Non-normal Distributions in SPC - How do I Normalize Data?

[Chennaiite]

a correctly controlled precision machining process is a uniform distribution and not normal at all.

May I understand the uniform distribution and how far it is different from Normal??

We know that if you see a normal distribution in precision machining, it is evidence of being out of control, overadjusted, and the operator has become the process, and not the machine.

Normal distribution is believed to be the case of most of the manufacturing processes. An ideal process is perfectly normal. But then, the concept of Cpk calculation is based on theritical requirements or target tolerance zones of the process, in which case the target theoritical distribution is dependent on the specification. It is bound to be different for unilateral and bilateral.
Thanks

 

[bobdoering]

May I understand the uniform distribution and how far it is different from Normal??

Yes, it is discussed in detail here: Statistical process control for precision machining

Normal distribution is believed to be the case of most of the manufacturing processes.

It is an unfounded belief, and is certainly not true in precision machining. The details in the link above discuss why that is the case.

An ideal process is perfectly normal.

This is not an accurate statement.

A process in control is in the ideal state 100% conforming and predictable

-must remain stable over time
-must operate in a stable and consistent manner
-must be set at the proper level
-the natural process spread must not exceed the product’s specified tolerance

and this can occur with the uniform distribution rather readily.

But then, the concept of Cpk calculation is based on theoretical requirements or target tolerance zones of the process, in which case the target theoretical distribution is dependent on the specification. It is bound to be different for unilateral and bilateral.
Thanks

Only the endpoints - what happens in between is up to the process, not the specification. IT IS TRUE that if you have a naturally limited unilateral process, such as one bounded by zero (flatness, roundness, etc.), the closer your process is to zero, the less normal it will be. It will NOT be half-normal, though. That is just a back yard estimation. In fact, if your process stinks, and the process is far away from the limit, you maybe completely normal. It depends.

 

[Miner]

May I understand the uniform distribution and how far it is different from Normal??



Normal distribution is believed to be the case of most of the manufacturing processes. An ideal process is perfectly normal. But then, the concept of Cpk calculation is based on theritical requirements or target tolerance zones of the process, in which case the target theoritical distribution is dependent on the specification. It is bound to be different for unilateral and bilateral.
Thanks

In order to clarify this discussion, I have to add to bobdoerings response.

It is unfortunate that the name Normal distribution is used instead of Gaussian distribution. This has led to the unfortunate belief that any other distribution is abnormal. As bob said this is not the case. The Normal/Gaussian distribution is indeed COMMON in manufacturing, but is not always the correct distribution. In precision machining, economic control leads to a uniform distribution long term. Other, skewed distributions may also be common, especially when dealing with a physical boundary as in a flatness spec.

In short, you may encounter many valid distributions other than the Normal/Gaussian distribution. And yes bobdoering, other than the Uniform distribution. Precision machining does exist, but so do other processes.

 

[bobdoering]

In short, you may encounter many valid distributions other than the Normal/Gaussian distribution. And yes bobdoering, other than the Uniform distribution. Precision machining does exist, but so do other processes.

Yes, it is a wide world. But, my goal is to strip this misunderstanding away from precision machining. All too many people still suffer from this misinterpretation. Besides, it makes a great case that there are other distributions than normal, and the example is typically common enough for most people to understand, if they take the time! I will leave it to others to find their misinterpretations of the application of normal distribution and deal with them...at least for now.

 

[aproddutoor]

Most process in our company do not follow a normal distribution. Which Control chart should I use for a non-normal data? Is there any difference while interpreting the control charts for a non-normal data? How about Process Capability?

 

[bobdoering]

Which Control chart should I use for a non-normal data? Is there any difference while interpreting the control charts for a non-normal data? How about Process Capability?

What kind of processes, and what kind of distributions? Can you supply some sample data in time order sequence to ponder?

Which Control chart should I use for a non-normal data? Is there any difference while interpreting the control charts for a non-normal data? How about Process Capability?

The most accurate answer is "it depends" - and primarily on the kind of processes, and the kind of distributions as well as the opportunities for adjustment to maintain control.

 

[aproddutoor]

I'll post it ASAP

Thanks

 

[aproddutoor]

Hi,

So this is the data.
We use the software Magic Windows Professional. But I can't post the data from that. I ran it in Minitab. See the attached word document.

Most of our customers don't ask for the data to be Normal but the software calculates the Process Capability Ratio's assuming it to be a normal distribution by default and the process might not be in control either.

Is this a good practice? If not, Why?

How do I adopt a good practice for such situations?

Thanks

 

[bobdoering]

So this is the data.
We use the software Magic Windows Professional. But I can't post the data from that. I ran it in Minitab. See the attached word document.

Do you have specifications for this data?

Most of our customers don't ask for the data to be Normal but the software calculates the Process Capability Ratio's assuming it to be a normal distribution by default and the process might not be in control either.

Is this a good practice? If not, Why?

It is not a good practice, as it can over or underinflate the capability, giving inadequate data for understanding the capability. Worst case, it should be transformed. Best cast is to determine the capability based on the actual distribution, if possible.

 

[aproddutoor]

These are the specification limits

Nominal: 21
USL: 21.375
LSL: 20.625

That means the software should be capable of figuring out what the distribution is in the first place.

How about control charts can we use X-bar and R chart for a data like that?
How about interpretation?

Thanks