Six Sigma and the Clinical Laboratory, Part 1

In light of continuous quality improvement, it seems that more laboratories are trying to understand (and possibly implement) the concept of 6-sigma.

A good place to begin a foray into 6-sigma is with a bit of history. Especially as it is a history that we already have some knowledge of and use often. In 1809, Carl F. Gauss published, in German, 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, normal or Gaussian curve.

He was able to attach a formula to it in the form of y = xa. We won’t go into the “a,” but it is one wonderful and interesting number 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 x value gets farther from the mean, the y values grows smaller and smaller, but not in a linear manner (again, the “a”). 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 increases.

With this behind us, let us turn our attention to the idea of 6-sigma — by the way, sigma refers to the SD of the population (SD, when we use it, usually refers to a portion of the population. A sample.) A tiny bit more history will help:

In the 1980s, 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. At that time, the statistic used in most manufacturing procedures defects were measured per 1000. In other words, if your plant was sending out 7 defective parts per 1000 (e.g. chips, transmissions, microwave ovens, etc.) you had 7/1000 or 0.7 percent were defective. This could probably, and often did, result in waste at the plant or returned parts or a lost customer. Motorola wanted to save money on the waste and lost customers, and after studying the problem, decided to improve the manufacturing process to reduce defects from per 1000 to defects per 1 000 000 (PPM). One thousand times better or 1/1000th the number of defects from before. In our example, that is 0.0007 percent 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.

Imagine that you are a doohickey (DH) manufacturer. Doohickeys are made in different lengths to fit a client’s specs. Imagine that your client wants a DH that is 3.50 cm long. You say, “OK. What is the tolerance? How long or short can they be? Our machine is good to 0.01 cm.” The client says, “Good. We need them plus or minus 0.15 cm. That is 3.35-3.65.” You make a trial run of 100 DH and measure each of them. The average length is 3.49 cm with 1 SD of 0.005 cm. This is a 3SD range of 3.476 – 3.504, which within the client’s specs. So far, so good.

Working with the mean and SD of the trial run, your statistician calculates that the 6-sigma values are 3.46 and 3.52 cm if the mean remains 3.49. In other words, you will have no problem making the DH to the client’s specs (3.35-3.65). And, importantly, if the machine should suddenly start making DH 1-sigma longer (or shorter) — that is, 3.48 or 3.51 (on average) — they would still meet specs. What this means is that the machine (when it is working well) can easily make DH as requested, but even if it were off by 1-sigma, they would still be OK. 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 length of 20 DH for mean and SD and would stop if the 1-sigma level were exceeded. In a nutshell, with a tool that makes DH this well, we will rarely (0. 003 percent of the time) ship a defect DH. Being able to achieve a 6-sigma system gives the plan 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 6-sigma. The table shows defects per million opportunities, and since few of us turnout a million hemoglobins a year, we have included defects per 1000.

Table

Sigma (SD)

Defects/

Defects/

Level

million

thousand

2

308 777

309

3

66 811

67

4

6210

6

5

233

0.2

6

3.44

0.003

Keep in mind that the defects are not patients, but runs.

How could this concept be used in the clinical laboratory? There at least two areas where the concept is worth thinking about. First, in QC. We will use an imaginary analyte — ceramic — so no one thinks we can talk 6-sigma only for chemistry. Second, we will look at turnaround time for a ceramic from the ER/ED.

About The Author