Process Capability for Non-Normal Data - Philosophical Questions

[yerasij]

I am trying to answer some philosophical questions that came up in my discussions with my management. I am trying to find some answers to these questions on the Internet and my reference books. But, I have not been able to find one. Hoping that some one here might be able to help:

Background: We work with contract manufacturers (CM's) who make Injection molding parts for us. Historically, we used to collect 32Pcs. (not sure where that came from) data and calculate CpK (without understanding if the process is stable or if the distribution meets normality assumption). In the last year or two, we have been working with all our CM's to establish proper control charts and understand the stability and reduce "special causes". We overcame many challenges (trying to understand the root cause and eliminating them or adding the "causes" if it helps reduce variation etc.,) and now we are at a step where we want to improve how we understand and report out capability.

There are many CTQ's identified on the drawing (some are safety critical and some are critical to cosmetics). Now were are trying to understand the "real" capability of the process and understand # of defects shipped out.

The questions I have are:

Question 1: Lets assume an injection molded part (PC) has 5 characteristics (SPC A,B,C,D and E), and 4 of them (SPC A,B,C and D) are "non-normal". When I try to do best fit method (JMP or Minitab)- all the 4 curves have different distributions. Is it okay to pick different distributions for every characteristic ? (same parts coming from same cavities) or do I need to pick one distribution that has an "Okay" fit for all the characteristics.

Please note that I am only trying to understand the process capability (DPPM) and not trying to compare the characteristics.

The same SPC's follow a different distribution on the next set of tools (which has the same tool structured and similar process parameters). I did not see any statistical difference between the tools or cavities in means or variation.

Question 2: Why aren't the dimensions of a simple injection molded part always follow normal distribution ? I looked at the tool structure and wasn't able to find a "physical limit". Why are they not following normal distribution as expected ? Is that bad ?



Please let me know if you need any more information to help answer these questions.

 

[Miner]

It is certainly possible that different dimensions have different distributions. For example, a fixed dimension might have a different distribution than a closure dimension. Or a feature size versus a distance between features.

However, I would not expect the same dimension to vary its distribution from tool to tool unless you are including cavity to cavity variation. If this is the case, you are mixing process streams and fitting a distribution is a waste of time.

There are a number of things that cause a feature to follow a distribution other than normal. For example, take a fixed dimension such as outer diameter. The part cannot be larger than the diameter of the mold cavity, but may be smaller due to shrinkage. This would result in a skewed distribution. GD&T can artificially cause skewness by taking absolute values or using polar versus Cartesian coordinates.

 

[Miner]

If you attach data, we can better assess what you are seeing. I have Minitab, but Excel would ensure others could also assist.

 

[Proud Liberal]

I would be careful about fitting data to a distribution based on a correlation calculation (ie R square). The correct distribution should be determined by the physics of the process not the mathematics of the dataset. If the correlation to that distribution defined by the process isn't acceptable there are other factors at work that need to be identified and addressed.

(and to Miner's point, mixing process streams can only lead to false conclusions)

 

[howste]

(and to Miner's point, mixing process streams can only lead to false conclusions)

 

[Statistical Steven]

I assume the 32 pieces come from the number of cavities in the mold (4,8,16 or 32).

If you combine data across cavities for any feature, your data is not normal, it is multinomial. You have to look at Cpk by cavity, then combine the Cpks in order to understand that data. I will assume (might be wrong) that each cavity on its own is normally distributed.

Let me know if this helps.

I am trying to answer some philosophical questions that came up in my discussions with my management. I am trying to find some answers to these questions on the Internet and my reference books. But, I have not been able to find one. Hoping that some one here might be able to help:

Background: We work with contract manufacturers (CM's) who make Injection molding parts for us. Historically, we used to collect 32Pcs. (not sure where that came from) data and calculate CpK (without understanding if the process is stable or if the distribution meets normality assumption). In the last year or two, we have been working with all our CM's to establish proper control charts and understand the stability and reduce "special causes". We overcame many challenges (trying to understand the root cause and eliminating them or adding the "causes" if it helps reduce variation etc.,) and now we are at a step where we want to improve how we understand and report out capability.

There are many CTQ's identified on the drawing (some are safety critical and some are critical to cosmetics). Now were are trying to understand the "real" capability of the process and understand # of defects shipped out.

The questions I have are:

Question 1: Lets assume an injection molded part (PC) has 5 characteristics (SPC A,B,C,D and E), and 4 of them (SPC A,B,C and D) are "non-normal". When I try to do best fit method (JMP or Minitab)- all the 4 curves have different distributions. Is it okay to pick different distributions for every characteristic ? (same parts coming from same cavities) or do I need to pick one distribution that has an "Okay" fit for all the characteristics.

Please note that I am only trying to understand the process capability (DPPM) and not trying to compare the characteristics.

The same SPC's follow a different distribution on the next set of tools (which has the same tool structured and similar process parameters). I did not see any statistical difference between the tools or cavities in means or variation.

Question 2: Why aren't the dimensions of a simple injection molded part always follow normal distribution ? I looked at the tool structure and wasn't able to find a "physical limit". Why are they not following normal distribution as expected ? Is that bad ?



Please let me know if you need any more information to help answer these questions.

 

[Mike S.]

How much data do you have? Thousands of parts or hundreds of thousands? Should you really be calculating PPM?

Maybe look up Dr. Wheeler's column "The Parts Per Million Problem".