Overview

Welcome to this applied analytics course from the Tabtrainer® Certified Series - your trusted source for advanced industrial statistics and engineering optimization.In this training, you will learn to use polynomial regression in Minitab® to model and optimize a real-world heat treatment process from the Smartboard Company, where skateboard axles undergo precipitation hardening. Using historical production data, you'll build, compare, and validate linear, quadratic, and cubic regression models to predict material strength based on annealing time.Your final model will support a confident reduction of annealing duration by nearly 80% while still meeting strength specifications - with full statistical backing.Taught by Prof. Dr. Murat Mola, TÜV-certified Six Sigma expert and Professor of the Year 2023 in Germany, this course demonstrates how data-driven modeling can enable process improvements without costly experiments, applying aerospace-grade analytics to everyday manufacturing.In this training unit, we explore the use of polynomial regression to solve a real-world engineering problem in the heat treatment department of the Smartboard Company, where skateboard axles undergo a complex metallurgical process known as precipitation hardening.To meet the required material strength, the axles are currently subjected to a lengthy three-step heat treatment process. The third step-annealing at 200°C for 5 hours-has become a bottleneck in production. The management wants to investigate whether increasing the annealing temperature to 350°C could allow for shorter annealing times while still achieving the target material strength of 280 MPa ±15 MPa.Since there are neither sufficient experimental resources nor time for new trials, the team turns to regression analysis based on historical production data. The goal is to build a mathematical model that allows a statistically reliable prediction of the necessary annealing time at the increased temperature.The dataset includes 90 observations, each consisting of an ID, the annealing time in minutes, and the resulting material strength in megapascals. Initial correlation analysis using Pearson's method reveals a strong positive linear correlation (r ≈ 0.993) between annealing time and strength.We then perform a linear regression, which yields a high R² value (approx. 98.5%). However, a U-shaped residual pattern suggests that a purely linear model might not fully capture the underlying relationship. Therefore, we also evaluate quadratic and cubic regression models.While the quadratic term turns out to be statistically non-significant, the cubic regression model not only shows the best fit (adjusted R²) but also fulfills all residual assumptions-including normality and independence. Based on this model, we conduct a response optimization to identify the required annealing time for achieving 280 MPa.The result: with a 95% confidence level, the model recommends an annealing time of approximately 54.75 minutes at 350°C to meet the required strength-thus reducing the current process time by nearly 80%.This data-driven approach enables a statistically reliable process improvement, increases production capacity, and avoids costly experimental iterations. Moreover, it demonstrates the power of polynomial regression in modeling complex nonlinear relationships in industrial settings-applying the same principles used in aerospace engineering to the world of skateboards.

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