Relevance of Design of Experiments to the Industry (Additive Manufacturing Case study with Minitab)

Introduction

Design of Experiments (DOE) is an effective tool to maximise learning using limited resources. Through effective strategizing, it allows identification of relationships between cause and effect, providing an understanding of interactions among causative parameters, determine controllable parameters in order to optimize reliability and even improve the robustness of a design or process to variation. With these benefits, it is evident that any industry stands to benefit from this tool from an economical, operational, and technical development point of view.

Even as DOE was first introduced in the early 1920s by Sir Ronald A. Fisher, the rate of adoption between industries is relatively low and varies between different industries. [1] [2] [3] A survey by Tanco et al. [4] showed that European companies conducting in experiments tend to use strategies such as Best Guess, or One Factor at a Time (OFAT), and found that “76% of respondents believed that a methodology is truly needed and that the absence of a clear methodology was one of the main barriers in the application of DoE.” In this discussion, a case study is presented and discussed to try to prove that DOE is very much useful and relevant to the industry. The case study is on a manufacturing company replacing an existing component fabrication process to an Additive Manufacturing (AM) process by using a statistical software to acquire the right set of manufacturing design parameters.

Case Study

An injection moulding company is keen to purchase an Additive Manufacturing machine to meet market demands for manufacturing of core inserts with complex geometry that is unable to be fabricated conventionally, the Original Equipment Manufacturer (OEM) of the AM machine would usually offer free trials and even optimisation of component design and machine parameters for that specific component prior to the selling of the machine.

A few months into the successful adoption, the company’s management decided that the AM machine is under-utilised as has identified a second component, a mould insert with complex cooling channels, to be fabricated by this AM machine. Therefore, the AM process engineer is tasked to prepare for the process adoption. Due to the costly fees quoted by the OEM for testing and parametric optimisation for the mould insert, the engineer is inevitably forced by management to test it in-house with limited time and resources, on the basis of the engineer’s current understanding of the machine.

Based on some advice from the OEM and with the experience of the engineer, they identified 3 key parameters with each range of variables as shown in Table 1.1, with the critical response to be the component’s fatigue life. The question would now be — How and what method should the engineer use to acquire the best set of parameters to attain the longest fatigue life?

Table 1.1 Screened Key Parameters and their range of variables

Without any statistical knowledge, the engineer might intuitively use OFAT method, which basically is the varying one factor while keeping other known factors constant. The downside is that with a total of 10 runs, OFAT is unable to show the influence or interaction of one factor to another, therefore unable to attain the best recipe for highest fatigue life of the component. This is illustrated in Figure 1.1 (a), where the red circle represents the best set of factors to get the optimised response, which is outside of the range of the values set in the OFAT design, where else Figure 1.1 (b), shows the potential of using DOE as the optimised response falls within the parametric limits.

Figure 1.1 Cube plot of (a) OFAT and (b) DOE. Each circle represents an experimental run, red circle represent best set of parameters within the parametric limits

The engineer was therefore introduced to a statistical program called Minitab to set up a DOE trial using the same parameters but with 2 levels and a center point for each factor as seen in Table 1.2. Even without any statistical knowledge, the engineer is able to conduct the DOE by following step-by-step instructions inside the Minitab program, which will be briefly discussed here.

Table 1.2 Un-coded design matrix for DOE trial

With the base design of 3 factors, 8 runs and 3 center points, the total runs amounted to 11 (23 + 3). After subjecting each test component to fatigue testing, the engineer was able to conclude from the Minitab’s report that there is a relationship between fatigue life and all three factors at a 0.10 level of significance. Values for the first set of DOE trials and their fatigue results are shown in Table 1.3. The report was also able to highlight in a pareto chart, as seen in Figure 1.2, that the orientation of print was the most important factor influencing on fatigue life, closely followed by channel thickness. Finally, a report card was generated to explain that Minitab was able to detect a curvature from the data and that the linear model was insufficient to acquire the optimal response value. A suggestion and a guide were provided to include in the curvature.

Figure 1.2 Pareto Chart to show individual influence of various factors on the response.

Table 1.3 First set of DOE factors and response values

With an additional 9 runs as suggested by Minitab, a conclusive report was generated for a fit quadratic model for fatigue life that included a prediction and optimisation report, effects report, diagnostics (residual) report and a summary report. The additional runs and response values are listed in Table 1.4.

Table 1.4 Additional runs as recommended by Minitab

Figure 1.3 Final prediction and optimisation report generated by Minitab

As seen in Figure 1.3, Minitab shows the factor settings that optimise fatigue life, noting that this optimised response is in the range of the experiment levels. This means that a higher optimal response could be possible but might be outside the machine specifications (levels were set based on current process limitations), therefore this proposed factor setting is viable. The prediction and optimisation report also display alternative solutions that are nearly optimal, therefore Minitab recommends that if the settings form the optimal solution or one of the alternative solutions are adequate, the engineer should perform an additional 20–30 confirmation runs using those settings to verify the solution prior to implementation to their manufacturing processes.

Conclusion

In conclusion, the relevance of DOE to the industry should be justifiable for any product or process owner. With the help of modern software packages such as Minitab that is comprehensive, easy-to-use, flexible and capable of producing insightful output and graphics, engineers such as the one in this case study, will be able to formulate and carry out experimental designs to acquire the necessary knowledge to better understand their product or process substantially, which ultimately serves to benefit the owner, company and the industry as a whole.

Reference

[1] J Antony, Jiju & Viles, Elisabeth & Torres, Alexandre & Incerti, Taynara & Fernandes, Marcelo Machado & Cudney, Elizabeth., “Design of experiments in the service industry: a critical literature review and the future research directions,” The TQM Journal. ahead-of-print, May 2020.

[2] B. a. M. A. Bergquist, “Statistical methods — Does anyone really use them?,” Total Quality Management & Business Excellence, vol. 17, no. 8, pp. 961–972, 2006.

[3] M. Tanco, E. Viles, L. Ilzarbe, M. Álvarez, “Manufacturing Industries Need Design of Experiments (DoE),” Proceedings of the World Congress on Engineering , vol. II, 2007.

[4] M. e. a. Tanco, “Is Design of Experiments really used? A survey of Basque Industries,” Journal of Engineering Design, vol. 19, no. 5, pp. 447–460, 2008.