I have just been asked a question by our customer service department, and I do not have an answer. This site came to mind and I will post here to see if there is a solution available.

We collect variable data during production runs on various characteristics on the part. Process capability was conducted from a specific lot of production and the following Expected Overall Performance was calculated in Percent Nonconforming.

Characteristic Length %<LSL 0.29%, %>USL 1.9%

Characteristic Warp %<LSL 2.33%, %>USL 26.97%

Characteristic Hole Position %<LSL 0.92%, %>USL 4.07%

Note: LSL (Lower Specification Limit) and USL (Upper Specification Limit.

The question I was asked is a way to determine the Overall Percent Nonconforming from the above. I do not know any way to do this that I would be confident enough to give an answer.

The question is it possible to calculate the overall nonconforming percentage from the lot? If so, how can this be done.

Best regards.

The problem is that you do not know the correlations between the defects (or at least you have not stated anything about them here).

Rounding slightly, you have


2.2% nonconforming due to length
29.3% nonconforming due to warp
5.2% nonconforming due to hole

It is quite possible that only 29.3% are nonconforming. You might only get bad length or bad holes when the material is already warped.

It is possible that 2.2% + 29.3% + 5.2% = 37% are bad in a worse-case scenario where you never get two different nonconformities on the same piece.

If the defects are randomly distributed, then the the odds of getting no defect on a part are (1-0.022)*(1-0.293)*(1-0.052) = 0.655 = 65.5% conforming = 34.5% nonconforming.


So somewhere between 29.3% and 37% are nonconforming, but you really can't say more without more data.

Tim

Characteristic Warp %<LSL 2.33%, %>USL 26.97%

Characteristic Hole Position %<LSL 0.92%, %>USL 4.07%

Note: LSL (Lower Specification Limit) and USL (Upper Specification Limit.


I would imagine that the characteristics "Warp" and "Hole Position" are measurement values that are unilateral (having only an Upper Specification Limit) where the LSL is a boundary that can only be approached... but not crossed.

Just an observation... so then the values %<LSL may be invalid. Hopefully someone has examined the type of distribution for these values since distributions for unilateral tolerances are typically non-normal.

Paul

I guess you can do all of this...but I find two things that bother me.

One, you are developing a conclusion on truncated data. Much like when you sort, your distribution is truncated on the ends, now you truncated the middle, then try to develop a statistic to describe what you have done.

Two, my preference for a capability analysis would be related to direct, actual measured data versus the specification, rather than the manipulated data of percentages. I would find that a little easier to analyze, visualize and create conclusions from.

My :2cents:, and I don't get a vote....

Thanks to all of you for your quick response and advice. I will take this all into consideration and review this with the group.

You are the best.