    surface we just kept factors with Text as type constant throughout the experiment and wevaried the remaining five numeric factors.

    33 runs 2 blocks. The data is collected on two days; each day is a block Cube points: 16 Center points in cube: 6

    Axial points: 10 Center points in axial: 1

    Response Surface Regression: VOLUME versus Block, AMOUNT, COOKING TIME, ...

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    The analysis was done using coded units.

    Estimated Regression Coefficients for VOLUME

    Term Coef SE Coef T P

    Constant 156.229 15.85 9.859 0.000

    Block -3.342 15.60 -0.214 0.832

    AMOUNT 38.067 18.08 2.105 0.045COOKING TIME 49.867 18.08 2.758 0.011

    COOKING POWER % 34.437 16.21 2.125 0.044

    S = 77.4186 PRESS = 203304

    R-Sq = 37.70% R-Sq(pred) = 15.47% R-Sq(adj) = 27.73%

    Analysis of Variance for VOLUME

    Source DF Seq SS Adj SS Adj MS F P

    Blocks 1 2621 275 275.1 0.05 0.832

    Regression 3 88054 88054 29351.3 4.90 0.008

    Linear 3 88054 88054 29351.3 4.90 0.008

    AMOUNT 1 19068 26565 26564.6 4.43 0.045COOKING TIME 1 41920 45586 45586.0 7.61 0.011

    COOKING POWER % 1 27066 27066 27066.2 4.52 0.044

    Residual Error 25 149841 149841 5993.6

    Lack-of-Fit 9 55759 55759 6195.5 1.05 0.443

    Pure Error 16 94082 94082 5880.1

    Total 29 240516

    Interpretation:

    Analyses of variance table shows the following:

    Blocks: data are collected on two consecutive days. The P-value of block 0.832(not less than

    0.05) indicates that block does not have significant effect on the response.

    Regression: The regression model is significant (0.008) which indicates that atleast one of the

    term in regression equation has significant effect on the mean response.

    Squared Effect: Squared term indicates whether or not there is curvature term in response

    surface. It is evident from the above results that there is no square term so there is no significant

    evidence of quadratic effect. So our model is Linear.

    Lack-Of-Fit: indicates the variation due to model inadequacy. The P-value(0.443) is not

    significant which indicates that we have not eliminated any important term from the model

    We followed the same procedure for both unpopped and taste.

    Response Surface Regression:UNPOPPED versus Block, AMOUNT

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    The analysis was done using coded units.

    Estimated Regression Coefficients for UNPOPPED

    Term Coef SE Coef T P

    Constant 76.236 3.637 20.963 0.000

    Block 2.396 3.611 0.664 0.513AMOUNT 22.720 4.192 5.420 0.000

    S = 18.0340 PRESS = 10713.1

    R-Sq = 52.12% R-Sq(pred) = 41.58% R-Sq(adj) = 48.57%

    Analysis of Variance for UNPOPPED

    Source DF Seq SS Adj SS Adj MS F P

    Blocks 1 4.3 143.2 143.2 0.44 0.513

    Regression 1 9554.1 9554.1 9554.1 29.38 0.000

    Linear 1 9554.1 9554.1 9554.1 29.38 0.000

    AMOUNT 1 9554.1 9554.1 9554.1 29.38 0.000

    Residual Error 27 8781.1 8781.1 325.2Lack-of-Fit 2 226.3 226.3 113.1 0.33 0.722

    Pure Error 25 8554.8 8554.8 342.2

    Total 29 18339.5

    Response Surface Regression: TASTE versus Block, aMOUNT OF FAT

    The analysis was done using coded units.

    Estimated Regression Coefficients for TASTE

    Term Coef SE Coef T P

    Constant 3.1532 0.1742 18.100 0.000

    Block -0.1802 0.1742 -1.034 0.310

    aMOUNT OF FAT 0.4336 0.1825 2.376 0.025

    S = 0.874260 PRESS = 24.8327

    R-Sq = 20.22% R-Sq(pred) = 4.00% R-Sq(adj) = 14.31%

    Analysis of Variance for TASTE

    Source DF Seq SS Adj SS Adj MS F P

    Blocks 1 0.9143 0.8174 0.8174 1.07 0.310

    Regression 1 4.3155 4.3155 4.3155 5.65 0.025

    Linear 1 4.3155 4.3155 4.3155 5.65 0.025

    aMOUNT OF FAT 1 4.3155 4.3155 4.3155 5.65 0.025

    Residual Error 27 20.6369 20.6369 0.7643

    Lack-of-Fit 3 1.6429 1.6429 0.5476 0.69 0.566

    Pure Error 24 18.9940 18.9940 0.7914

    Total 29 25.8667

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    Response Optimization:Response optimization is used in product development to determine the optimal operating

    condition that will result in product with desirable properties.

    Response Optimization

    Parameters

    Goal Lower Target Upper Weight Import

    VOLUME Maximum 20 100 100 1 1

    TASTE Target 2 3 4 1 1

    YNPOPPED Minimum 100 100 110 1 1

    Global Solution

    AMOUNT = 0.5

    COOKING TIME = 3.875aMOUNT OF FAT = 5.94019

    COOKING POWE = 100

    Predicted Responses

    VOLUME = 248.702 , desirability = 0.65802

    TASTE = 3.000 , desirability = 1.000000

    UNPOPPED = 30.795 , desirability = 0.94698

    Composite Desirability = 0.85413

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    Using this optimized factor setting we manufactured 20 optimal batches and assessed its

    performance using SPC.

    CONTROL

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    As we have performed sufficient modeling and having optimized the process of popcorn making,

    our obvious next step is to control the process output. Control is critical to our project since we

    need the process to give products which vary less compared to each other.

    In order to control our process output we resort to Statistical Process Control.

    Initially we verify whether the dataset is normally distributed. This can be verified by

    performing a normality test. For taste, we found that the p-value is less than 0.005 indicating that

    the dataset is not normally distributed. We can also verify from the plot if the red spots are not

    closely spread about the line. If the red spots lie similar to blue line we can confirm normality.

    Our dataset was found to be non-normal. Therefore we correct for this non-normality by

    performing a Box-Cox transformation using lambda value to be zero. By taking zero for lambda

    we perform a natural logarithmic transformation.

    From the above Capability analysis and Capability six pack we can find that we can find that we

    attain a mean of 3 within the range of 1-5. The standard deviation was found to be 0.1974. We

    find our within (0.561565) std Deviation to be very close to their overall standard deviation

    (0.561951). Our Cpk value was found to be 0.89 which means most of our outputs meet

    requirements. Cpk value should be equal or more than unity. From our value of 0.89 we all infer

    that we have scope for little improvement.

    We need to infer the R-chart first and then the X-bar chart. Both suggest that the process is in

    control since they dont exceed the lower and upper control limits. Our R-chart says that the

    differences within subgroups consistent. The X-bar says that the subgroup averages vary within

    limits.

    Volume:

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    Count:

    Sampling Plan for SPC:

    We perform SPC to assign cause to variation. We need a sampling plan to perform a SPC study.

    The idea behind sampling plan is to detect shift in the process. This shift could be in short or in

    the long run.

    Our plan was to make a big batch of input mixed kernels. For the batch we added all the raw

    materials (kernels, fat, salt etc) together. Then we mixed all these together to make it as

    homogeneous as possible. Then we would take half tbs measure of kernels and make our

    batches. We used two similar microwaves and produced our output. This was to assign the cause

    for within and between subgroups. Microwave should be the cause for within subgroup variation.

    Batch preparation should be the cause for between subgroup variations.

    Our subgroup size is two. We performed the study in two batches: one of 5runs and one of 15

    runs. This helps us to verify the shifts in the short and long runs. By doing such a sampling plan

    we can assign causes to variation arising due to microwave and due to mixing.

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    Conclusion:

    The process optimization was done to get the best cooked, maximum volume and least count

    of un-popped kernels. The optimum condition was taken as 100% microwave power, cookingtime of 3.8mins, amount of kernels was a half teaspoon and amount of butter was 6%. This led to

    a taste of 3, un-popped count of 13 and volume of 182ml. Therefore we have shown that our

    model is satisfactory. Our process seems to be in control and all the variability seems to arise

    from within the subgroups. If we are not constrained by time, cost and man power we can

    probably have a much more efficient design.

    References:

    Montgomery, D.C, Design and Analysis of Experiments. Ed. 5 th. John Wiley and Sons. Montgomery, D.C, Statistical Quality Control. Ed. 5th. John Wiley and Sons. http://www.isixsigma.com/library/downloads/charter.pdf Jaspreet Singh, N. S. (1999). Effects of different ingredients and microwave power on

    popping characteristics of popcorn.Journal of Food Engineering.