Charting Bi, Tri or More Modal Distributions to combine results from two machines

M

M Greenaway

#1
Would it be OK to combine results from two machining fixtures into one control chart if the underlying populations would in effect create a bi-modal distribution, but we are using a sample size of 5 in our sub-groups ?

Would combining even more data that would in effect create tri-modal, quatro-modal or penta-modal and above (if those are the correct terms !) ?

I understand that using average and range charts means that no matter the underlying distribution, the sample means will always conform to a normal distribution - is this true and therefore could I apply the above logic ?
 
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Miner

Forum Moderator
Staff member
Admin
#2
If you already know that you will see a multi-modal distribution, you definitely do NOT want to combine them into a single chart. While you are correct, that an Xbar chart will tend to normalize this data, the fact that the process is multi-modal will inflate the average range, which in turn will inflate the control limits making the chart less sensitive to process shifts. Your averages will appear to hug the central line off the Xbar chart.
 
M

M Greenaway

#3
Could I do this if I were using purely tolerance based charting ?

I know this isnt great SPC, but would it have any value in controlling a process at all ?
 

Miner

Forum Moderator
Staff member
Admin
#4
If you have a statistically capable process, you could legitimately use a method such as Pre-control. I do not recommend trend charting within tolerance limits.
 
J

jefnik3201028

#5
Agree with Miner...if bi or multi modal distribution exists the results will be inflated average range and worst the overall average may not mean anything. Example is if you have bi modal, in this condition the Xbar is meaningless as it falls on an imaginary area. Say if you have peaks at 3 and 5, the Xbar will show 4 but there are actually few readings on this area.
Separate SPC charting is the best way of approaching this.
 
D

duecesevenOS - 2009

#6
I'm curious about this as well. What if you have a customer that is accepting on Cpk of the process. Is it even a valid number to give them if the you know the population is multi-modal.

It doesn't really matter because the multi-modal data actually hurts your Cpk quite significantly but we still mix the populations and pass with an okay Cpk. The problem is we spend a ton of time making the process as tight as it is and I don't think the numbers we supply to our customer mean anything because it's a non-normal distribution.



P.S. Customer is the US Government so there isn't much arguing with them.
 
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