Design of Experiments for Optimisation

Explore how a linear regression model relates cost to minutes talked, with y = beta0 + beta1 x; interpret the intercept and slope in this non-experimental example.

Fit a linear regression to experimental data, estimate beta_0 and beta_1 from pollution count and oxygen purity, using matrix notation and beta-hat, then evaluate the model in R-Studio.

Build a linear model in R to predict purity as a function of pollution count and interpret the regression output, including coefficients, t-tests, p-values, and R-squared.

Analyze the analysis of variance of the regression model, interpreting the F-statistic, df, and p-value to test whether the explanatory variable influences the response, with F=90.13, df=1 and 13, p=3.3e-7.

Build three residual plots against experimental results, predicted values, and the regression variable to confirm random residual distribution in the DoEOpt01 data.

Visualize experimental results with a scatter plot and regression line, interpreting the slope and intercept, and noting R-squared and the limits of validity outside the data range.

Explore multiple linear regression models that describe a single response variable using two or more explanatory variables, including interaction and quadratic terms, and learn the matrix-based estimation of coefficients.

Apply multiple linear regression to analyze designed and non-designed data. Use regression over ANOVA to handle missing observations, inaccurate factor levels, central points, and potential second-order models.

Explore 2^k factorial designs for screening multiple two-level factors, coding natural variables into x, and modeling responses with interactions to test linearity.

Add central points to a 2^k design to test linearity, partition residuals into pure error and lack-of-fit, and use an F-test to assess model adequacy.

Build a 2^3 design with central points in R using the RSM package, convert coded variables to natural variables, and save the design as a CSV for analysis.

Analyze a 2^3 design with central points in R, using the rsm package to model yield from coded xT, xP, xC and natural temperature, pressure, concentration.

Interpret a 2^3 design with central points by analyzing the regression model with coded variables, noting R-squared 0.9206, p-value, and that pressure yields 21.25% and temperature 11.25% increases.

Learn to handle designs with missing observations and inaccurate factor levels using a regression approach, correcting coded variables with coded–natural variable relationships, demonstrated in R.

Correct the coded levels from natural variables, run an rsm first-order model with two-way interactions, and verify model adequacy with residuals and a contour plot.

Explore the response surface methodology (RSM) to model and maximize a response influenced by multiple variables, using a 2^k design with central points and a quadratic model to locate optimum.

Apply the starting design of response surface methodology using a 2^2 factorial design with a central point to maximize yield, linking coded and natural variables and analyzing results in R.

Build a first-order model for yield with a not significant two-way interaction using coded time and temperature; interpret the contour plot to follow the direction of the steepest ascent.

Shows applying the steepest ascent in response surface methodology to follow the gradient toward higher yield, adjusting time and temperature and using a central-point design.

Shows why a first-order model with interaction is inadequate for the yield data, due to lack-of-fit and non-linear time and temperature effects, and advocates a second-order quadratic model with design.

Explore the central composite design for optimisation, including axial points, alpha calculation, and factorial-to-axial relationships, with practical data visualization and R analysis.

Build a central composite design in R using the CCD function, define alpha, configure factorial and axial points across blocks, add central points, and export the design as CSV.

Analyze a central composite design in R with the rsm package, fit a second-order model for yield, and identify the stationary point for maximum yield.

Analyze multiple responses—yield, viscosity, and molecular weight—to optimize conditions that meet goals like yield above 78.5%, viscosity 62–68 mPa s, and molecular weight 3400 g/mol, considering linear model coefficients.

Analyze multiple responses simultaneously by examining yield, viscosity, and molecular weight. Explore temperature and time effects, build a response surface, and identify the optimal region via contour overlays.

Use desirability functions, popularised by Derringer and Suich, to convert each response into 0–1 scores and multiply them to optimize yield, viscosity, and molecular weight within defined limits.

Learn to implement desirability functions in R, using targetD, maxD, and minD to optimize yield, viscosity, and Mw across coded x1 and x2, then compare with manual overlap.

Explore central composite design for three factors to fit second-order models, including factorial, axial, and central points, totaling 15 runs and 10 regression parameters.

Explore a central composite design used to optimize sealing of one-pound Starbucks coffee bags. It tests plastic viscosity, clamp pressure, and plate gap to minimize leakage.

Analyze a three-factor central composite design by converting natural to coded variables and building the relationships with R code for the Starbucks coffee bag case study.

Load the rsm library and add coded variables x_v, x_p, and x_g from viscosity, pressure, and plate gap to the DoEOpt07 dataset, preparing data for analysis of tear and leakage.

Analyze a full second-order model with coded x_v, x_p, and x_g to explain tear results for the Starbucks coffee bag, including linear, two-way interactions, and quadratic terms, and assess fit.

Develop a complete second-order model for leakage, with plate gap as the significant linear and quadratic terms, then apply backward elimination guided by p-values and adjusted r-squared.

Analyze tear and leakage with contour plots of viscosity, pressure, and plate gap; identify interactions and optimal settings such as 185 psi and 2 mm to minimize leakage and tear.

Apply desirability functions to Starbucks coffee bag case study, a three factor optimization of viscosity, clamp pressure, and plate gap, minimizing tear and leakage through grid testing and model predictions.

Examine face-centered and Box-Behnken designs for three factors—liquid-to-solid ratio, extraction time, and microwave power—to optimize microwave-assisted extraction of essential oils from sweet cherry flowers, noting central points and rotatability.

Prepare data in a run-based table, load rsm in R, code variables numerically, and fit a full regression model before simplifying and checking residuals, then build contour plots for interpretation.

Solve a box-behnken design with response surface method to maximize microwave-assisted extraction yield, identifying a stationary point at R 51.6 ml/g, t 26.3 min, P 435.6 W.

Build face-centered and Box-Behnken designs in R with the ccd and bbd functions, set alpha as faces, convert to natural variables x1, x2, x3, and save as a csv.

Designs should distribute data points across the region of interest, use replicates to test lack-of-fit, and allow blocking while progressing from 2^k to quadratic models with three levels per factor.

Determine runs from the ANOVA and regression model, ensuring five degrees of freedom for error and treatments for parameters in a 2^2 design with central points, nine to eleven runs.

Celebrate completing the course by planning and analyzing your experiments with more confidence. Share your rating and feedback to help others understand the course quality.