# Six Sigma and the clinical laboratory.

In light of continuous quality improvement, it seems that more laboratories are trying to understand (and possibly implement) the concept of Six-Sigma. The chances are that you will be introduced to this idea either from folks from way up on the totem pole or from people closer to the laboratory who are interested in quality control (QC).

Here our plan is to ensure that you do understand what Six-Sigma is all about. both the ideas and the statistics, and how Six-Sigma could help the laboratory. We will spend a little time on the history of Six-Sigma and illustrate with an example or two of why it may not be applicable to the instruments you use but can be useful in other parts of the laboratory.

The history of Six-Sigma can be said to have begun in 1809, more than 200 years ago, when Carl F. Gauss, a German, published a book of mathematics in which he described a curve based on data obtained by measuring the same thing many times. You know this curve as the bell, the normal curve or the Gaussian curve. (Fig. 1)

After studying a histogram of the data, Gauss was able to attach a formula to it in the form of y = [x.sup.a]. We won't go into the mathematics of this equation, but it is one wonderful and interesting equation that includes pi and more. As you know the curve is symmetrical about the middle (the mean). The curve is interesting in the fact that as the horizontal value (x) gets farther from the mean, the vertical values (y) grow smaller and smaller, but not in a linear manner. Actually, the curve NEVER touches the x-axis. (Although too often in texts it does touch.) Areas under the curve have been measured (assuming that the total area is 1.0 unit) even though the curve has no end on either side. Fig. 2 shows the areas under the curve going from -3 SD to +3 SD in 1 SD steps. As you can see, the area between SDs becomes smaller as the SD values increase. As a matter of fact, the area under the curve beyond 3 SDs is quite small.

Before we go further, let us touch on the use of the words sigma (ct) and standard deviation (SD). Sigma refers to the SD of the population. (SD, when we use it, usually refers to a portion of the population--a sample.) Think of every vial in the entire lot of a control as the population. Then consider that your shipment is a sample of that lot and each vial in your shipment is a sample of your sample of the population. It would be quite rare for the laboratory to have the entire population (of a lot of control or reagent). Even validating a reference interval yields data from a part of the population (a sample). We use sigma together with SD (sigma/SD) early in this article but when we look at examples in QC, we will use SD.

The story of 6-Sigma/SD as a way to improve quality (reduce errors, save money and time) began in 1980 when Motorola was making computer chips by the hundreds of thousands almost daily. It struck them that their system for detecting errors was not sensitive enough. That means too many defective chips were being shipped to customers. At that time, the statistic used in most manufacturing procedures was "defects per 1,000." In other words, if a plant was shipping 6 defective parts per 1000 (e.g., chips, ball bearings, etc.), you had 6/1000 or 0.6% were defective. This could probably, and often did, result in waste at the factory, returned goods or even a lost customer. Motorola wanted to save money on the waste and lost customers. They studied the problem and decided to improve the manufacturing process to reduce defects from per 1000 to defects per 1,000,000 (DPM, sometimes DPMO or defects per million opportunities), one thousand times better or 1/1000th the number of defects from before. In our example that is 0.0006% defective. Virtually none. In other words, they did not extend their limits on what they would accept, but to be better at what they were doing.

They quickly saw that just by saying, "Let's do the job better;" or "Tighten that bolt. That will fix it." They needed an entire, ongoing process. This process, which is on-going--you never stop looking for improvement --is divided into five parts: 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. It is never done.

Imagine that you manufacture gizmos. Gizmos are made in different diameters to fit each client's individual specs. Imagine that your client wants a gizmo that has a diameter of 3.50 cm. You say, "OK. What is the tolerance? What are your specifications? Our gizmo machine is precise to 0.01 cm." The client says, "Good. We need them plus or minus 0.15 cm. That is 3.35-3.65cm." You make a trial run of 100 gizmos and measure each of them. The average diameter is 3.49 cm with 1 SD of 0.005 cm. This is a 3 SD range of 3.475-3.505, which is within the client's needs. So far, so good.

The Six-Sigma/SD values are 3.46 and 3.52 cm if the mean remains 3.49 cm. In other words, you will have no problem making the gizmo to the client's needs (3.353.65 cm). And, importantly if the machine should suddenly start making gizmos 2-sigma/SD thicker---that is 3.50 (on average)---they would still be acceptable. What this means is that the machine (when it is working well) can easily make gizmos as requested, but even if it were off by 2-sigma/SD they would still be good. You are happy because you are able to supply your client even if the machine is slightly off. Of course every 20 minutes your foreman checks the diameter of 20 gizmos for mean and SD and would stop if the client's specifications were exceeded. In a nutshell, with a tool that makes gizmos this well, we will rarely (0.003% of the time) ship a defect gizmo. Being able to achieve a Six-Sigma system gives the plant a margin of error, error budget, or wiggle room. The table shows the decline in faulty parts as we move from a system with only 2-sigma up to Six-Sigma. The table shows defects per million opportunities, and since few of us turn out a million hemoglobins a year, we have included defects per 1000. A defect could refer to a single control in a run, rather than a single patient. (The number of patients affected by a run being 'out' is difficult if not impossible to determine.)

Below is Table 1 illustrating 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).

How could this concept be used in the clinical laboratory? There are at least two areas where the concept is worth thinking about. In the next installment we will use an imaginary analyte---ceramic---so no one thinks we can talk Six-Sigma/SD only for chemistry. Then we will look at turnaround time for a ceramic assay from the ER/ED to study a larger project.

David Plaut, Plano, TX, is a consultant, AMT's book reviewer, and frequent speaker at AMT national and regional meetings.
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Table 1

Sigma/SD    DPM       DPT

1          158.5     0.1585
2          22.75    0.02275
3           1.35    0.00135
4           3.15    0.00315
5          0.2865   0.000287
6          0.001    0.000001
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