This posting describes the corrective action using an experimental design to reduce a machine’s cycle time. The machine is a plasma cutting machine, and a Lean Six Sigma (LSS) team identified it as the bottleneck operation in producing electrical switchboards by an electrical manufacturer. The previous posting describes the identification of the machine as the bottleneck with a cycle time of 42 minutes using a Value Stream Map. The purpose of the project was to improve the throughput of the switchboard production process. Chen, LI and Shady (2010) describe the LSS project.
The LSS team started by using the “5 Whys” method to identify the root cause of the long plasma cutter cycle time. The team noted that the plasma cutter was creating defects that needed to be reworked, and that inspection time was added to correct the defects. The root cause of the defects was that the plasma cutter was not operating at optimal parameter settings. These desired parameter setting were not known, and the team decided to conduct a DOE (Design of Experiment) study to identify effective parameter settings. The experimental design and results are presented by Chen, Li and Shady (2010), but Chen, Li and Cox (2009) give a more in depth presentation of the design and the analysis of results.
The plasma cutting machine produces holes on work pieces for installing hardware. Holes having excessive beveled edges and poor circularity cannot be used. A beveled edge is one where the hole is not perpendicular to the face of the switchboard. Figure 1 shows the Bevel Magnitude which is the bevel performance measure. Figure 2 shows the Smallest Diameter Deviation, |Dnormal – Dsmallest|, which is the circularity performance measure. Figures 1 and 2 are similar to Figures 5 and 6 in Chen, Li and Cox (2009).
The LSS team identified four controllable factors, i.e., Tip Size, Feed Rate, Voltage, and Amperage), and two uncontrollable noise factors, i.e., Air Pressure and Pierce Time. The manufacturer is unable to control the uncontrollable factors. They decided to run the experiments with three levels for the controllable factors and two levels for the uncontrollable (noise) factors. The following tables shows values appearing in Figure 8 of Chen, Li and Cox (2009).
|Controllable Factors||Level 1||Level 2||Level 3|
|Feed Rate (inches per minute)||83||93||103|
|Uncontrollable Factors||Level 1||Level 2|
|Air Pressure (lbs/in2)||45||60|
|Pierce Time (seconds)||0.70||1.40|
Taguchi Parameter Design
The LSS team chose a Taguchi Parameters Design because they claimed it allowed for a reduction in the time and money to conduct the experiment. That is, the Taguchi design would require fewer experiments than a factorial design.
Taguchi Parameter Design is an example of a Robust Parameter Design, Montgomery (2012). Taguchi developed his experimental designs to:
- Develop products that are robust to external variability sources.
- Minimize variation about target values rather than conform to specifications limits.
A key objective for Taguchi Parameter Design is to reduce variability. Taguchi uses a loss function of the form L(y) = k(y – T)2 , where T is the target value and y is the observed outcome. The loss function is used in identifying the preferred factor levels. Note the similarity between this loss function and the Six Sigma objective measure.
Montgomery (1997) describes the Taguchi Parameters Design, and gives an example similar to the one used by the LSS team with four controllable factors having three levels and three uncontrollable factors having two levels. The complete design consists of two arrays: an inner array containing the controllable factors and outer array containing the uncontrollable factors. The inner array is a L9 orthogonal array, and the outer array only needs to be an L4 orthogonal array since the LSS team only had two uncontrollable factors. The numbers 1, 2 and 3 in the following tables denote the factor levels. See Table 14-17 in Montgomery (1997) for a similar experimental design.
L9 Orthogonal Array for Controllable Factors
|Run||Tip Size||Feed Rate||Voltage||Amperage|
L4 Orthogonal Array for Uncontrollable Factors
|Run||Air Pressure||Pierce Time|
Each of the 9 runs in the inner array was tested across the 4 runs in the outer array by the LSS team. That gave a total sample size of 36 runs. This type of design is called a crossed array design, Montgomery (2012).
The next posting will present the experimental results.
- 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.