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June 6, 2018 | Gregory Vance, Rockwell Automation Inc., and Todd Vick, Universal Instruments Corp.Estimated reading time: 5 minutes
Table 2. Sample range of placements per panel versus count of assemblies and forecasted panel volumes.
The idea of using simple regression to develop a model of “placements per panel” to CPH began to develop. This relationship was first studied using production history.
Machine Mathematical Model for CPH
A report was available that contained panels built and total time to build a work order. This report was used to calculate the average CPH per panel for an SMT machine model. A scatter plot with a smoother line was used to view the relationship between the variables for a machine model. The smoother line is a line fitted to the data to explore the potential relationships between two variables, without fitting a specific model, such as a regression line.
There is a relationship between “placements per panel” and CPH but there are points that do not follow the smoother curve. The other observation is that actual CPH values vary greatly compared to the specification value the manufacturer stated.
Since production data was used to model this relationship, all the problem areas outlined earlier represent part of the performance and added noise in the model. Another idea was to use generic product simulation data from the manufacturer. The product simulation information included:
1. Quantity of placements per panel
2. Simulated cycle time for a SMT machine
3. CPH (calculated)
This would filter out the noise from production and machine configuration issues and could then be used to establish a realistic CPH equation. With the simulated cycle time data, the relationship between “placements per panel” and CPH was then studied.
The scatter plot revealed a relationship between “placements per panel” and CPH. Using the Pearson Correlation Coefficient, the strength of the relationship is assessed. At 0.536 it is considered moderate and P-Value of 0.000 means the relationship is statistically significant. This indicates that “placements per panel” is a good predictor of CPH.
To read the full version of this article, which appeared in the May 2018 issue of SMT007 Magazine, click here.
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