response surface regression

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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 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 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.



Response Surface Regression1/8/2017Ronald Morgan Shewchuk5

Click on Stat DOE Response Surface Define Custom Response Surface Design on the top menu.




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.




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.




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.




Click on Stat DOE Response Surface Analyze Response Surface Design on the top menu.




Select C6 Yield (%) for the Response field in the dialogue box. Select the radio toggle button for uncoded units. Click Terms.




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.




Click Results.




Select the radio toggle button for Coefficients and ANOVA table. Click OK. Then click OK one more time.




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.




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.




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.




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.




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.




Click Terms. Click

response surface regression

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