# How to understand the source of variability and "stream-to-stream variation"

#### andreww

##### Involved In Discussions
Can someone please explain following questions?

1) What is the meaning of "stream-to-stream variation"? CQE Primer (Quality Council of Indiana) says " The distribution of products flowing from different streams (machines, tanks, dies, etc.) may produce variabilities greater than those from individual streams. "What does it mean? Any example?

2) Read the primer, within lot variation minus lot-to-lot variation equals to within stream variation; within stream variation minus stream-to-stream variation equals to within time variation; within time variation minus time-to-time variation equals to within piece variation; within piece variation minus piece-to-piece variation equals to inherent process variation. How to understand that?

#### Steve Prevette

##### Deming Disciple
Staff member
Super Moderator
Re: How to understand the source of variability and "stream-to-stream variation"?

On number 1, let us say we have six assembly lines making product. I can run a control chart of the total number of product made per hour. It will likely have a high standard deviation (variation) and I might end up interpreting that the process is in control. However, if I were to make 6 control charts of the individual six lines, each production line likely has its own average baseline rate, and a lower (than the overall) variability. One or more of the individual lines may be displaying "out of control" behaviors that I might not see when all the data were added together into one big amalgam.

#### andreww

##### Involved In Discussions
Re: How to understand the source of variability and "stream-to-stream variation"?

Thank you very much! Steve. Can you please explain question 2?

#### Steve Prevette

##### Deming Disciple
Staff member
Super Moderator
Re: How to understand the source of variability and "stream-to-stream variation"?

Thank you very much! Steve. Can you please explain question 2?
I'm not sure what they are getting at in number 2. Perhaps it is some form of Analysis of Variance. Do keep in mind you do NOT add standard deviations together, but the squares of the standard deviations (the variance).

If I have two assembly lines added together for a total output and IF they are independent from each other, then the Variance of the sum is equal to the sum of the variances.

#### Bev D

##### Heretical Statistician
Staff member
Super Moderator
Re: How to understand the source of variability and "stream-to-stream variation"?

#2 is trying to describe components of variation studies. typically these are Nested studies not crossed. I think you have misquoted it...because the sequnce of the math you describe is backwards and incomplete.

Say you're making dowels and you have two lathes. working from the lowest level up you have within dowel variation, dowel to dowel variation, lathe set-up to set-up, wood lot to lot variation, time to time variation (such as season to season) and lathe to lathe variation. Within piece and piece to piece variation make up within set-up variation. The approach is to calculate the within set-up variance and subtract the within piece variance. The remainder is the piece to piece variance...

Not sure of the last statement about inherent capability...that is an opinion or operational definition not a law physics...

#### bobdoering

Trusted Information Resource
Re: How to understand the source of variability and "stream-to-stream variation"?

On number 1, let us say we have six assembly lines making product. I can run a control chart of the total number of product made per hour. It will likely have a high standard deviation (variation) and I might end up interpreting that the process is in control. However, if I were to make 6 control charts of the individual six lines, each production line likely has its own average baseline rate, and a lower (than the overall) variability. One or more of the individual lines may be displaying "out of control" behaviors that I might not see when all the data were added together into one big amalgam.
Conversely, each stream may be under very good control, but when they are combined (due to their various means) you get a much more dramatic multi-modal distribution that may infer worse capability. The capability is not that bad. The decrease in capability is due to sampling error - in this case mixing the streams in the sample. As soon as you do that, some of the statistical requirements for standard capability indices (Ppk and Cpk) are violated and make them erroneous. Not only that, you have inserted significant "special cause" variation - the multiple streams. Why is it special cause? Because it does not affect each part the same (i.e., not 'common') and it could be eliminated (just use one stream). This can be true within one machine, such as a multi-spindle turning center. Each spindle is a unique stream, with a unique mean and distribution. The output of the machine, therefore, is truly and dramatically multi-modal (non-normal).

This is another reason why the distribution you see in incoming has no bearing on the true process variation.

#### bobdoering

Trusted Information Resource
Re: How to understand the source of variability and "stream-to-stream variation"?

Say you're making dowels and you have two lathes. working from the lowest level up you have within dowel variation, dowel to dowel variation, lathe set-up to set-up, wood lot to lot variation, time to time variation (such as season to season) and lathe to lathe variation. Within piece and piece to piece variation make up within set-up variation. The approach is to calculate the within set-up variance and subtract the within piece variance. The remainder is the piece to piece variance...
Another tool to describe this is the "total variance equation". It clarifies why nearly every process is multi-modal - as each variation listed presents its own distribution. Some may think that mixing many distributions gives you a normal distribution (a la mixing all colors of pigment gives you black) but, it simply doesn't work that way. People who are convinced of that have generally been fooled by too much measurement or gage error that masked the other errors with their significant normal distributions.

#### andreww

##### Involved In Discussions
Thanks all. My understanding on question 2) is that:

a) Process spread (overall variation) - Lot-to-Lot variation = Within Lot stream
b) Within Lot stream - Stream to Stream variation = Within Stream variation
c) Within Stream Variation - Time-to-Time variation=Within Time variation
d) Within Time variation - Piece-to-Piece variation=Within Piece variation
e) Within Piece variation-Measurement error = Inherent Process variation

#### bobdoering

Trusted Information Resource
Thanks all. My understanding on question 2) is that:

a) Process spread (overall variation) - Lot-to-Lot variation = Within Lot stream
b) Within Lot stream - Stream to Stream variation = Within Stream variation
c) Within Stream Variation - Time-to-Time variation=Within Time variation
d) Within Time variation - Piece-to-Piece variation=Within Piece variation
e) Within Piece variation-Measurement error = Inherent Process variation