Process Performance and Statistical Process Control for Lower Detection Limits (May 20)

Some quality characteristics, such as trace contaminants and trace impurities, cannot be detected at less than the instrument’s lower detection limit (LDL). Zero does not mean zero in these situations; it means only that the amount is below the LDL. Such measurements are also called “nondetects.”

This means the process performance index (Ppk) cannot be calculated with traditional textbook methods, and traditional statistical process control (SPC) charts cannot be used either. If however the underlying statistical distribution is known (and it is unlikely to be the normal or bell curve distribution), its parameters can be determined with the maximum likelihood estimation (MLE) method that can account for nondetects. Once the parameters are available, the nonconforming fraction above the upper specification limit can be calculated, which yields Ppk = PPU (there is probably no PPL as there is no lower specification limit). The median of the distribution is then the SPC chart’s center line, and its upper 99.865% percentile is its upper control limit. StatGraphics uses the MLE method, which can also be used with Excel’s Solver feature.

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