## 2018

ONE GOOD IDEA

# Designing for Accuracy

## Using regression, DoE to model production rates

by J.L. Navetta

There are times when engineered standard production rates are no longer accurate. Examples I’ve come across include:

- The initial model is based on one product or product line, and isn’t valid for all applications.
- The initial model is based on limited sampling, resulting in many outliers.
- A simple linear equation is used instead of a more complex model.
- There is no model. It’s a combination of best guess and historical data.

For this column, I used regression analysis and design of experiments (DoE) to create a model for predicting production rates in a paper stock cutting facility.

The historical modeling of production rates for cutting paper stock reflected the second and third scenarios. Thickness of the stock and the number of times the stock was cut were primary, linear factors.

But that is precisely where the initial model failed—in assuming only two factors and linearity. Some jobs required the operator to manipulate more stacks on the cutting table, which caused delays and production rates that differed from the standard.

Online Figure 1 shows the actual production rates compared with the
engineered standard, or predicted rates, using this model. The coefficient of
determination (R^{2}) is 0.45, indicating the actual production rates
are below the acceptable limits set by the standard. The model is poor at
explaining the correlation between standard and actual rates, and the ratio is
inaccurate—comparing a 5,000 pieces per hour actual rate with a 15,000
pieces per hour standard rate. From this model, we could not accurately predict
the performance of the operator.

Fortunately, I could perform a DoE for the different types of jobs performed by the operators. The operators experimented during actual production using factors not taken into account in the old model, and performed trials on scrap stock. From the DoE and using regression analysis on historical data, I developed a new model for predicting production rates.

Using this new model, we could more accurately predict the operators’ production rates and saw improvement when applying the historical data to the new model. For example, job ABC was rated for 10,000 pieces per hour using the original model. The operator actually cut 7,000 pieces per hour. Accounting for the factors in job ABC in the new model, we found the operator produces 10,350 pieces per hour.

Figure 1 shows the results using historical data, not the experiment data. Because the DoE results were used to build the new model, they shouldn’t be used as data for the model.

### Tricks of the trade

There are two schools of thought in rate prediction. One is that you use a variety of operators to perform the DoE. On average, you’ll be accurate with the "as-is" rate. The other suggests using experienced operators. This helps identify operating equipment efficiency opportunities and puts the onus on management to institute best practices. Short-term loss will drive action, and the planning rate may be less than the standard.

A few tips for modeling production rates:

- Your study is only as good as your product mix. If all testing is done on one type of material, don’t assume similar results on a different type. Sometimes, a simple add-on is all you need—creating a field that proportionally modifies output for a special factor. If it does not follow a simple linear model, you must create a new factor (and retest) or create a different model.
- Don’t engineer rates in a vacuum. I logged much floor time with operators in this case. After the tool was developed, I periodically visited the operators to ask: Was it still working? Were there new products that didn’t fit the model?

This tool could be applied in several industries—machining, pick zones and handwork lines lend themselves to this application particularly well. Regardless of where it’s applied, keep three takeaway points in mind:

- Use regression analysis to see how you fare from actual production to the standard (predicted) rate.
- Consider DoE to model the prediction tool.
- Plug
your historical values back into your new model and rate R
^{2}.

**J.L. Navetta** is a continuous improvement engineer for MISA
Metal Fabricating in Louisville, KY. Navetta earned a
bachelor’s degree in mathematics for quality management at Empire State
College, State University of New York. He is a senior member of ASQ and an
ASQ-certified quality engineer and Six Sigma Black Belt.

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