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MANE 6313 - Design of Experiments

RSM Project Assignment

Assignment Date: April 28, 2025

Due Date: May 15, 2025 (no late submissions)

Purpose

This project allows you to demonstrate your mastery of the principles of statistics and design of experiments by implementing a response surface methodology (RSM) project. This project includes all of the stages of an RSM project: screening design, method of steepest ascent/descent, second-order modeling and graphical analysis and optimization.

Process Description

You are to investigate the performance of an injection-molding machine used in the manufacturing operations of the Mouse Factory. The response (output) variable is percentage molding shrinkage. Ideally, shrinkage should be minimized.

The range of settings for each factor is shown below. For safety reasons, the plant can not be operated above the upper range or below the lower range. Range checking is not performed and it is the experimenter's responsibility to ensure that settings do not exceed the tabled minimum or maximum values.

Variable Settings
VariableMinimum ValueMaximum ValueUnits
Melting Temperature440460degrees F
Injection Speed595%
Injection Pressure11001500psi
Holding Pressure400600psi
Holding Time1040seconds

Assignment

You are to conduct a complete response surface methodology analysis. The major steps in this analysis are:

  1. Initial setting analysis,

  2. Fractional factorial design and analysis,

  3. Improved setpoint from fractional factorial analysis,

  4. Steepest descent search for optimal region,

  5. 2nd order experimental design and analysis

  6. Optimal setpoint from 2nd order experiment, and

  7. Comparison of initial, improved and optimal setpoints.

Initial Setting Analysis

Your analysis should contain three major components: a graphical analysis of shrinkage, a numerical summary of shrinkage and predictions of future performance of shrinkage in both a point estimate and interval estimate (with appropriate significance level).

Fractional Factorial Design and Analysis

You are to design and analyze a fractional factorial design. You may select from a one-half or one-quarter fraction (the one-half fraction is easier to analyze). You are allowed to manipulate each factor plus or minus 10% of its range from the value of its starting point. The value of the starting point will be provided in the web-based application.

Improved Setpoint from Fractional Factorial Analysis

Clearly identify the important variables found in your fractional factorial analysis and present an optimal setpoint from one of your experimental treatments that minimizes shrinkage. Your setpoint analysis should contain three major components described in the initial setting analysis section.

Utilize the steepest descent search to find a region to conduct a second order response surface design. Start from the experimental treatment that minimized shrinkage in the fractional factorial experiment. Your report should contain a table showing the experiments conducted and the values of shrinkage observed. Identify a region to conduct a second order design of experiments.

2nd Order Experimental Design and Analysis

Identify an appropriate second order experimental design and perform an analysis in the region identified by the steepest descent search. Your initial model should be a full quadratic and you should find the model that best describes your data. Identify the characteristics of the response surface using graphical techniques and suggest an optimal setpoint to minimize shrinkage.

Optimal Setpoint Analysis

This section should analyze the setpoint found from the second order experiment. Your analysis should include the three components mentioned in the initial setting analysis section.

Comparison of Initial, Improved and Optimal Setpoints

Your response surface analysis project investigates three setpoints: the initial setting, an improved setting from the fractional factorial design and an optimal setting from the response surface methodology. Prepare a graph that displays all three sets of data. Construct a table containing summary statistics from the three samples displaying important statistics. Perform a hypothesis test to determine if there are any differences in the three settings. If possible, utilize a means separation technique.

Deliverables

You are to provide the following deliverables by the deadline:

  • A professional, type written technical report. All data used for analyses should be included in appendices (at the end of the report)

  • An analysis of the initial setting,

  • Fractional factorial design and analysis,

  • An analysis of the improved setting found from the fractional factorial analysis,

  • A description of the steepest descent search,

  • Second order design and analysis

  • An analysis of the setting found in the second order experiment,

  • A comparison of the three settings

To assist you in completing this assignment, the rubric for this assignment is available and a report guide is also available.

Resources

The following resources are available to help complete the RSM Project:

Note: the overview video for the RSM project references Minitab. You are to perform all analysis using R Markdown instead of Minitab.