Finding a flat or not modeling distribution: how to manage it?

bobdoering

Stop X-bar/R Madness!!
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#11
Yes, in the blog it explains how - if you are not overcontrolling the process - you can use (USL-LSL)/(UCL-LCL) as your capability for the uniform distribution.

Here is a modern day explanation of distributions and stability. You car has a check engine light. What causes it to turn on, and how? People often say "senors" turn it on, but sensors do not have the capability of understanding if there is a problem, they only know what the current condition is. The computer knows what conditions are good or bad. But, how does it know? It has an algorithm, or "model" that it compares the current conditions to. This model was developed by people who looked at the processes over time and determined what the process conditions are when it is behaving well, and what they are when it is not. When they are not behaving well, or have conditions out of the expected model, the signal - in this case the error codes and check engine light, are activated. You need to understand the correct model for your process tor turn on the signals at the correct time. That model is the correct distribution for the process. Use the wrong one, and you make wrong decisions. That is how important using the correct model is! Stability is running within the defined correct model - which cannot be rubber stamped as the normal distribution.
 
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Bev D

Heretical Statistician
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#12
What Bob said...
You are wise to come to a place this to ask questions. Even the seemingly simplest statistical 'tools' like SPC or capability studies and the fake statistical tool, the capability index, require knowledge and deep thought. Remember that knowledge isn't the same as casual exposure to some terms, a few formulas and and idealized examples.
 
#13
What Bob said...
You are wise to come to a place this to ask questions. Even the seemingly simplest statistical 'tools' like SPC or capability studies and the fake statistical tool, the capability index, require knowledge and deep thought. Remember that knowledge isn't the same as casual exposure to some terms, a few formulas and and idealized examples.
I don't know if I understood well, but if you intend I'm improvising in this area, it should not be.
I studied a little on statistic books, I made some introductive courses and started to use SPC and distribution analysis at my job, and I discovered a new world.
I just made a structured test on cold steel stamping with a new article, taking unchanged other characteristics and changing only the raw material, to verify if the thickness and mechanical characteristics are the main causes to average drifts during production and in the time.
So, I know it's not so simple SPC and data science, but I'm trying to improve my knowledge and professionalism just with the help also of elsmar!
Please then, every suggestion, for a generic approach too, is well appreciated!
 
#14
Yes, in the blog it explains how - if you are not overcontrolling the process - you can use (USL-LSL)/(UCL-LCL) as your capability for the uniform distribution.

Here is a modern day explanation of distributions and stability. You car has a check engine light. What causes it to turn on, and how? People often say "senors" turn it on, but sensors do not have the capability of understanding if there is a problem, they only know what the current condition is. The computer knows what conditions are good or bad. But, how does it know? It has an algorithm, or "model" that it compares the current conditions to. This model was developed by people who looked at the processes over time and determined what the process conditions are when it is behaving well, and what they are when it is not. When they are not behaving well, or have conditions out of the expected model, the signal - in this case the error codes and check engine light, are activated. You need to understand the correct model for your process tor turn on the signals at the correct time. That model is the correct distribution for the process. Use the wrong one, and you make wrong decisions. That is how important using the correct model is! Stability is running within the defined correct model - which cannot be rubber stamped as the normal distribution.
Bob, about a stable process, the meaning is clear, no doubts.
I'm trying to hear again the CorrectSPC video to understand better all the presentation, some phrases are difficult for me to understand due to foreign-speaking speed, but I'm not able to wait asking you some doubts:

1. Why other kinds of drifting charts, like trend charts, shows measurement errors instead of process characteristic?
2. Why is necessary in Xhi-lo-R chart of two bands to verify the mean? Or better, it's about the diameter measurement method, another issue, and then, the better method is to use a GD&T machine, because it's not the max. and min. diameter the issue, it's the larger and smaller points in the surface found, a different thing, isn't it?
3. Why 75% of USL and LSL value to get the process and then chart limits? If the process is not ruled with a normal distribution, but with a uniform distribution, so all values with the same frequency, there're no tails that justify an inner compression of process limits then specification limits, do I make wrong statistical thinking?

Thank you for your support.
Kind regards.
 

bobdoering

Stop X-bar/R Madness!!
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#15
1. Why other kinds of drifting charts, like trend charts, shows measurement errors instead of process characteristic?
The key is what the process behavior should be. If it makes sense that the process behavior should be random, but suddenly you see a trend, then you have evidence of a special cause. All Shewhart charts are designed to do is sense signals that the process that is expected to have a random and independent output has a special cause that is causing it to be non-random. However, if your output is a function, such as tool wear, plating bath concentration (from drag-in and drag-out), etc. Then you are looking for a special cause that would cause the output to long longer exhibit the function output - such as become random or have an incorrect function.
Measurement error tends to be random, independent and (for bilateral characteristics) normal. When it is large enough it will mask the underlying function, if it exists. That is where you run into problems.

2. Why is necessary in Xhi-lo-R chart of two bands to verify the mean? Or better, it's about the diameter measurement method, another issue, and then, the better method is to use a GD&T machine, because it's not the max. and min. diameter the issue, it's the larger and smaller points in the surface found, a different thing, isn't it?
As shown in the videos, ignoring the within-part variation when trying to determine the process variation, you will confuse measurement error with process variation. The Hi/Lo values eliminates the error of within-part variation. The definition of a round feature is NOT its average size (in fact physically it is meaningless.) A diameter is defined by the zone of values exhibited about a central point - described as either the high and low or the average AND range (never average alone.)


3. Why 75% of USL and LSL value to get the process and then chart limits? If the process is not ruled with a normal distribution, but with a uniform distribution, so all values with the same frequency, there're no tails that justify an inner compression of process limits then specification limits, do I make wrong statistical thinking?
The 75% goes back to using 1.33 as a comfortable capability - for customers and producers - that both accommodates the various errors that exist in the process in addition to the process variation found in the Total Variance Equation, especially sampling error (the process variation between samples), but also including gage error, etc. If it wasn't for the other errors in the Total Variance Equation, you could run to the specification. But, they are there, so you can never run to the spec on the shop floor without risking making bad parts - even in control.

Hopefully,that will help.
 

bobdoering

Stop X-bar/R Madness!!
Trusted Information Resource
#16
I just made a structured test on cold steel stamping with a new article, taking unchanged other characteristics and changing only the raw material, to verify if the thickness and mechanical characteristics are the main causes to average drifts during production and in the time.
Believe it or not - and your process people do, even though they do not statistically know why - the stamping function is tool wear. With a stamping die, you have one sawtooth - not many that we see when we have the luxury of offsets. It starts when the die is new and may last many years until the die is worn and must be replaced. This is why a new die is not made to run at mean. If you did, it would only have half the life - and that is very costly mistake in stamping dies! There are very noticeable variables within those years of tool wear that affect the output, material variation in both size and physical properties. But, guess what....those are special causes! You really don't need a chart to tell you they are special causes. What you need is - just as in any SPC chart, even Shewhart charts - a reaction plan for when a special cause is found. And I will say this: in the long history of SPC charts, the least successful part of its implementation across the world is a meaningful reaction plan for what to do when you get out of control condition (are under the influence of a special cause). The reaction plans, if any, are horrible.
 
#17
As shown in the videos, ignoring the within-part variation when trying to determine the process variation, you will confuse measurement error with process variation. The Hi/Lo values eliminates the error of within-part variation. The definition of a round feature is NOT its average size (in fact physically it is meaningless.) A diameter is defined by the zone of values exhibited about a central point - described as either the high and low or the average AND range (never average alone.
I already understood the needs to verify the whole condition of the circle, it's clear, but it's the method to measure and the meaning of roundness that need some considerations: the diameter of a circle is an approximation of surface errors that generates an irregular form than a theoretical circle, made with a GD&T machine, you'll get the best approximation possible, with the least-squares method, and the roundness, a value to define the form error from the approximated calculated diameter, is the min. circumscribed diam. - the max. inscribed diam., get from the minimum point and the maximum one found (not diameters, that could not find the smallest and bigger values if not speculars!).
So, with a GD&T measuring method, that should be the more precise even if possible with only diameters but less precise, is sufficient a chart for approximated diameter from low level to hig, or viceversa, and a normal X-bar chart for roundness, do we agree?

The 75% goes back to using 1.33 as a comfortable capability - for customers and producers - that both accommodates the various errors that exist in the process in addition to the process variation found in the Total Variance Equation, especially sampling error (the process variation between samples), but also including gage error, etc. If it wasn't for the other errors in the Total Variance Equation, you could run to the specification. But, they are there, so you can never run to the spec on the shop floor without risking making bad parts - even in control.

Hopefully,that will help.
Sorry, Bob, what I want to say is that, the uniform distribution that I should find, if it's inside the project spec. when measured at least 30pcs, it already has the whole errors of the equation, so, if it's uniform and has no tails like the normal one, and is inside the specifications, why has to be reduced to 75% the process limits? (uniform distribution stops parts to its bords, so what you see in frequency is what is possible to have with that distribution, no more, isn't it?)
 
#18
Believe it or not - and your process people do, even though they do not statistically know why - the stamping function is tool wear. With a stamping die, you have one sawtooth - not many that we see when we have the luxury of offsets. It starts when the die is new and may last many years until the die is worn and must be replaced. This is why a new die is not made to run at mean. If you did, it would only have half the life - and that is very costly mistake in stamping dies! There are very noticeable variables within those years of tool wear that affect the output, material variation in both size and physical properties. But, guess what....those are special causes! You really don't need a chart to tell you they are special causes. What you need is - just as in any SPC chart, even Shewhart charts - a reaction plan for when a special cause is found. And I will say this: in the long history of SPC charts, the least successful part of its implementation across the world is a meaningful reaction plan for what to do when you get out of control condition (are under the influence of a special cause). The reaction plans, if any, are horrible.
Thank you so much for the stamping issue, it's important for me and for whoever has business with it, because it's a process with a huge investment before, to get many many pieces during work with very low costs and time after.
But as you wrote, it has special causes like material change within thickness (probably about the 80% of effectiveness) and mechanical characteristics (20%), and temperature.
About the function in toolwear along much time, could be but I didn't find it now directly a problem, also with old parts in production since decades.
However, the problem it's often found with this process is the mean shifting when those special causes act.
I don't understand what you say at the end with: "What you need is - just as in any SPC chart, even Shewhart charts - a reaction plan for when a special cause is found. And I will say this: in the long history of SPC charts, the least successful part of its implementation across the world is a meaningful reaction plan for what to do when you get out of control condition (are under the influence of a special cause). The reaction plans, if any, are horrible."
Why reactions plan are horrible? Probably because they'll increase the instability? But I don't think so, if the effect is a mean shift.
Rather than this, the mean problem is that solutions to permanent decrease special causes effects are expensive and to be tested or probably not possible, like stamp climatization and punch male and female on stations to be changed when occurred.
 

bobdoering

Stop X-bar/R Madness!!
Trusted Information Resource
#19
Why reactions plan are horrible? Probably because they'll increase the instability? But I don't think so, if the effect is a mean shift.
Rather than this, the mean problem is that solutions to permanent decrease special causes effects are expensive and to be tested or probably not possible, like stamp climatization and punch male and female on stations to be changed when occurred.
Specifically, what are the steps you take when a process is out of control? Do you validate you measurement by measuring again? Nothing like adjusting a process to an incorrect measurement. Was it a singular random occurrence, as in chucking on a chip in machining? Hate to adjust the process, only to have the chip leave and make every part after it scrap. Do you clean the tooling? Do you remaster the gage? Do you ask for help from engineering or maintenance? Do you quarantine parts and sort? For how many parts? Specifically, step by step in time order, what do you do?

Part of the issue is you are trying to apply this process that is easier explained in machining to stamping. That can be frustrating. Stamping is a little more discrete. You can find the smallest diameter in a stamped hole, and that location on consecutive parts should still be the smallest diameter. That is also the best one to track, since most holes function are best described as a maximum material condition. That is also why mean still las little value to you. You could track that one diameter and watch the tool wear, or effects of your special causes. In your case, roundness is physically not the same thing as in a turned part - which has a lot to do with the harmonics of the machine versus the rotation of the part. For you it is die error from the original manufacture of the die or some unusual wear characteristics of the die (very unlikely).
 

bobdoering

Stop X-bar/R Madness!!
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#20
Sorry, Bob, what I want to say is that, the uniform distribution that I should find, if it's inside the project spec. when measured at least 30pcs, it already has the whole errors of the equation, so, if it's uniform and has no tails like the normal one, and is inside the specifications, why has to be reduced to 75% the process limits? (uniform distribution stops parts to its bords, so what you see in frequency is what is possible to have with that distribution, no more, isn't it?)
Every process is multi-modal, based on the Total Variance Equation. Tool wear - the predominate variation in precision machining - is a continuous uniform distribution, but most other errors, such as sampling error, gage error, etc. are normal or otherwise tailed. Add them all up and you get a predominately uniform distribution with small tails contributed by the other factors in the equation.
 
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