Posted by Sten Westgard, MS

Here's a user-submitted quandry: how do you draw control limits for your method if you standard deviation is zero and your coefficient of variation is zero?

Here's the "proof" that this scenario actually happens:

As you see for line 006, the SD and CV for BUN is 0.0

So what's the problem, and what's a laboratory to do?

A system solution would be to expand the number of decimal places, so the report would display you the actual SD and CV. Then you would have some numbers to be able to work with. In some programs, the number of decimals places is adjustable - the laboratory can modify it and get more decimal places. In other systems, this setting is hard-wired - the laboratory cannot make modifications and they are stuck with zero.

In this case, there is a saving grace: the cumulative data:

Again, look on line 006 and follow it across to the cumulative SD and CV. Those are, happily, actual numbers. It would be acceptable to use that SD of 0.1 and CV of 1.2% to set control limits. Indeed, if performance had been stable during that cumulative period, it is actually *desirable *to use those estimates over the shorter-term, smaller sample size estimates on the left.

The moral of the story is, laboratories are often stuck with systems that don't deliver the performance necessary for ideal care and operation. So "work-arounds" are needed. Here, if we can't modify the system to give us more decimal places, we can fall back on a cumulative estimate of SD and CV.

To see another example of how data rounding can impact QC design, click here.

Actually, there is yet another possible explanation to a SD of 0.

If you have a method that is very reliable, few significant figures in the result and furthermore as few results as 20 you can get 8.0 20 times as a result. The SD of this serie would be 0.

The solution to this problem would, of course, be the same as the solution to the one above. Use the cumulative data.

Posted by: Tomas Persson | February 29, 2012 at 08:44 AM

Would it not be appropriate,in the abscense of cum data, if the method could only be reported in whole numbers to use the limits of the next reportable value. As could be the case with cpk where no decimal place reporting occurs, setting the sd to 0.5 gives you a 2sd w on the next reportable value.

Posted by: Lane | February 29, 2012 at 03:04 PM