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MANE 6313 - Design of Experiments

Response Surface Methodology Project Report Guide

Report Guide Purpose

This report guide is intended to provide additional information to enable students to write better project reports. Before reading this guide, please print the RSM Project Report Assignment and RSM Project Rubric and read these documents carefully before reading this report guide.

Technical Report Purpose

The Response Surface Methodology offers students the opportunity to perform a complete response surface methodology project and evaluate the effectiveness of the project. The major phases of the project include analysis of the initial setting, performing a fractional factorial design, conducting a steepest descent search, implementing a second order experimental design and analysis of set points.

Technical Report

You are to prepare a technical report. There are several implications and rules involved with writing a technical report. The first implication is that you will submit your report as a single file prepared using a word processing software program. The second implication is that your report should follow the structure of the rubric. Adding an introductory and concluding section to the topics listed in the rubric will create an excellent report (and likely increase your grade). Consider the writing rules:

A final request is to submit your report as a single pdf file. Often there are problems opening equations created in Microsoft Word on different computer platforms.

Initial Setting Analysis

This section should analyze the initial setting for the RSM project provided by the web-based application. A description of the sample size selected should be provided. The sample size should be large enough to be statistically valid but not be overly large. The analysis of the initial setting should contain three components. The first component is a graphical analysis that provides information regarding the characteristics and shape of the data. The second component is a statistical analysis of the initial setting data. The final component is the prediction of future values of shrinkage in both a point estimate and interval form. The interval estimate of future values of shrinkage should clearly state the significance level used in the interval construction.

Fractional Factorial Design and Analysis

The second portion of the report describes the design and analysis of a fractional factorial experiment. You may select either a one-half or one-quarter fraction (I personally think that it is easier to analyze the one-half fraction). You may set the values of each factor to be the initial setting plus or minus ten percent of the range of that factor. One of the goals of this section is to determine which factors are important and which factors are not important. Clearly describe the final model found from your analysis of the fractional factorial design. Your data for the design should be included in an appendix at the end of the report.

Fractional Factorial Setting

Using the final model from the previous section of your report, clearly identify a new setting that will reduce shrinkage. The new setting must be one of the experimental treatments from the fractional factorial design. Perform an analysis of the new setting following the procedure described in the Initial Setting Analysis section. Please ensure that a graphical analysis, summary statistics and prediction of future values of shrinkage in point and interval forms are provided.

Once a reduced set of variables is found from the analysis of the fractional factorial design, an improved operating region must be identified. The method of steepest ascent/descent is commonly used for this purpose. An excellent model for this analytical approach is found in Example 11.1 of Montgomery's Design and Analysis of Experiments. A table similar to the one shown in Table 11.3 on page 495 should be constructed. Please ensure that all variables stay within their defined ranges. Also the values for the response variable should be taken from the web-based simulator and not the fractional factorial model. An optimal operating region should be found in the steepest descent search.

Second Order Design and Analysis

Once an optimal region is found, a second order design (CCD or Box-Behnken) should be employed. Care must be exercised in selecting the factor settings so that the safety limits for each factor are not violated. Consider using your optimal point plus or minus fifteen to twenty percent of the rage of each factor. Your analysis of the 2nd order model should include refining the model, employing graphical analysis to describe and characterize the response surface and the identification of a new setting.

Second Order Setting Analysis

Use the optimal setting found from your second order analysis. Perform an analysis of the new setting following the procedure described in the Initial Setting Analysis section. Please ensure that a graphical analysis, summary statistics and prediction of future values of shrinkage in point and interval forms are provided.

Comparison of Initial, Improved and Optimal Setting

Your RSM project has identified three settings: an initial setting, a setting from the fractional factorial and a final setting from the RSM model analysis. Present a graphical analysis of the three settings that shows the characteristics and shapes of the distribution for each setting on a single graph. Prepare a table containing the summary statistics for the three settings and discuss your findings. Finally perform a statistical test of hypothesis to determine if the three settings have the same mean shrinkage values. This is best implemented as a one-way analysis of variance. If possible, utilize a means separation technique to determine which settings are statistically difference from each other.