Six sigma in the laboratory--part two.
1) The data is symmetrical about the mean (regardless of the value of the mean or the SD);
2) As the curve moves away from the mean, less and less of the area lies between adjacent SDs. The curve approaches (but NEVER) touches the x-axis. Table 1 illustrates the number of defects per million (DPM) and per thousand (DPT) on one side of the mean (e.g., +1 SD above the mean, on the right side).
As you see, after 3SD there are very few defects (rejects) occurring when the method is working as expected. "Defects" is the word used in manufacturing (such as ball bearings or computer chips or light bulbs). In our work in the laboratory, perhaps a better word is "rejects" or "less than our specifications required or are wanted." Reject here refers to a QC value that came from a method that was performing as expected, but the value exceeded a SD limit.
Let's look at the first example of how the concept of Six Sigma and its five words might be used in assessing a QC program. Here are the five words and their meanings:
(* Recall that sigma and SD are calculated the same way. The difference is that the word sigma is used when an entire population is used [rarely if ever in the laboratory], and SD is used for a sample (i.e., a control or a group of patients).
Define (the problem), Measure (the size or extent of the problem), Analyze (the problem, its source(s) or cause(s), Improve (reduce or even eliminate the problem) and C (control the process to maintain the fix). DMAIC. The cycle continues and never ends.
We will use the imaginary analyte ceramic so that no one and no department/section feels left out. Indeed, any analyte that can be measured can be one about which Six Sigma might be discussed.
The laboratory's ceramic mean and SD are 101 mg/dL and 3 mg/dL, respectively. The group mean is 100 mg/dl. First, let's measure the Total Error (TE) as SDs (sigma).
TE(SD) = (absolute [lab mean - group mean]/lab SD + 2)
TE(SD) = (101 - 100)/3 + 2 = 0.33 + 2 = 2.33
TE as SD (sigma) = (0.33 + 2) = 2.33. In words, this tells us that Total Error is equal to 2.33 measured in our SD. If our mean and/or SD were different, the TE would be different.
The next step is to find the Total Allowable Error (TEa) for ceramic. The CLIA/CAP limit for ceramic is 15%. Next, we convert 15% of the group mean into mg/dL (0.15 % x 100 = 15 mg/dL). Now we can find how many of our SDs are in that 15 mg/dL (15/3 = 5 of our SDs). Thus, TE < TEa (2.3 SD < 5.0 SD). What does this mean? It means two things. First, it tells us that at the edge of our TE (2.3 SD) we are 2.7 (5.0-2.3) of our SD from exceeding the TEa. Very simply, our TE has a margin of error (ME, error budget or wiggle room) between the TE and TEa. Figure 2 illustrates this.
Now that we have measured the ME (2.7), we can say that we have a 2.7 sigma method OR a 4.7 sigma method. When you look at 4.7 and 2.7, you see that they are 2 (of our) SDs apart. That 2 is the same 2 we added in the TE formula. That is, if we calculate our sigma 'value' from our mean, we have a 4.7 sigma method. If we calculate the sigma 'value' from the outer edge of our TE, we have a 2.7 sigma method (because we used 2 sigmas calculating the TE). Take another look at Figure 2.
What can we do with either a 2.7 sigma method (calculated from the usual TE) or a 4.7 sigma method (calculated from our mean)? Either of these numbers can be used to determine our primary accept-reject Quality Control (QC) point. Look now at Figure 3.
Imagine this curve is a plot of the last 100 points on a ceramic control. The x-axis has a 0 at the middle indicating that the mean is 0.0 SDs (sigmas) from the mean. About 34% of the ceramic values lies on each side between the mean and 1 SD (sigma). This tells us that 68% (rounded) are between -1sigma and +1sigma. (This is true not only of this control, but it is true for any control on any instrument measuring any analyte as long as the method is stable (without a change in the mean or SD). From -2 to +2 sigmas (SDs) lies 95% of the data, or only 5% (2.5% on either side) lies outside those limits (as long as the method is stable). This is the source for the usual TE formula.
TE = [lab mean - group mean]/lab SD + 2 SD
Another way of looking at this is to realize that if the analytical system is working as it should, there is a 5% chance of a 'good' value (for it came from a stable method/instrument) falling beyond SDs (that is 'out' of control.) Are we "allowed" to set another limit? Farther from 2 SD? Voila! You now know why sigmas (SD) are of interest to us. If we have a method that is, say, 4.7 sigma (that is our mean is 4.7 sigmas (SD) from TEa), and we set our limit at 2 SD, we will have 5% rejection of good data (these are false rejects, FR) with 2.7 sigmas (SDs) of error budget (wiggle room). What would the results be were we to change from a QC limit for the method from 2 SD to, say, 3 SDs,? There are two results of such a change: 1) By moving the limit farther from the mean, we reduce the number of false rejections when the system is stable. In this case, the reduction is from 5% for that single control to 0.3% for the same control. In other words, from 1 in 20 runs to 3 in 1,000 runs! Something to consider. 2) By moving the limit, we are closer to the TEa. Such a change will yield an ME of 1.7 sigma (SDs)--1.0 SD less than the 2.7 before. If something happened to the analytical system, would we detect it before 'bad' data would leave the laboratory?
The way we approach this question is in two parts. Part 1: If the QC limit is set at 3.0 SD (which is what the CAP recommended in 1974 when SDs were much bigger), we will significantly reduce the numbers of False Rejects. This will save us, the patients and their doctors time, and resources for the laboratory and the hospital overall. Part 2: If our limit after the change in the primary QC limit is still 1 or more SDs from the TEa, we are almost guaranteed to detect an error that would exceed the TEa. There are caveats to this approach. 1) The TEa may not be a perfect limit for all situations. 2) If our SD is not established and used properly at all times, we might miss that error. 3) Using the rule(s) we entered on the computer, if an error is detected and one chooses to ignore that error for any reason, one is responsible for missing the error. With these caveats in mind, there is little doubt you have a win-win situation.
This discussion has dealt with only the primary QC rule, the one that we first looked at. The other rules that we recommend are certainly important and helpful. If we use the 1 3SD rule as primary, the number of FR if we use 2 controls is 6 per thousand runs (not patients). The second rule we recommend is the 2 2SD rule (that is consecutive control value exceeding the same 2 SD limits) which is capable of detecting smaller systematic errors and has a FR occurrence of 2.5 per thousand runs. The third and last rule is the R 4S rule. This rule is used to detect random errors: If two controls within a run have a difference or range between them of 4 SD or greater, that constitutes a reject and there is most likely a problem in the analytical system (such as pipetting or tubing), not calibration or reagents.
To recap, assessing the status of a QC system (your mean and SD, the group mean, and the TEa) using the idea of Six Sigma gives us a clear picture of how we are doing in terms of our TE and the TEa. We worked out an example on how to measure YOUR sigma 'score.' We have developed an Excel template that will let you determine your sigma score for any analyte you want by entering only the four numbers we listed above. The computer does the rest. (Send email@example.com and he will send the template back by email.)
Should you think of trying to raise your '6-sigma score', you need to keep in mind that the two variables over which you have some control--your mean and your SD--are not the easiest to change, especially if you have established them correctly. Of these two statistics, the SD is easier to reduce. Think about the variables that affect SD--line voltage, pumps, pipets, tubing and others. Changing any of these might reduce the SD, even significantly for your sigma. But ... it will take time and resources. Before you decide to move in that direction, think about whether a need for a higher sigma score is necessary and whether you want to undertake the task. Do you not agree with us that the variables we listed can deteriorate (again), leading at some time in the future to another change of tubing, etc? Or next time the SD increases, it might be due to a different one of the variables? How do you find which of many is the cause of an increased SD this time? Having said this, we are certainly in favor of assessing the sigma status or just measuring your distance in SDs from your TE to TEa. They both work to tell how well this system is doing now. We are not advocating trying to make every test a Six Sigma test.
In the next installment we will discuss how Six Sigma may be applied to a larger project--Turn-Around-Time..
David Plaut, Plano, TX, is a consultant, AMT's book reviewer, and frequent speaker at AMT national and regional meetings. Deena Davis, MLS, is Point of Care Coordinator for Bozeman Deaconess Hospital, Bozeman, MT; Nathalie LePage, PhD, is Biochemist at Childrens Hospital in Ottawa, Canada; Kim Przekop, MBA, MS, is Instructor at Rutgers University, NJ.
Table 1. Sigma/SD DPM DPT 1 158.5 0.1585 2 22.75 0.02275 3 1.35 0.00135 4 0.315 0.000315 5 0.02865 0.000287 6 0.00100 0.000001 Figure 2 Group Lab + 2 SD Margin TEa Mean Mean (lab) of CLIA/ Error CAP mg/dL 100 101 SDs 0.3 2.3 2.7 5.00
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|Author:||Plaut, David; Davis, Deena; Lepage, Nathalie; Przekop, Kim|
|Date:||Jun 1, 2015|
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