Six Sigma 之来由

要了解Six Sigma这个名词的来由，就必须由Sigma（）这个字谈起。相信很多人都知道，在数学里，Sigma其实就是我们常说的Standard Deviation。

以当今的科技，无论你使用多么精准的机械，始终无法连续制造出一摸一样的成品。无可否认，很多成品外表看起来都很相似，但是，如果经过详细的测量，我们会发现到所有的产品都有一些小小的偏差。这些偏差或许可以小得令我们很不在呼，可是，很多时候这些小小的偏差对整个成品生产过程带来诸多的问题。

在现实的世界里，偏差是无法避免的。在成品生产过程当中，我们需要原料，机械及人力。原料与原料之间的差异，机械与机械之间的差异以及人与人之间的差异，造成了一个不完善的制成品。偏差永远存在，无可避免，唯一能做的，就是想尽办法减少差异。

Six Sigma的意思是在某个成品的Standard Deviation 相等于( UCL – mean ) 或是 ( mean – LSL ) 的六分之一，我们能够以为该成品制造过程的能力已达到Six Sigma的标准。也能够合理的推测，在百万个制成品当中，最多只有3.4个不合规格的成品。所以，想要达致Six Sigma的标准，并不是一项简单的工程了。

Hidden Factory

Hidden factory are non value added activities hided or embedded in any process operation. Because it is invisible to us, therefore we are not aware of it most of the time.

Toyota production system ( Lean ) classify the non value added processes as waste in the production system. Waste in the production system affecting process efficiency, resulting of higher operation cost.

Founder of Toyota production system Taiichi Ohno & Shigeo Shingo identified 7 critical wastes that need to remove from the main stream process flow. There are;

1. Overproduction
2. Waiting
3. Transportation
4. Inappropriate processing
5. Excess inventory
6. Unnecessary motion
7. Defect

Out of the 7, I would like to add one more: Inspection

Wastes listed above is not unique to Toyota, it exist in our work place as well. We did not aware the existence most of the time, because it is invisible or it is being accepted as part of the main stream process operation.

When a company accepts hidden factory build up in their main stream process operation, a portion of the company resource will be take up to support the invisible operation that do not generate income for the company.
Hidden factory will growth over time. The cost to maintain the hidden factory will roll like a snow ball if management did not clean up their main stream process regularly. The bigger the size of the invisible factory, the more money will be taken up by the invisible monster.

Last update : 31/05/07

Can Lean Implementation To Service / Finance Industry ?

This is to reply a comment left on my earlier post.

“Do have any idea of lean implementation to service/finance industry?”

Answer to you : Yes

Don’t forget, the original concept of Lean Production System is to eliminate wasted / or non value added activities that build in the business processes.

Business processes refer to a chain of activities taken to materialize a product from the point of customer order to delivery or even after sale service.

Products can be a finish product or service that customer pay for and expected.

I have seen Lean and Six Sigma heavily apply in banking industries to improve loan and credit card application.

I don’t see any problem to further enhance the concept in service sector like banking and insurance.

Last Update 16/04/08

Ppk Estimation For Non Normal Distributed Data

Non normal data is the data that do not fit into the shape of normal distribution. In fact, we are facing this type of data most of the time in the actual process.

As an engineer or manager, we should understand our process well and know what kind of distribution a particular process should behave.

Process capability calculation for non normal data isn’t straight forward as what we did for normal distributed data.

In fact, I am not so sure how to estimate the Cpk value this type of distribution manually. I still rely on Minitab when dealing with this kind of data.

I tried to search through Minitab Help and here the formula I get.

The formula looks simple, but I still can’t get a correct answer by substituting the figure I have into the equation. How come? Anyway, I need not to worry so much as Minitab can do all the statistical analysis for me.

Here the problem I have, can anybody tell me how Minitab work out the PPL = 0.4?

Last update : 18/02/07

The 1.5 Sigma Shift

This is a topic that many Six Sigma practitioners put in lot of effort in their Six Sigma research.

Actually, there is no evident to prove most manufacturing process shift within 1.5 Sigma over a long term process.

Experience from Motorola shows that Sigma level of a long term process may be shift within the 1.5 sigma range due to uncontrollable external factors. Don’t forget, Motorola is a big organization that involves many complicated manufacturing processes. At which process the engineers encounter the shift and can 1.5 sigma level shift applicable to all processes under Motorola organization? This is still a big question mark.

I would say, 1.5 is just an artificial number for benchmarking. It is not necessary applicable to all, therefore, why bother so much about the magic number?

Last update : 27/03/08

Cpk vs Ppk - Part 5

Here the sample data collected from the SPC activities, subgroup size = 15. Tape_1 refer to 0.53” tape and Tape_ 2 for 0.46” tape.

From the raw data, without doing any statistical analysis, believe you can tell the adhesiveness of Tape_1 is stronger than Tape_2. Common sense lah… Tape_1 is wider than Tape_2.

Now, look at the chart below, without doing any complicated calculation, you can tell that Tape_1 will have higher Cpk value than Tape_2. Common sense lah… Mean value of Tape_1 is higher than Tape_2.


Ok, now the capability analysis of Tape_1 and Tape_2.




From the data spread, both data set having more or less equal standard deviation, Cpk / Ppk Tape_1 = 2.50/2.47 and Cpk/Ppk Tape_2 = 1.48/1.51. Oh no… Cpk and Ppk Tape_2 is not meeting the industrial standard. How can we conclude that the process of putting smaller tape on the PCA is not capable therefore we should put in more effort to increase the Cpk and Ppk value at least to the industrial standard ?

There are two possible way to increase the Cpk / Ppk value if you want it. You can either increase the adhesive strength or reduce the standard deviation of the smaller tape. Anyway, Tape_1 and Tape_2 having similar material property. Practically it is not possible to make the smaller tape stronger than the larger tape. Now, the only solution to increase the Cpk / Ppk is to reduce standard deviation. The chart above shows that standard deviation of Tape_1 and Tape_2 are more or less equal, it gives me an impression there is no abnormally or special cause happen. Yes, you can try to minimize the process variation, but I m not sure how much we can achieve and how much impact to the Cpk or Ppk value.

Ok, after the long story, is time for conclusion. Cpk and Ppk is a measure for process capability, 1.67 is an industrial standard benchmark. I don’t have any objection on this. When we decided to choose the index as a guide line to measure the process capability, we have to understand the background and nature characteristic of the process. Of cause, we hope everything can be 1.67, but unfortunately not everything can be done. However, it is not the end of the world if 1.67 cannot be done. As a manager, we must have the knowledge to weigh the situation and set practical target.

My personal opinion, Cpk/Ppk 1.48/1.51 is good enough for Tape_2 because I know the natural characteristic of the process. I don’t worry too much about the process shift because overall distribution is far away from the LSL. What I suggest is to continue monitor the process stability through SPC.

Last update : 19/06/08

Cpk vs Ppk - Part 4

Case 2

Peel test is part of a process control I used to monitor in the SPC data. This is an important data I need to monitor because I may face high field return from customer if the process is not in control.

The story happen in one of my large scale printer PCA project. The printer was design in such a way the PCA panel will stick on the enclosure of the printer with a 6” long strong double sided tape. Two type of tape width were use for different application.

We apply the double sided tape manually on the PCA after final test. It is a critical process because the PCA will fall down from the enclosure if the operators did not apply the right pressure when putting the tape on the PCA. In order to control the process stability, SPC is the easiest way. The original intention I add in peel test in SPC is to monitor the process stability, unfortunately fall into a Cpk trap and end up a never ending story.

Picture below shows double sided tape dimension to be place on the PCA, for safety reason, both tape have to withstand a minimum 2kg pull force.


From the tape dimension itself, we can sense that peel strength is proportional to the tape width. Smaller tape width will give lower peel strength, larger tape width will give larger peel strength, it is a common sense.

One evening a new engineer call me up and tell me he want to stop the line for smaller tape because SPC data shows the Cpk is not meeting the requirement, i.e. 1.67. I don't know where he get the number and ask him why 1.67. He reply, oh... it is a industrial standard. The process is not meeting the industrial standard, therefore he have to shut down the line.

A day later, I receive a mail from his manager regarding the same issue, he ask why process is not capable for smaller tape whereas no problem for larger tape. He demands a further improvement on the process to bring up the Cpk value for smaller tape size, at least to the level of industrial standard.

Do you ever face the same problem ?

I will show you why we end up two different Cpk in the same process and material property.

Last update : 16/06/08