Authoritative Proof, or Misinterpretation by Dietary Advocates?

Author Archive From the perspective of data analysis, rare events are problematic. Until we have an event, there is nothing to count, and as a result many of our time periods will end up with zero counts. Since zero counts contain no real information, we need to consider alternatives to counting the rare events.

This article will consider simple and complex ways of working with rare events. While spills are not desirable, and while everything possible is done to prevent them, they do occasionally happen.

Over the past few years one plant has averaged one spill every eight months. Of course, if the plant averages one spill every eight months, then those months with a spill will be percent above average! When dealing with small counts a one unit change can result in a huge percentage difference.

Assuming that these counts are reasonably modeled by a Poisson distribution we could put these counts on a c-chart. The central line for this c-chart would be the average count. During the first four years there were a total of six spills.

Six spills in 48 months gives an average of 0. For a c-chart the upper limit is found by multiplying the square root of the average count by 3. This gives the upper limit of 1.

The number of spills per month on a c-chart In spite of the fact that a single spill is percent above the average, the c-chart does not show any points outside the limits. Here it would take two spills in a single month to make this chart signal a change.

Only percent above average! So, while the use of a c-chart might be justified with these counts, it is of little practical use because it is so insensitive.

What about using an XmR chart with these counts as I suggested last month? Using the first four years as our baseline the moving range chart would have an upper limit of 0. This makes every month with a spill into a signal of a change in the system!

Clearly this is not a reasonable interpretation of these data. The problem is that this XmR chart suffers from the problem of chunky data.

Chunky data can occur with any type of data. Count data tend to be chunky whenever the average count falls below 1. Chunky data will artificially tighten the limits of a process behavior chart and will result in an excess number of false alarms. More about the problem of chunky data next month.

Thus, with counts of rare events the specialty charts become insensitive and the XmR chart breaks down. This is not a problem with the charts, but rather a problem with the data themselves.

Counts of rare events are inherently insensitive and weak.

No matter how these counts are analyzed, there is nothing to discover by placing the counts on a chart of any type. Yet there are other ways to characterize rare events.

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Instead of counting the number of spills each month counting eventsyou could instead measure the number of days between the spills measure the area of opportunity between the rare events. For these data the time intervals between the spills are computed as follows.

Determining the time between spills One spill in days converts into a spill rate of 0. Multiplying this daily spill rate by gives us a yearly spill rate of 1.

Thus, the interval between the first spill and the second spill is equivalent to having spills at the rate of 1.When imputing volatility into returns, the differential between what investors were promised (and this is a huge flaw in financial planning) and what actually happened to .

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