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7/29/2019 Quality Assurance Project
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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.