This post describes the results and their analysis of the experimental design to reduce plasma cutter cycle time. The experimental design is a Taguchi Parameter Design. The previous posting describes the experimental design, and refers to the Value Stream Map Case Study posting to review the Lean Six Sigma project that produced the experimental design.

**Performance Measures**

The Taguchi design consists of an inner array specifying controllable factor levels and an outer array specifying uncontrollable factor levels. In this case, the inner array has 9 rows and is an orthogonal L_{9} array. The outer array has 4 rows and is an orthogonal L_{4} array. Let y_{ij} be an experimental result where i specifies the inner array row, and j specifies the outer array row. For each inner array row, an average value of y_{ij} is calculated for the 4 values of j. Taguchi recommends analyzing variation using a **signal-to-noise ratio (S/N)**. When small values of the performance measure are best, the S/N is:

where j = 4 in this case.

For both Bevel Magnitude and Circularity Measures the target value T is zero and smaller values of y_{ij} are preferred. A value of S/N is computed for each inner array row. Large values of the signal-to-noise ratio (S/N) are preferred.

Taguchi’s Parameter Design philosophy is to emphasize the reduction of variation rather than determining whether the experimental result is within specification limits. This is similar to the Six Sigma philosophy.

A Taguchi design produces two response variables for a performance measure. That is, the average value and the signal-to-noise ratio (S/N). Each response variable is calculated for the nine values in the inner L_{9} orthogonal array. That is, the four values of the outer L_{4} array of uncontrollable factor level experiments are used to calculate an average Bevel Magnitude and an average Circularity Measure.

**Experimental Results**

Figure 1 Bevel Magnitude Results

Figure 1 gives the Bevel Magnitude results which were created based on data provided by Chen, Li and Cox (2009).. Small values of the average Bevel Magnitude are preferred. Thus, the small Tip Size, a Feed Rate of 83 inches per minute, a Voltage of 105 volts and an Amperage of 63 amps gave the best results based on average Bevel Magnitude. Large value of the S/N ratio are preferred. Thus, the small Tip size, the Feed rate of 93 inches per minute, the Voltage of 100 volts, and the Amperage of 53 amps gave the best results based on S/N ratio. For Bevel Magnitude, the only factor that had the best results for both the average Bevel Magnitude and the S/N ratio was the Tip Size.

Figure 2 gives the Circularity results also based on data in Chen, Li and Cox (2009). For Circularity, the small Tip Size, 93 inches per minute Feed Rate, 100 volts Voltage, and 63 amps Amperage gave the best results. Based S/N ratio, the same factor levels are best.

**Figure 2 Circularity Results**

To resolve this conflict among the results the LSS team decided to select the factor levels that had the highest number occurrences. The following table summarizes the results.

Selection Criteria |
Tip Size |
Feed Rate |
Voltage |
Amperage |

Average Bevel | Small | 83 in/min | 105 | 63 |

Bevel S/N Ratio | Small | 93 in/min | 100 | 53 |

Average Diameter Deviation | Small | 93 in/min | 100 | 63 |

Diameter S/N Ration | Small | 93 in/min | 100 | 63 |

Preferred Setting | Small | 93 in/min | 100 | 63 |

**Project Effectiveness**

The effectiveness of the Preferred Setting for the four factors was verified by 30 work pieces where each one of them met the quality requirements for subsequent assemblies (Chen, Li, and Shady (2010). The cycle time of the plasma cutter was reduced from 47 minutes to 30 minutes since the time spent of inspection and rework was reduced. That reduced the fabrication operation cycle time to 106.5 minutes so it was no longer the bottleneck operation. In addition, the output quality of the product was improved.

**Improved Approach and Controversy**

This case study clearly shows that Robust Parameter Design can improve system efficiency and effectiveness. It can improve the mean output and reduce variability. Montgomery (2012) notes that Taguchi Parameter Design was used in the 1980s by large corporations such as AT&T Bell Labs, Ford Motor Company and Xerox. However, later studies showed that the experimental procedures and data analysis methods advocated by Taguchi could be significantly improved. The next posting will describe problems in using crossed arrays in Robust Parameter Designs.

**References**

- Chen, J. C., Y. Li, and B. D. Shady (2010). “From Value Stream Mapping Toward a Lean/Sigma Continuous Improvement Process: An Industrial Case Study.” International Journal of Production Research
**48**(4): 1069-1086. - Chen, J.C., Y. Li, and R. A. Cox (2009). “Taguchi-based Six Sigma Approach to Optimize Plasma Cutting Process: An Industrial Case Study”. International Journal of Advanced Manufacturing Technology
**41**: 760-769. - Douglas Montgomery (1997). Design and Analysis of Experiments, Fourth Edition, John Wiley & Sons, New York, 622-641.
- Douglas Montgomery (2012). Design and Analysis of Experiments, Eighth Edition, John Wiley & Sons, New York, Chapter 12.

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