PowerPoint Presentation
1/8/2017Ronald Morgan Shewchuk1Manufacturing processes can be
complex, with multiple inputs, outputs and measurement systems
collecting real-time data.This results in a plethora of information
being available from the factory floor.Process data can be
downloaded from plant data historian logs.Measurement data can be
downloaded from laboratory data bases.But how to differentiate the
important factors from the less important factors?And how can we
build a modeling equation which will allow us to optimize our
process for a particular Key Process Output Variable
(KPOV)?Response surface regression analysis is well suited to the
evaluation of historical data, sometimes referred to as data
mining. It involves grouping your data into a series of columns
which represent the input variables (KPIVs) and the output
variables (KPOVs) which you want to investigate. This approach
avoids the costs of material losses and/or downtime which can occur
during structured Design of Experiments (DOE)The data is free since
it is part of your historical process/product records.We will use
the batch chemical reaction data of Case IX to understand the steps
required in conducting a response surface regression analysis.
Response Surface Regression
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Response Surface Regression1/8/2017Ronald Morgan Shewchuk2Case
Study IX: Response Surface Regression Analysis of Batch Chemical
ReactionAmy Liang is excited to be the project manager of a new
specialty chemical plant in Chengdu. The commissioning of the plant
has gone well but the European headquarters is puzzled why the
yields are significantly below those of the Belgium plant for which
the Chengdu plant was based upon. Amy has decided to review the
historical data using response surface regression. The historical
batch data has been compiled along with four factors which Amy
thinks are important to the yield reaction temperature, reaction
time, agitation speed and catalyst concentration. Refer to Figure
8.19.
Figure 8.19 Historical Batch Yields - Chengdu
Response Surface Regression
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Response Surface Regression1/8/2017Ronald Morgan Shewchuk3Amy
first graphed the effect of the individual four factors on yield in
Figure 8.20.
Figure 8.20 Effect of Temperature, Reaction Time, Agitation
Speed and Catalyst Concentration on Yield
Response Surface Regression
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Response Surface Regression1/8/2017Ronald Morgan Shewchuk4There
appears to be an optimum reaction temperature at which the yield is
maximized but there is no clear relationship between yield and
reaction time, agitation speed or catalyst concentration. Amy
proceeded to conduct the response surface regression
analysis.Figure 8.21 Steps for Response Surface Regression
Analysis
Open a new worksheet in Minitab. Copy and paste the reactor
batch data into the worksheet.
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Click on Stat DOE Response Surface Define Custom Response
Surface Design on the top menu.
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Select C2 Reaction Temperature (C), C3 Reaction Time (min), C4
Agitation Speed (RPM) and C5 Catalyst Conc. (moles/l) for the
Factors field in the dialogue box. Click Low/High.
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Click the radio toggle button for Uncoded data in the dialogue
box. Minitab will scan the factors and select the low and high
values respectively for each factor under consideration. Click OK.
Then click OK one more time.
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Notice that Minitab has added four columns entitled StdOrder,
RunOrder, Blocks and PtType. This is to facilitate the Design of
Experiment (DOE) analysis of the historical data set.
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Click on Stat DOE Response Surface Analyze Response Surface
Design on the top menu.
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Select C6 Yield (%) for the Response field in the dialogue box.
Select the radio toggle button for uncoded units. Click Terms.
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Select Linear for the terms to be included in the regression
analysis. This is the simplest model. Amy resists the temptation to
include all quadratic terms and interactions at this point. Click
OK.
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Click Results.
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Select the radio toggle button for Coefficients and ANOVA table.
Click OK. Then click OK one more time.
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The session window indicates a poor fit for the regression
modeling equation (R-Sq = 20.70%). Press CTRL-E to return to the
previous dialogue box.
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Click Terms. Select Linear + squares for the terms to be
included in the regression analysis. This will include quadratic
(curvilinear) functions in the regression model. Click OK. Then
click OK one more time.
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Click Terms. Select Linear + squares for the terms to be
included in the regression analysis. This will include quadratic
(curvilinear) functions in the regression model. Click OK. Then
click OK one more time.
The goodness of fit is much improved (R-Sq = 88.89%).
Significant factors in the model are indicated by P-values below
0.1. Press CTRL-E to return to the previous dialogue box.
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Click Terms. Select Full quadratic for the terms to be included
in the regression analysis. This will include all squared factors
and two-way factor interactions (eg Factor A * Factor B) in the
regression model. Click OK. Then click OK one more time.
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The goodness of fit is only slightly improved (R-Sq = 90.15%).
Our reduced regression model should include only those terms with
P-values below 0.1. Thus, Amy focuses her attention on Reaction
Temp and Reaction Temp2. Press CTRL-E to return to the previous
dialogue box.
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Click Terms. Click