• Lean cannot bring a process under statistical control
• Six Sigma alone cannot dramatically improve process speed or reduce invested capital
• Both enable the reduction of the cost of complexity

The Army’s deployment is one of the largest anywhere. The Army’s Lean Six Sigma program has trained more than 1,450 senior leaders. As of the date of the report on their web site, the Lean Six Sigma community has completed nearly 5,200 projects, and more than 1,900 projects are currently in progress. Completed projects have yielded significant financial and operational benefits at organizations across the Army.

The Army’s use of Lean Six Sigma is part of its effort to transform the Army through the establishment of the Institutional Army Transformation Commission in August 2011. The Secretary of the Army, John M. McHugh, established the Commission in a Memorandumon 15 August 2011. According to the Secretary, “reforming and restructuring the Institutional Army – the Generating Force – is critical to building the Army of the future and supporting the forces of today. It must be as nimble, agile and adaptive as our Operating Force – driven by ideas, innovation and a determination to bring the best services and equipment, training and leaders, medical care and support to our Soldiers, civilians, and their family members.”

I think its safe to say that creating an organization that is nimble, agile, adaptive, driven by ideas, innovation, and a determination to bring the best are all goals that any leader can embrace. I believe that the Army is correct in believing that Lean Six Sigma can help them achieve these goals.

Recently some prospective clients asked me for a demonstration project to help them determine if six sigma would be a good idea at their company. I advised them against it. Such a demonstration only shows management’s lack of commitment to the success of six sigma. Although philosophical issues are important, there are more concrete problems with such “toe in the water” projects. In particular, major quality improvements can sometimes yield little or no bottom-line cost impact. The result of such projects is to convince management that six sigma adds cost without adding value. This belief is, of course, totally wrong. But it’s also a logical result of the demonstration approach itself.

For example, Sam was a six sigma enthusiast. He’d studied its use at several major companies and was convinced that it would save his company, which we’ll call Acme, millions of dollars. The hype had also caught the attention of the senior leadership at Sam’s company. But before diving headlong into six sigma, they wanted Sam to conduct a demonstration project to see if the savings reported by the press could actually be obtained at Acme.

The company’s main product was a complex assembly, which Acme sold to a large aerospace customer. The assembly- manufacturing process was in statistical control and producing an average of 10 defects per assembly. With management’s support, Sam documented the cost of noncompliance to be about $1,000 per assembly. After months of diligent effort, Sam’s six sigma team was able to redesign the process. To their delight, they were able to reduce the number of defects per assembly by a full 50 percent, from 10 defects per assembly to five.

Management was also interested in the project. But the accounting department had carefully monitored the costs for the assemblies, and to everyone’s surprise, accounting found only a minuscule 0.7-percent cost savings.

Based on these results, leadership’s conclusion was simple: Quality doesn’t pay. The company won’t pursue six sigma any further.

Did accounting make a mistake? In a word, no. The problem arose because Sam measured quality as defects. The truth is that most costs are incurred because of defectives rather than because of defects. (Thanks to Mikel Harry of the Six Sigma Academy for this insight.) A defective is a unit of product or service that contains one or more defects. Whether a unit contains one defect or several is irrelevant. Customers generally react to defective units by returning them for warranty repair, refunds or other options. Internally, defective units must be identified through costly inspection and then routed through equally costly rework processes, or else scrapped entirely. A unit with one defect costs nearly as much as one with several.

Mathematically, the Poisson distribution describes the relationship between defects and defectives. The equation for the Poisson distribution is

In the equation, x represents the number of defects in the sample, and P(x) means the probability of finding x defects. For example, P(1) is the probability of finding one defect. The symbol μ is the average number of defects per unit of product or service. For Sam’s project, the average assembly had 10 defects before six sigma was applied, so μ = 10. The efforts of the six sigma team reduced the average number of defects per assembly to 5, for a 50 percent improvement in quality.

Let’s plug these numbers into the equation and see what happens. Because we are interested in the probability of an assembly being defect-free, we want to know P(0) for each of the two quality levels. Before six sigma, with μ = 10 we get

In other words, there were virtually no defect-free circuit assemblies before applying six sigma methodologies. After applying six sigma, the probability of getting a defect-free assembly at Acme was

Thus, a 50-percent improvement in the quality level as measured in defects produces only a 0.7-percent improvement in the number of defect-free circuit assemblies. A complete graph of this relationship is shown in Figure 1.

Figure 1-Quality Improvement vs. Cost Savings

The real cost-reduction benefits only start to appear when quality reaches very high levels. This relationship explains the commonly observed phenomenon of quality programs not paying off in the short term. Only when companies stick with it long enough to begin to approach six sigma quality levels do they get the desired results. Too often, “toe in the water” projects scare companies out of the pool before they even start to swim.

I recently attended a presentation using a control chart. The control chart showed a process in statistical control at about an 8-percent reject rate. The presenter noted that the process was stable and went on with her presentation. I barely avoided shouting that, while stability is nice, an 8-percent reject rate is not acceptable. The 8-percent level represents a certain amount of ignorance about the process; a level I find unacceptable. The problem is that the presenter didn’t think of it that way at all. To her, 8 percent represented a considerable accomplishment.

This blog is for those of you who, like me, want to scream that, as long as improvement is economically justified, “It’s never good enough!” I will present a way of measuring ignorance; a simple-to-compute statistic which highlights the fact that there is always something to learn about how to improve a given process.

First, let’s take a look at the philosophy that underlies statistics. In his book, The Art of Thinking, philosopher Leonard Peikoff wrote, “Statistics are applicable only when: 1. You are unavoidably ignorant about a given concrete; 2. Some action is necessary and cannot be deferred.”

In other words, if you’re trying to determine a course of action, your best bet is to acquire knowledge, not to blindly use statistics to guide you. While it’s true that we don’t want to tamper with a stable process, it’s also true that we don’t want to settle for anything other than the best level of quality we can provide. Control charts guide us away from tampering, but they don’t tell us how we can improve the process. Only new knowledge can do that.

Statistical probability should be used only when we lack knowledge of the situation and cannot obtain it at a reasonable cost. If we have direct knowledge about a situation, or can get it through a bit of research or by consulting someone who has it, then we should not blindly follow the statistical probabilities. In other words, if you know something about the situation, you should act on what you know.

Statistics are an expression of ignorance. They should only be used when ignorance is unavoidable, i.e., when knowledge is absent and unobtainable. Statistics are not knowledge. They are a calculation that permits action in the face of ignorance. This is the critical point missed by the presenter. She assumed that if she simply stated the level of ignorance, further improvement was not necessary.

Properly used, statistics measure ignorance or, conversely, knowledge. For example, assume that you want to buy a new piece of production machinery. Think of the important variables in the process as a list of 100 items, all of them unknown. You begin by creating a list of those items you believe to be important and prepare a plan to control as many of these items as possible. Let’s say you start with 75 items. Assuming that every item on your list is actually an important variable, these 75 items are special causes–things that affect your process and must be controlled. The remaining 25 items are common causes of variation, unknown to you but also important causes of process variability even though any one of these causes will have only a small effect.

From this starting point, you conduct a process capability study and, using statistics, quantify your knowledge as explaining all but +/-0.003″ of variation in the process. There are some out-of-control data points. After investigating these, you identify five more important variables. The process stabilizes, i.e., all of the remaining points on the control chart fall within the control limits.

Let’s assume that the control limits for the X-chart are now +/-0.002″. In philosophical terms, this means that you acquired +/-0.001″ of new knowledge, but +/-0.002″ of ignorance still remains. As time goes by and you learn more, the control limits will measure the amount of your learning. If in a year the control limits are at +/-0.001″, then you’ve learned enough to reduce the process variation by 50 percent.

As soon as you acquire this knowledge, the previous statistics become irrelevant. Gaining knowledge is the equivalent of converting special causes into common causes. This is like discovering more and more items on the list of things that cause your process to vary. You may never discover every item on the list, but with statistics to help you keep score, it’s fun to try. One way to make it even more fun is to plot a “knowledge chart.” Here’s how it works:

Record the process standard deviation from your most recent process control chart, for example, S₀ = 10.

For each subsequent complete control chart, compute the process standard deviation, for example, s₁ = 9.

Compute your relative knowledge,

k, as K=100% x (S₀-S₁)/S₀

For our example, K= 100% x (10-9)/10 = 10%

As you reduce your ignorance to zero, the knowledge measure will go to 100 percent. It’s a fun way to keep track of your quality progress!

April 12, 2008

Can you perform designed experiments on processes that are not in a state of statistical control? This podcast tells you where six eminent expert statisticians come down on this issue, and Tom adds his summary of the debate and his 2-cents worth. 10:19.