Understanding of Variation (Easy Learning 6Sigma)

1) What is Variations ?

=Case Study=
Mr.Var is on vacation now. He is at the east coast.
He steps on a diving board to release his stress.
In front of him, there is a sign saying "Caution : Average depth of water : 4 meters»
He is a good swimmer so he simply thought it is only 4 meters deep. So he jumped in. However when he jump to the water, unfortunatelly there are protrusion in the land that make water dept only 1 meter.

During a daily life, we depend on the average to make a decision.
Like in the picture, if you count on the average only, you will make a terrible mistake like Mr.Var does. There is always the variation in everywhere.
If Mr.Var consider the variation of sea bottom, he will not make such a mistake then.
"In other words, variation means change. Not only the average but also the size of change affect our making decisions."

2) Variation in daily lives
- Waiting hour to get baggage when arrived at the airport
what if it takes too long to get your baggage even you come down from the plane
- Waiting hour at the bank
impossible to estimate the waiting hour at the bank
- Report card of your children
how glad to have a stable result from your childrens academic report
- Commuting hour
the arrival time at your work is different everyday even though you leave home at the same time

3) Average and Variation

After-sale service center symbolizes the customer satisfaction. Their average repair time is 30 minutes.
*) When we say the repair time is 30 min., there is no information about variation. Then what is the quality the customers feel ? One case the repair time takes 40 min., then that customer might feel it as 40 min.
*) The company standard is the average of repair time, however, the customer standard is ¡°Standard Deviation¡±. We can find a huge gap between these two

As shown, we can summarize
^ The customers feel the variation, not average. That means we should set up the quality standard for the customer¡¯s viewpoint, that is variation.
^ A huge variation means the quality level the customers feel is a problem, as well as, our work accomplishment is not good.
^ The standard of output at work should be focused on the variation, not the average.

4) Variation measurement
We have measured the time required of task ¡°A¡± in a certain department. The data we got is ranged from 1 to 5 minutes.
There must be the variation in task ¡°A¡±. How can we describe this size of variation ?
The graph shows you the answer.
First, we should think of the average time required.
It is 3 minutes to do task ¡°A¡±.
The way to measure the size of variation is to see the wideness centering the average.
You should calculate each time required and distance from the average. Then get the average from them. That will be the average distance.
The formula is like the below ;
Average distance equals that we divide average distance
(that is data minus average) by number of data.

Let¡¯s summarize
	the average distance is called ¡°Standard Deviation¡± and marked as (ò). The bigger the standard deviation is, the farther the distance is from the average. That means the variation is big. If we measure the size of standard deviation of output in each department, we could confirm the accomplishment level of department accordingly. The bigger the standard deviation is, the lower the work accomplishment of department is. In order to innovate or improve our works, we must reduce this standard deviation for the first.

5) Understanding of Sigma Level
Repair time is average 30 min. and its standard deviation is 5 min. in After-sale service center.
--
When you hear the standard deviation is 5 min., you will not judge it as a big or small one. What do you think of it ?
To judge standard deviation, that is Sigma, we need another standard. If comparing to the average, we could figure out the size.
The numerical value compared to standard deviation (sigma) is called "Sigma Level".
For the detailed calculation, I will handle on the next page.
We can apply this sigma level to Tolerance in R&D, Specification in Factory and Customer Needs in other departments.

6) Calculation of Sigma Level

Using the example of after-sale service center from the previous page, we will calculate Sigma level now.
* Average repair time is 30 min. and its standard deviation is 5 min.
* Customer needs is between 20 and 30 min.
The graph shows ;
How many of standard deviation are there between 25 min and 30 min. ?

"A : Standard deviation is 5 min. so there is only one. In this case, Sigma level is 1.

In other words, Sigma Level means the number of standard deviation within a standard range."

Summary
	Sigma level means the number of standard deviation within a standard range. The bigger sigma level is, the smaller standard deviation is and our work accomplishment level is high.