June 1, 2023
 H. James Harrington Davis Balestracci Jack West Thomas Pyzdek Qlty. Curmudgeon

## Is Three Sigma Good Enough?

Costs don’t always justify striving for near-perfection.

There’s no doubt about it--we should all try to do everything perfectly. Anything that is scrapped or rejected or doesn’t meet customer expectations is waste. We all should schedule the time to do everything the best that we can. But do we really think this is the right thing to do all the time?

In theory, operating at a six sigma level is good, but in reality it applies best to production environments that make 2 million or more widgets per year. Even then, it may not be the best answer. Sometimes less is better, and other times a six sigma level may not be good enough when life and death is on the line.

We need to remember that poor-quality cost has an optimum operating point that must be considered. Walter A. Shewhart called this the “economic cost of manufactured quality.” Therefore the problem is, “How much may the quality of a product vary and yet be in control and produced at minimum cost?” In other words, how much variation should we allow?

Let’s work with a simple example. We are going to start with 1 million widgets that have a total value at the check point of \$10 each or a total value for the group of \$10 million.

Let’s assume that the drift over time is ±1.5 sigma, as the Six Sigma approach recommends.

Figure 1 shows the quantity of good widgets per sigma levels, one through six.

Now let’s calculate the cost per good widget. (See figure 2.)

You will note that cost savings diminish as you go from one sigma through six sigma. At the five sigma to six sigma point, there is very little savings from an internal failure basis. This does not consider the case where the external failure cost is greater than the internal failure cost. In this case we are looking at it from the standpoint of a single widget that is being sold to a customer. If we look at it as the cost savings to the organization, we do see a slightly different result as we move through each sigma level. (See figure 3.)

The average costs for a Six Sigma project is equal to the cost of eight people working two days a week for 13 weeks. At an average hourly cost of \$65 per person, that is equal to 2 × 13 × 8 × \$65 = \$13,520, plus the implementation cost and any added resources required as a result of the change. Figure 3 is a worst-case condition where the drift over time is ±1.5 sigma. If the drift is only one sigma, the savings from going from four sigma to five sigma would be only \$10,000, in place of the \$58,000 savings at the ±1.5 sigma drift level. Often it is better to reduce the drift than to improve the sigma level. This example explains why for the past 60 years professionals have set the certification for individual process steps at a Cpk of 1.4. In the example I used, it is usually justified to put a team to work to reduce variance from three to four sigma or better. At the four sigma or less level, if you focus on internal failure rates only, continual improvement or lean approaches are better than assigning a Six Sigma team.