Having learned of impressive DOE triumphs in other manufacturing industries, a Forma Scientific researcher attended a workshop offered by a DOE training and software company, Stat-Ease, Inc., Minneapolis, MN.

DOE provides important information about how factors such as pressure, temperature, and voltage, for example, interact in a system. Engineers and researchers can no longer afford to experiment in a trial-and-error manner, changing one factor at a time, the way Edison doggedly did in developing the lightbulb.

A far more effective method is to apply a systematic approach to experimentation that considers all factors simultaneously. That approach is DOE. Companies worldwide are adopting DOE as a cost-effective method for solving the problems plaguing their operations.

DOE provides information about the interaction of factors and the way a total system works, something not obtainable through testing one factor at a time while holding others constant. DOE shows how interconnected factors respond over a wide range of values, or levels, without requiring the testing of all possible values directly. This is done by fitting response data to mathematical equations.

Collectively, these equations serve as models that predict what will happen for any given combination of values. Using these models, engineers can optimize critical responses and find the best combination of values.

Which are the critical factors?

During Forma Scientific’s cooler design stages, several factors and interactions were known to be affecting its performance. However, no one knew with certainty which factor(s) would potentially help or hinder the unit.

Dennis Smith, strategic products manager at the company, wanted a precise mathematical solution to the cooler’s design. Said Smith, “We wanted to accurately determine what factors would affect, either directly or indirectly, cooling coil temperature. They would be a good indicator of the unit’s thermal capacity.”

He added, “Our first steps were to determine which factors to test, the high and low level of each factor, and the responses we needed to measure. After brainstorming, the factors we chose for testing were refrigerant charge, voltage, and ambient temperature.”

High and low levels for refrigerant charge are 7.5 to 11.5 oz. For voltage, they are 105 to 126 V, and for ambient temperature, 18° to 30°. Responses, or characteristics thought to be affected by the selected factors, are thermal capacity, cooling coil temperature, and duty cycle.

In applying DOE, two-level factorial methods work well because factors are held to only two levels, high and low. These levels collect information that is used in the evaluation of a setting’s effect, producing a parallel testing scheme that is more powerful than one-factor-at-a-time methods.

By restricting tests to high and low levels, experimenters minimize the number of experiments needed. The contrast between levels provides the driving force that uncovers the most dominant effects.

With the help of Design-Expert™ DOE software from Stat-Ease, Forma Scientific researchers constructed a random testing sequence. Randomized run orders eliminate potential errors that can be caused by time-based variables. For example, if a manufacturing area gets warmer in the afternoon, randomization compensates for the differing temperatures by randomly assigning test times throughout the day.

The experimenters conducted a 2³, or “two-to-the-three full factorial,” experiment. Testing all possible combinations of three factors required eight experiments (2³ = 8).

Each of the three responses — thermal capacity, cooling coil temperature, and duty cycle — was evaluated to determine those factors having the greatest influence. A half-normal plot of cooling coil temperature (Figure 2) shows the magnitude of the effect of the various factors and interactions.

The interaction between factors A and C, charge and ambient temperature, was chosen as the first to analyze because its position off and to the right of the line shows it to be one of the “significant few among the trivial many.”

Verifying data

Underlying assumptions about the data were confirmed with a handful of diagnostic plots. For example, a plot of residuals vs. predicted values is used to verify that variation is relatively constant across all response levels. A “good” plot shows random point scatter.

The final step in the analysis was to plot the graph of factor interactions. The interaction graph shows cause-and-effect relationships between ambient temperature and refrigerant charge in the unit, and how they affect cooling coil temperature.

Compared with one-factor-at-a-time testing, fewer tests were needed to statistically prove that cooling coil temperature could be decreased while still providing ample refrigerating capacity. The savings from this finding exceeded $18,000 because an environmentally controlled testing facility was not needed.

Researchers also found that cooling coil temperature was dependent on an interaction between the amount of charge in the unit and ambient temperature. At low charge, cooling coil temperature was fairly constant across the ambient temperature range. At high charge, however, coil temperature increased as the ambient temperature increased.

The charging process was less critical because the design was robust to ambient temperature fluctuations at low levels of charge, like those used in production. This produced more savings since $60,000 to $70,000 did not need to be spent on a refrigerant-dispensing machine.

Additionally, because the DOE model provided useful information about the cooler’s operation in response to ambient temperature changes, Forma Scientific is better able to predict manufacturing capabilities. This provides higher confidence in design robustness.

Although DOE was invented in the 1920s, it remained dormant because of laborious hand calculations for even the simplest experiments. Until the number-crunching capability of PCs became widespread, DOE languished in mathematics departments.

Today, however, software easily sets up and analyzes statistically sound DOEs in just hours — dramatically faster than traditional methods. Substantial savings are being achieved as the norm.

Wager is a mechanical engineer with Forma Scientific, Inc., Marietta, OH. She can be reached at 740-376-2853; rwager@forma.com (e-mail).