Let me start by saying there are many competent quality practitioners using the term Six Sigma. I have a great deal of respect for many of these experts and do not disparage any of them. Of course like any field there exists a huge range in the level of skill, knowledge and wisdom among practitioners, from the novice posing as an expert to the polished professional.
The Six Sigma campaign has been a marketing success. Many people have been exposed to process improvement and undoubtedly many companies have benefited. Still the original theory that led to the term Six Sigma has some critical flaws that can only lead to confusion. The theory conflicts with key tenets of Shewhart and Deming with respect to variation and management. I would like to bring those out here to stimulate discussion. The ideal would be to conserve the best aspects of Six Sigma but place it on a firm footing with a system of profound knowledge.
The term Six Sigma can refer to a basket of tools used to track down problems and defects and improve processes in an operation. My concern here is with the actual name Six Sigma, as I think the original theory developed by Motorola is mistaken and will lead to loss. The more experienced Six Sigma professionals do not rely on the original Six Sigma tool, but instead use process improvement tools developed in the U.S., Japan and other parts of the world over the last 150 years. To explain my objection to the name “Six Sigma” we need to understand the basic principles of statistical process control and how and why they were developed.
The story begins at the Bell Laboratories of AT&T in the 1920s. AT&T was the largest phone company in the US, probably the world, and they also had a huge manufacturing operation to service their network. They had access to the best minds and the best consultants of the day including Frederick Taylor the developer of what would become industrial engineering. The company sought out the best minds, employed brilliant engineers, scientists and mathematicians and created a great environment to work. Despite this leading edge expertise and knowledge there was a problem they could not solve.
AT&T promised customers uniformity, each phone was to be just like the last. Yet the more they tried to achieve this, the worse the results. A young physicist, Walter Shewhart, was assigned the problem. Shewhart pursued this riddle. He thought, experimented, read the literature on statistics and developed new concepts, theories and terminology that proved to be extremely powerful and useful.
He found that in a process there are two kinds of variations. One kind is inherent in the system and he called this natural variation. If you use your best efforts to eliminate variation by making the process as uniform as possible with each step being performed exactly alike you would still have this inherent natural variation. Visual control, visual attempts to make the process uniform will take you so far and no further.
Natural Variation and Tampering
Natural variation will occasionally cause a large amount of variation in the end product. The natural reaction of most people when this happens is to adjust some part of the process: a machine setting, room temperature or some other factor. But the underlying process has not changed; the average or center point has not changed, so on the very next try the process could produce an extreme in the other direction. As an example suppose a process produced an output with an average measure of 98 with variation from 97.5 to 98.5. At one point it happens to produce an output of 98.5 at the top end of natural variation. We might be tempted to adjust the process mechanisms down by .5 since the ideal outcome is 98.00. The thinking is that the process has shifted upwards excessively and therefore we have to adjust it downward. But the higher results of 98.5 was just the result of natural variation, nothing special happened at all yet we treated it as such and made an adjustment. What we have done is to re-aim the process. Now from hereon in the process will produce at an average of 97.5 with a range from 97 to 98.0. If at one point we get a result of 97, something that is bound to happen, we are forced to make another adjustment. Left alone the process would produce between 97.5 and 98.5. With adjustments the process will have a much wider range, maybe from 97 to 99.0 or even greater.A process that is stable will have a fairly predictable range and it will continue to produce product or deliver a service with the same mean or average. But every now and then it will produce an extraordinary value outside its usual range. What should we do? Anyone with experience will tell you that processes tend to deteriorate. They follow the second law of thermodynamics or one or more of Murphy’s laws. Therefore we need to monitor any process. But we need to be very careful to leave a process that exhibits natural variation alone unless we get a real signal that something has changed.
There is a second kind of variation, which Shewhart said had an assignable cause. That is to say that they were caused by something unusual that could be identified and probably eliminated. And further most of the time they could not readily be seen. Sometimes these causes entered the system caused a problem or increased variation and then exited the system. But the fact that they had entered the system means they could enter it again and cause havoc. Often assignable causes are early warning signs of the process deteriorating. There might be a bearing starting to fail, a new employee being untrained or improperly trained or a supplier changing his process. If you could identify these causes and eliminate them, you could further improve the system and allow it to run at its economic maximum.
Another assignable cause is when the process shifts its aim. In our first example the process produced product between 97.5 and 98.5 with an average of 98.00. The process had an aim of 98.00, that was the ideal measurement. The spread can widen so that the range moves from 1 to say 1.5. But the process can also shift so that it is no longer aimed at 98.00 but instead at, say, 98.3. Either one of these occurrences is a problem that will lead to loss and you need to be able to identify when they occur so that you can take action to correct and improve. At the same time you do not want to confuse normal variation with either of these assignable causes.
Natural causes are now called common causes and assignable causes are referred to as special causes. There are two kinds of signals that are important from the point of view of quality and uniformity:
1. A change in the average of a process and
2. A change in its range.
There is no absolute foolproof way of determining whether something is a special cause or a common cause. The two both produce variation so we need to think statistically. We can search for a special cause and find one and eliminate it. This is an ideal outcome. But we can search for that special cause and after much work not be able to find anything to explain the variation. We made a mistake, the cause was common and we treated it as being special in nature and there is cost associated with this mistake. There was no benefit but someone had to take time to search for it, may have run some experiments, may have questioned others and time was taken away from other useful activities. Shewhart initially called this a type I error, but we now call it a type I mistake. There is a cost in time and money associated with a type I mistake.
On the other hand we could see a large change in the mean or the range of a process and ignore it and it turns out it was just natural variation and the process is operating fine. This is ideal. But if we ignore a change and it turns out there really has been a change, a special cause has entered our system and this can cause many more expensive problems in the near future. There is a cost to ignoring a special cause and we now call this a type II mistake.
How Were 3 Sigma Control Limits Determined?
What Shewhart had to do was minimize the loss from these two kinds of errors. One could eliminate type I errors by making many type II errors and vice versa. But he needed a robust way of minimizing the total loss from both kinds of errors for many different kinds of processes. To do this he developed Control Limits. What he found through observations and experimentation over a broad range of processes in many areas of business was that if the control limits were set at 3 sigma they seemed to work. Three sigma control limits minimize the loss from making these two types of errors. They were empirically determined. And they have held up remarkably well over the 80 years since Shewhart published his first book. No one has found a better way.
3 Sigma Control Limits are computed in the same way that standard deviation is computed, but the term 3 sigma is better. People who hear the term standard deviation automatically assume that the underlying process distribution is a normal distribution but it is not. At one point it was thought that once a process is in statistical control, meaning there are no special causes at work, the underlying distribution would be a normal distribution. When that failed to be the case it was hoped that a family of distributions might fit the data, but as Shewhart stated in 1939 all hope for that has been shattered.
This turns out to be very upsetting to many people who confuse mathematics with reality. A further explanation might require a lengthy article but for now I just wish to point out that a normal distribution assumes specific ideal conditions with no environment. Alas reality is not so simple.
Returning to the main topic, however, once we remove all special causes our process is said to be in statistical control. Of course it has to be monitored to preserve that state as statistical control is a very unnatural condition that requires effort and vigilance to maintain. But suppose our process has a mean of 98.00 as stated above and s range of 97.5 to 98.5. What is the defect rate? Which are the defective products?
Voice of the Process, Voice of the Customer
The surprising answer is that from what we have covered so far there is no way of knowing. All we have discussed so far is the process. The process if it is in statistical control has a capability. It has an average that persists over time and it has a spread that persists over time. This is called the voice of the process. But whether the output of this process is good, within specifications, defective or fit for use depends on outside considerations.
What will the product be used for, how will it be used and what are the requirements of the user. It is a statement about the environment, the larger system in which the product of our process is but a part. In a production system, or a service system the user or customer is the next step in the process. This is the voice of the customer. The traditional way of stating fit for use of a product are specifications.
If the specifications are that the product (or service) should have a mean (or ideal) of 98.00 and a range from 97.00 to 99.00 then everything produced by our process is good. If the required range (specification) is 97.5 to 98.5 then we will occasionally have defects as it is possible though rare that our process will produce sometimes outside this range. But if the specifications are tighter such as 97.75 to 98.25, then we have a major problem as our system will produce many defective items. In the last two cases those who manage the process need to focus on decreasing the range of the process. This is done not by adjustments which as has been stated will increase the variation, or by edict but by lessening the common cause variation in the process. For a stable system, that is to say one that is in statistical control, this requires improvements in the system. A control chart is invaluable for systemic improvements as well as for eliminating special causes.
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