From: Stan Hilliard
Date: 4/16/2004
Time: 12:00:52 PM
Greetings Stan,
YOU SAID: "May I break the variables specification into two attribute, above or not above the lower spec, and above or not above the upper spec."
Consider the a characteristic with just one individual specification limit (ISL) first -- either an upper or a lower ISL. An item measured above the upper ISL can be defined as defective item, and an item measured below the lower ISL can be defined as defective. I see no problem with using an attribute plan on that pass/fail data except that you will have to pay the price of higher sample size when using attribute data.
Now consider a characteristic with both a lower and an upper specification. The ANSI std has both a Q method and a K method. The Q method takes into account both ISL's concurrently. With the K method you would apply two variables plans independently -- one for the lower ISL and one for the upper ISL.
The K method and the attribute method have that in common.
I think that it is appropriate to use the K method and the attribute method for a two-spec variable under certain conditions and not under other conditions.
Consider the K method variables approach. The simplicity of the K method's decision rule makes it easier for the inspector/operator/etc to implement. This is an important factor.
However, problem arises if the lower ISL and upper ISL are too close together. That happens when the lower-ISL and upper-ISL are too few sigma's apart, where sigma is the within-lot, or short-term standard deviation. In the extreme case, the maximum acceptance limit for the sample average from the upper-ISL plan will be below the minimum acceptance limit for the sample average from the lower plan. In that case no product can be accepted.
When the two specs are too close together, an attribute plan is vulnerable to the same problem.
To answer your question, (after that long-winded rant) I think that once you make the judgement that the two specification are far enough apart, an attribute plan will work OK.