In this series, we have emphasized statistical experiment design in cleaning operations. We have observed that many who would value this approach don’t use it, used the t-test to learn with what level of confidence two groups of cleaned parts are the same or different, and identified dynamic surface tension as a useful process variable.

This month we will describe the use of a powerful statistically-based process monitoring tool (CUSUM), using dynamic surface tension as the monitored process variable, to improve management of an aqueous cleaning process.

This emphasis on and use of these statistical techniques is not limited to critical cleaning. They should be used in clean manufacture, nearly all R&D, and the management of cleanrooms.

In October, we introduced a simple three-question recipe for experimental design:

What do we want to know? That our process always has the right amount of soluble surfactant, and we can take action in time if it doesn’t.Can we minimize the number of experiments? Let’s see.

How well do we want to know it? So we have 99% confidence that our information is what we think it is.

The simplest monitoring scheme is to plot the measured variable vs some control limits. Here, everything is based on the value of the last-received data point. This approach conflicts with our experiment design: we have no time to respond, and one can’t test for 99% confidence with one data point.

Instead, we plot the Cumulative Sum (CUSUM) of the deviations of the measured variable from the goal (mean). This approach meets our experimental design: (1) CUSUM can be tuned to always lead the measured variable in time and (2), we can use the t-test as described in a previous column to estimate the confidence level that one data set is different than another.

Here are the equations for calculating CUSUM using all operating data:

If the measured variable is above the mean:CUSUM = S(Measured - Goal - K⁺)

If the measured variable is less than the mean:

CUSUM = S(Goal - Measured - K^-)

K is a “tuning parameter” to make sure CUSUM doesn’t over- or underreact. My experience is K⁺ = K^-= 2 to 3 times the standard deviation of dynamic surface tension at the goal value (=s).

The upper and lower control limits (UCL = Maximum and LCL = Minimum) are calculated as: UCL 20 times s, and LCL 3 times s. UCL and LCL aren’t symmetrical because the relationship between surfactant concentration and surface tension isn’t linear.

Figure 1 shows a CUSUM plot. Note how CUSUM exceeds the UCL before the measured surface tension does. CUSUM anticipates and prevents excursion of limits to allow timely action. This was the first requirement of our experimental design.

Suppose our dynamic surface tension data appear normal. But our quality department reports excessive defects. Could the problem be mis-operation of the cleaning bath?

Figure 2 shows CUSUM data from “good” and “bad” operation. We use the t-test to compare both operations (see December C⁴).

The outcome is that there is a 99.05% chance of both data sets being the same, even though they visually diverge. This was the second requirement of our experimental design.

Are you practicing good design of experiments?