# Advice on Calculating Control Chart Control Limits

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#### kb103

I have parts with an orange plastic piece, the parts are placed in one of five nests, a keyence color sensor is fixed in place and monitors the orange piece. If the orange piece is present the sensor compares it to a trained value (from a 'nominal' target) and reads a match rate of 0-999. The nests were designed to force the orange piece on all parts to sit in the same area. attached is the data

How would you calculate the control limits from something like this? There is slight variation in part placement due to the nests but assume they're as good as we can get them.

Would you calculate the limits based on the entire 150 samples? Or the nest sample with the highest stdev? Just looking for some guidance, thanks.

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#### supreecha

?Models come in many different Sources (Data distributionforms)

Simulation is the application of models to predict future outcomes with known and uncertain inputs.

Should u defined Nest 61-65 data distribution Normal /or nonnormal

? By Apply Crystal Ball probabilistic methods .

Determine a set of input values that will influence multiple outputs to target values.

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#### kb103

So you would recommend making an I Chart from each nest. The using the lowest LCL (515.4) as the threshold?

A

The Data which you have provided for each nest is not normal and is not stable.
Each nest is not responding the same (equipment/testing issues)?
Before you build a control chart for each process line, the data must be stable and understand why it is not normal.

As Art Bender,one of the original 13 founders of ASQ & contemporary of Deming, use to say, "Show me the data." [Graph it!]
Translation: Do not crank numbers without understanding.

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#### Bill McNeese

##### Involved In Discussions
I am not sure I understand the process. Are there five separate lines and each line has its own nest? Are there one line feeding five nests? If there are five separate lines, then a chart on each one makes sense.

Building a control chart will tell you if the process is stable and the data does not have to be normally distributed for this. But, as stated, you should understand why the data has the distribution it does. And 30 points for each nest is not a lot of data to make a decision about the type of distribution. It is a big difference if there is one line or five lines feeding the nests.

Please remember rational subgrouping. You subgroup your data (including individual charts) to explore the variaition your are interested in. Without more knowledge of your process, that is hard to do.

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#### Bev D

##### Heretical Statistician
Super Moderator
I will remind us that a process doesn't have to be Normal for SPC. To work. This is a myth...
The process stream must be homogenous or we need to use rational subgrouping and/or the correct chart type. But Normality is not required.

Additionally, control limits can be applied to an unstable process. The limits help delineate the instability. Applying limits is diagnostic as well as a means of control. It is an iterative process...

A

Let me clarify my posting.

I assumed the following: the data collected came from one process stream feeding 5 nests (test stands) and the 150 parts were consecutive.
Or, the data collected came from 5 process streams feeding 5 nests (test stands) and the 30 parts to each nest were consecutive.

The first thing which I do with data is to plot it on a Normal Probability chart. [It is easiest chart to produce quickly which will provide clues to the process measurements quickly.]

In the case presented, the Normal Probability chart suggests that each nest is measuring a process which has at least a tri-modal distribution with the higher and lower modes having some type of physical or mathematical boundary. The middle mode appears to have a normal distribution. Additionally, the data from each stand, while producing similar distribution trends, has much variation in their median and spread values. [Note: There was no mention of rational sub-grouping or process analysis.]

I continued my analysis with run charts to determine if there was any obvious pattern. No specific pattern was observed based upon quick visual analysis, therefore, I created preliminary "control charts" for each nest.

The preliminary "control charts" show a tendency in each nest to have a process component which displays that the highest "tri-mode component" value is skewing the spread (stdev) displayed on the chart.

Based upon this brief and very limited knowledge of the process being analyzed, I concluded he process producing the data values was not understood and, therefore, I classified it as "unstable" for effect.
[I.e.: If you don't know what it is, then do not assume the easy, standard solution.]
Since I could see at least a tri-modal with some type of upper and lower limiting distribution, I classified it as "non-normal," again for effect.

I am sorry that my first posting was so curt, but most posters are looking for a "give me a number to use" solution for which I have little patience. I use their postings for analysis exercises only. I do not wish to provide thorough solutions to those unwilling to study and understand the application of basic "statistical control." Art Binder would kick me out of his office many times until I could and would show him my data analysis (no numbers only/number cranking analysis.) I do not provide commentary on the finer methods of control charting until I know that the receiver has a good understanding of the basics.

As for bar graphing data and placing a "bell curve" over it, again I will say, there are major flaws in this type of analysis. The bucket size (value width and center placement) is more art than science and the eye will tend to believe the bars fit a bell shape if it is imposed making it appear normally distributed. [Poor graphs can be misleading. Look at the many examples on business scorecards not based upon statistical rules as noted above, such as month-over-month or year-over-year percentage changes.]

#### Bev D

##### Heretical Statistician
Super Moderator
In my expereince a multi-vari of the data is the single best graph at really understanding your data. You visually SEE all components of variation, trends, cycles, shifts, etc.

The problem with saying a process "isn't Normal", is that people will assume it must be Normal for SPC to work. Saying that a process "isn't stable" when it may in fact be quite stable, but with one or more components of variation that are larger than piece to piece (as would be seen in a homogenous processs stream) is also misleading as to the nature of stability. These are the ways these myths are perpetuated. our words count.

#### Bev D

##### Heretical Statistician
Super Moderator
sorry this has taken so long...busy times at work but I have attached waht i would have done.

in this case the data is very 'flat', no set-up or lot to lot or material lot changes so the analysis is fairly quick.

the first pass is to just look for nest to nest and time sequence trends. the graphs - without any mathematical statistics - clearly show that there is a nest to nest variation.

the second pass is throw control limits on each nest and each nest is in statistical control...

it does beg a question: is it the nest? or are the pieces going in to the nests coming from 5 seperate process streams.

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