How to assess Process Capability for parallelism

[Chris Skowron]

Here is a “real-life” example: There is a drawing specification for parallelism: 0.005”. The target is zero, the upper specification limit is 0.005”.

The manufacturing produces components with the actual parallelism 0.002” – 0.004”.

How to assess the capability of this process? What formulas should be used to calculate indices? What are the acceptability criteria?

 

[Al Dyer]

Possibly use Cp which measures the spread of the process within the spec limits. Your not going to be centered (Cpk) with a one-sided spec. since yout spec is zero.

That is the conundrum of parallelism, the target is zero but under and over spec are the same thing, your either parallel or not.

Measurement gurus please!!!

 

[Paul F. Jackson]

The orientation tolerance "parallelism" defines the size or width of the zone required to contain the axis, centerplane (of a feature of size), or points of a surface relative to the stated datum features.

There is only one answer per part. Even though points on the surface are infinately displaced, it is the width of the zone that is required to contain them that will be examined statistically.

For capability (assuming process in-control) compare the mean of those zone widths and their associated distribution to the Upper Specification Limit.

 

[fyu111 - 2005]

CpK - Rememeber that the Zmin lowest is the true cpk if you calculate it to the upper spec it should qualify. Some software programs allow you to input one sided tolerance. Regardless, usually with parallelism all you care about to the tolerance is approaching the max. 0 would be perfectly parallel and the optimum.

 

[Dave Dunn]

Agreeing with fyu111, Cpk would be appropriate, caculating only for Zupper since it is a one-sided specification.

One question about your data: does your measurement method resolve just to increments of .001" or can it accurately display finer increments? If only .001" your capability calculation might not give you a very clear picture since your number of discreet categories would be limited (0, .001, .002, .003, .004, .005)

 

[Darius]

Beware on one specs. Cpk doesn't has a good behabiur on "one specs" at least if you care more about being on target than with lower variation. Cpmk can be more helpfull because the target is included and in Cpk the other limit is implicitelly added (you are taking it as it is a simetrical leap around the mean and the "not included" spec limit at the same distance from the mean that the other, but didn't noticed - the only way to have the same value).

Just playing with numbers but if you have a time series with
average of 104.7148
stadard deviation of 2.957962
Upper Spec 115
so .... your Cpk is 1.159042

if you take the lower Spec as average - ( Upper Spec - average)
So ... your virtual lower spec is 94.42959
and .. your Cpk for the lower bound is 1.159042


:mg:

 

[cyberspider]

An idea

I think you may use mean sqare error or Taguchi's loss function here straight way. Use the letter one to appreciate what is the deviation.

If not clear pl. post reply for this..

 

[Arvind]

Parallelism data is non-normal in most cases in real life

It is a well known fact that most cases of parallelism or out of roundness data is not normal. In such cases, you cannot assume normality assumption and calculate capability.

In addition, you have only one sided (upper) specification. You may use Weibull analysis to fit the data. It will tell you DPMO exceeding the upper specification.

 

[Jim Wynne]

It is a well known fact that most cases of parallelism or out of roundness data is not normal. In such cases, you cannot assume normality assumption and calculate capability.

Sorry, Arvind, but this doesn't make sense. How can you assume lack of normality? What if an entire lot of say, 1000 units is made, and the same parallelism error is present in all of them? (I've seen it happen; all it requires is careless setup and failure to check the feature until it's too late.) Of course, one should never assume normality when calculating Cpk, but out-of-spec isn't always equal to non-normal.

You may use Weibull analysis to fit the data. It will tell you DPMO exceeding the upper specification.

No, it will allow you to estimate PPM out of specification, not necessarily DPMO, although there's no good reason to invoke "millions" when you're not actually making a million of something.