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Handling lower detection limits for SPC and process performance

Bill Levinson

Industrial Statistician and Trainer
#1
Has anybody had experience with SPC and process performance indices for processes in which the instrument has a lower detection limit, e.g. "0" can mean anything from 0 to 0.5 parts per million of an impurity? Does it sound reasonable to characterize the process with the same well-known reliability statistical techniques for censored data?

In reliability testing, the equivalent of an upper detection limit is usually the issue, e.g. testing is stopped at 1000 hours, 10,000 cycles, or whatever, and some items have not failed. There is no failure data for these, all we know is that they survived past the end of the test. StatGraphics and other software packages have functionality that can fit the data to, for example, a Weibull distribution. (The nature of the distribution must be known.) The same techniques will however work on lower detection limits. Then it looks like we can use the fitted process parameters to set SPC control limits, and also calculate a process performance index based on the nonconforming fraction.
 
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Steve Prevette

Deming Disciple
Staff member
Super Moderator
#2
Yes. It is a bit of a nightmare. If you look up "truncated data" on the internet, there are several techniques in use. I generally settled on the simplistic use of two charts - a p-chart for proportion less than threshold, and a xmR set of charts for the readable values. Ideally, if one can get from the equipment - I know that is it "below detectable" but could you tell me what the meter read and I will understand it has high variability, that is great, but most metrology folks won't acquiesce to that request.
 
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