Posts Tagged ‘many things’

Thinking Outside the Box

Sunday, June 7th, 2009

The “P” in SPC stands for process, not product.

A common problem with SPC is that the world appears too complicated for a statistical approach to work. In complex electronics products, for example, circuit boards may have thousands of holes and microchips may have millions of transistors. Plotting control charts of each and every dimension is clearly not feasible. What can be done?

To answer this question, consider a simple product: the box in Figure 1. How many things could we measure on this box? It turns out, a great many. Length, width and height are obvious choices. But we could also measure the diagonals on all six sides, interior diagonals front-to-back and back-to-front, linear combinations of these measurements and a great many more. We could conceivably come up with dozens of measurements on this simple box.

But–and this is critical–we don’t need these measurements to control the box process. The “P” in SPC stands for process, not product. When we focus on the product, we lose sight of the fact that we’re not trying to control the product. Control of the box process may be a great deal more simple than controlling the product. And if we control the process properly, the product will take care of itself.

The statistical technique known as principle components analysis can help us determine just what is important and what is not. Most statistical software packages can perform PCA. To illustrate the approach, I measured an assortment of boxes (see figure 2). The measurements I obtained are shown (in inches) in Table 1.

When these data are crunched through PCA, we find that three principle components explain 99 percent of the variation in the data set: Component No. 1 explains 76.9 percent of the variation, component No. 2 explains 14.1 percent, and component No. 3 explains 8 percent. The PCA clearly shows that these three components are associated with A, B and C respectively. Thus, the “box process” can be characterized almost entirely by controlling these three characteristics. If we do that, the other dimensions will be OK, too.

When these data are crunched through PCA, we find that three principle components explain 99 percent of the variation in the data set: Component No. 1 explains 76.9 percent of the variation, component No. 2 explains 14.1 percent, and component No. 3 explains 8 percent. The PCA clearly shows that these three components are associated with A, B and C respectively. Thus, the “box process” can be characterized almost entirely by controlling these three characteristics. If we do that, the other dimensions will be OK, too.

An example of using this approach in the real world involves CNC machining. A defense plant machined parts for use in guided missiles. The parts were extremely complex, with thousands of holes, cutouts, etc. on each. However, when the data were analyzed using PCA, it was determined that four principle components accounted for nearly all of the process variation. Further study showed which measurements were correlated with each principle component.

From this, the engineers determined that, for all the apparent complexity, the machining process was, in fact, quite simple. The four principle components corresponded with the machining center’s four axes of movement: X, Y and Z movement of the bed, and the rotation of the table on which the parts were mounted. SPC could be accomplished by selecting those features most difficult to position in each axis of movement. Often, a single feature could measure more than one axis; for example, a hole furthest from the “home” position in both the X and Y axes. The result: One or two control charts suffice for the control of a process placing thousands of features.

Note that the features selected for SPC may be of little or no importance to the product itself. In fact, some parts were designed with “process control features” that were later removed from the part entirely. This makes sense when remembering that P stands for process, not product. If you keep that in mind, the complexity you face might just evaporate before your eyes.

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Preventing Hospital Falls

Friday, June 5th, 2009

Hospital processes produce many things. Most of them are desirable outcomes, such as healthy newborn babies, new hip joints, cancer-free patients and blood flowing freely through once-blocked coronary arteries. In other words, happy, healthy and satisfied patients. These results are why health care professionals chose their field. They generate revenue that patients are happy to pay because the value they receive exceeds the cost.

But not all of the things hospitals produce are desirable. Hospitals also produce botched surgeries, surgical sponges sutured into patients, X-rays that must be taken repeatedly, falls, infections and many other unwelcome errors. These things also result from hospital processes, but because they are not part of the planned outcome, we tend to overlook the fact that they, too, are caused. Instead, many health care professionals look upon these poor results as unfortunate occurrences that appear without cause. Of course, they tend to accept these events as inevitable, which in turn assures continual recurrence.

The quality profession’s major contribution to the world is the ability to scientifically investigate process variation. This helps people see which outcomes, pleasant and unpleasant, are created by the system itself, and which are created by factors outside the system. Armed with this knowledge, workers can determine which action will most likely improve the process. Improvement can be an increase in the desired outcome, a decrease in undesired outcomes, improved efficiency or any combination of these. The approach is generic. It can–and has been–applied to improving health care processes. Let’s look at an example.

Falls. As I waited outside my father’s hospital room for him to finish dressing to come home, I heard a noise. The sound was distinctive: a body hitting the hard floor. I rushed in, a nurse close at my heels. My father’s elderly roommate lay on the floor, embarrassed as he tried to stand. The nurse and I helped him to his feet.

“I’m OK,” he assured us. “I leaned on the table, but it rolled and I fell.” He pointed to the small cabinet between the two beds. The nurse nodded as she guided him to the chair.

“That happens all the time,” the nurse responded. “They should replace those darned tables. They’re on rollers to make it easier to move them for patient access and cleaning of the room, but they cause a lot of accidents.”

Luckily, only the gentleman’s pride was hurt. But as I continued to wait for my father, I took note of the fact that the nurse continued with her rounds. If she ever reported the event, it was long after it occurred. Chances are it was never reported.

Later that day, I phoned the hospital and asked if they kept data on falls. “Of course,” I was told. “Hospitals re-cord everything.”

Not quite everything, I thought to myself as I recalled the event earlier that day. Probably anything that caused an injury. Only part of the story, but worth looking at in any event. The hospital faxed me the data on falls (see Table 1).

All organizations keep such data. However, it’s in a form that’s seldom used. The data contains information, but not in a format that people can easily interpret. To help us glean some knowledge from this data, let’s consider three statistical process control tools: the histogram, run chart and control chart.

A histogram shows the empirical distribution of the falls data. It would show that the number of falls reported each month varies from zero to six, with four falls per month being the most common. The number of falls appears to be fairly consistent; no months contain a great number of falls.

Where the histogram is a snapshot, the run chart is a movie. In Figure 1 we see the falls data stretched out over time. Applying statistical tests produces no significant data patterns. The run chart helps put the data in a context, which helps prevent misconceptions caused by looking only at a portion of the data.

While run charts allow us to examine patterns, they are less helpful in analyzing outliers or freak values. Control charts provide control limits that help do this. Creating a control chart of the falls data requires first determining the number of patient care days (PCDs) for the hospital each month. After all, one way to reduce falls to zero is to admit no patients! The U chart in Figure 2 shows reported falls per 100 PCDs. It also includes a centerline showing the process average and an upper control limit on the number of falls per 1,000 PCDs. Note that the UCL rises and falls as the number of PCDs changes.

The control chart shows that the rate of falls is “in control.” This means that if nothing is done each month, the hospital can expect to average about two serious falls per 100 PCDs. Some months no people will fall and hurt themselves, other months a half-dozen or more injuries might occur. That is, unless someone takes the time to look into the reasons why people fall. When management decides to do that, a whole host of techniques can be brought to bear on the problem, such as cause-and-effect diagrams and Pareto analysis.

And maybe, just maybe, those darned tables will be replaced!

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