Table 1. Three factors represent a liekly scenario affecting the cooler. High/low levels are boundaries encoutnered during reagent cooler operation. Responses are those characteristics thought to be affected by the selected factors.
For years, researchers have had to experiment in a trial-and-error manner, changing one factor at a time, the way Edison doggedly did in developing the light bulb. A far more effective and less tedious method is to apply a systematic approach to experimentation that considers all factors such as pressure, temperature, and voltage simultaneously. That little-known statistical approach is design of experiments (DOE), and companies worldwide are adopting the strategy as a cost-effective method for solving many problems plaguing their operations.

Although the design of experiments method was invented in the 1920s, it remained dormant because of laborious hand calculations for even the simplest of experiments. Until the number-crunching capability of PCs became widespread, DOE languished in mathematics departments. Today, however, DOE software easily sets up and analyzes statistically sound DOEs in just hours - drastically faster than the months spent testing only a handful of factors using the traditional method. Hefty monetary savings are the norm.

Figure 1. Design Builder helped experimenters set up a 23 factorial design - one of the most efficient. Color-coding similar to a stoplight represents safe (green), cautious (yellow), and risky (red) design options. White squares, used by Forma Scientific in this experiment, indicate a full-factorial problem.

Theory into Action

To some, the numerous manufacturers within the medical laboratory industry are known as appliance makers. Forma Scientific, Inc. (Marietta, OH) was a member of that appliance group as a maker of over 300 different types of biomedical, pharmaceutical, clinical, and industrial laboratory products. But a little over a year ago, the company broke from the crowded appliance pack when they began using DOE. In doing so, they not only discovered ideal factor settings for a reagent cooler they were building for Johnson & Johnson, they also saved nearly $100,000 in the process.

Forma Scientific's cooling unit, approximately 3 ft high by 1 ft by 1 ft, is a critical component that sits within a blood analyzer being built by Ortho-Clinical Diagnostics, a Johnson & Johnson company. To do its job well, the cooler's specification called for a constant 6°C temperature with enough capacity to remove heat introduced during operation.

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

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 other factors 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 optimize critical responses and find the best combination of values.

Figure 2. A half-normal plot shows the significant effect to be AC - the interaction between ambient temperature (A) and charge (C).

Which are the Critical Factors?

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

Dennis Smith, strategic products manager within Forma, wanted a precise mathematical solution to the cooler's design. Says 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." Smith adds, "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." Table 1 shows the factors and the high/low levels, along with responses Smith and the other researchers chose to measure.

Figure 3. A Plot of Residuals verifies constant variance across response levels.

DOE Tools

Two-level factorial methods work well because factors are held to only two levels - high and low. These levels collect information that evaluates 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 aid of Stat-Ease's Design-ExpertT DOE software, Forma Scientific researchers constructed a random testing sequence (a run order matrix). 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 (said: "two-to-the-three full factorial") experiment (Figure 1). Testing all possible combinations of three factors required eight experiments (23 = 8).

Each of the three responses from Table 1 (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 (Ambient Temperature and Charge) was chosen as the first to analyze because its position off and to the right of the line signifies it as one of the "significant few among the trivial many."

Figure 4. Cooling coil temperature is dependent ont he interaction between the amount of charge in the unit and ambient temperature.


Underlying assumptions about the data were confirmed with a handful of diagnostic plots. For example, a plot of residuals versus 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 (Figure 4) shows cause-and-effect relationships between ambient temperature and refrigerant charge amount 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. Since the need for an environmentally controlled testing facility was avoided, savings from this finding exceeded $18,000. 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. ES